USER’S MANUAL
DYNA6
Dynamic Analysis of Foundations for the Effects of
Harmonic, Transient and Impact Loadings
PDF_V1.02
Contents
0.0 SYSTEM REQUIREMENTS AND INSTALLATION .................... 6
0.1 System Requirements ................................................................................. 6
0.2 Installation and activating the program ........................................................ 6
0.2.1 Standalone version .................................................................................. 6
0.2.2 Network version ....................................................................................... 7
1.0 PURPOSE OF THE PROGRAM ................................................. 9
2.0 TYPES OF FOUNDATIONS AND BACKGROUND THEORY .. 10
2.1 Footing on Piles (Pile) ............................................................................... 10
Single Pile Analysis ........................................................................................ 12
Low frequency range ...................................................................................... 12
Pile tip condition.............................................................................................. 16
Weak zone ...................................................................................................... 17
Free length ..................................................................................................... 18
Battered piles .................................................................................................. 18
Pile groups ...................................................................................................... 18
Static interaction factors ................................................................................. 19
Frequency variation of interaction factors ....................................................... 21
Groups Containing Battered Piles................................................................... 24
Option for group stiffness output ..................................................................... 24
Flexible Caps .................................................................................................. 25
2.2 Footing on Homogeneous Half-Space (half-space)................................... 26
2.3 Footing on Homogeneous Layer (stratum) ................................................ 27
2.4 Footing on Layered Medium (rigid body) ................................................... 28
2.5 Footing on Layer Overlaying Half-Space (composite medium) ................. 30
2.6 Flexible Rectangular Mat on Half-Space (mat) .......................................... 33
2.7 Soil nonlinearity ......................................................................................... 34
2.8 Soil material Damping ............................................................................... 34
3.0 TYPES OF DYNAMIC LOADING .............................................. 36
3.1 Loading Type 1: Transient ......................................................................... 36
Type 1 – Transient Loading ............................................................................ 37
Type 2 – Stationary Random Loading ............................................................ 37
Type 3 – Harmonic Loading ............................................................................ 37
3.2 Loading Type 2: Random .......................................................................... 38
3.3 Loading Type 3: Harmonic ........................................................................ 38
3.4 Loading Type 4: Shock (IMPACT Option) ................................................. 39
One mass foundations .................................................................................... 41
4.0 UNITS ....................................................................................... 43
5.0 NOTATION ............................................................................... 45
6.0 DATA INPUT ............................................................................ 46
6.1 General Keywords ..................................................................................... 46
6.2 Foundation Description (general) .............................................................. 52
6.2.1 Pile Foundation ...................................................................................... 52
6.2.2 Half-Space Foundation .......................................................................... 63
6.2.3 Stratum Foundation ............................................................................... 63
6.2.4 Rigid Body Foundation .......................................................................... 65
6.2.5 Composite Medium Foundation ............................................................. 68
6.2.6 Mat Foundation ...................................................................................... 70
6.3 Load Description (general) ........................................................................ 72
6.3.1 Harmonic Load ...................................................................................... 72
6.3.2 Transient Load ....................................................................................... 74
6.3.3 Random Load ........................................................................................ 76
6.3.4 Impact Load ........................................................................................... 77
7.0 FOUNDATION BLOCK CALCULATIONS ......................................... 79
8.0 RUNNING THE PROGRAM MANAGER AND OTHER UTILITIES
........................................................................................................ 86
8.1 Contents of the DYNA Package ................................................................ 86
8.2 DYNA 6 User Interface 3DVIEW ............................................................... 86
8.3 View and Print Results of DYNA 6 ............................................................ 91
8.4 Graphic Depiction of DYNA 6 Results ....................................................... 91
9.0 FREQUENTLY ASKED QUESTIONS ....................................... 93
9.1 Negative Stiffness Constants .................................................................... 93
9.2 Natural Frequencies Are Not Returned by DYNA ...................................... 93
9.3 Very Low Efficient of Pile Groups .............................................................. 94
9.4 Sharp Peaks in Pile Groups Stiffness ........................................................ 94
9.5 The effect of the Keyword ENDBEARING ................................................. 95
9.6 Mass Participation Factor .......................................................................... 95
9.7 Validation of DYNA Results ....................................................................... 96
10.0 EXAMPLE PROBLEMS .......................................................... 97
Example 1: Single Vertical Pile Under Constant Amplitude Harmonic Load ... 99
Example 2: Single Battered Pile Under Constant Amplitude Harmonic Load108
Example 3: Transient Load Applied to Rigid Body on Half-Space ................ 118
Example 4: Two Mass Hammer Foundation on Half-Space (Embedded)..... 129
Example 5: Half-Space With Weak Zone and Harmonic Load ..................... 139
Example 6: 8-pile Foundation With Pile Interaction and Stiffness Printout ... 149
Example 7: 8-pile Foundation With Pile Interaction and Stiffness Printout ... 159
Example 8: Random Load Applied to Rigid Body on Half-Space ................. 169
Example 9 : Random Load Applied to Rigid Body on Stratum ...................... 175
Example 10: One Pile Foundation With Parabolic Soil Shear Modulus
Distribution and Harmonic Load................................................................. 181
Example 11: Transient Load Applied to Silo Supported by Embedded Rigid
Body .......................................................................................................... 190
Example 12: Composite-Medium With Uniform Layer and Harmonic Load
(Dimensionless Amplitudes) ...................................................................... 198
Example 13: Embedded Pile Foundation With Battered Piles and Harmonic
Load........................................................................................................... 204
Example 14: Flexible Mat Foundation (MATF) Under Vertical Harmonic Load
and a Couple ............................................................................................. 213
Example 15: Piles Battered in a General Plane with Printing of Group Stiffness
Matrix in Vertical and Lateral Directions .................................................... 221
11.0 REFERENCES ...................................................................... 231
0.0 SYSTEM REQUIREMENTS AND INSTALLATION
0.1 System Requirements
DYNA 6.1 and DYNA License Server requires an IBM compatible PC wit following
minimum specifications:
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Windows XP©, Windows Vista©, Windows 7© or Windows 8© OS,
1 MHz processor (Intel Celeron or better),
512 MB RAM (system memory),
50 GB of hard-drive space,
VGA capable of 1024x768 screen resolution,
Either a CD/DVD drive or a USB port for the installer media,
.NET 3.5 or newer.
Network version requires TCP/IP connection between the License Server
and the clients.
0.2 Installation and activating the program
0.2.1 Standalone version
Standalone version DYNA should be activated before using therefore, first run of
DYNA prompts an Activation/”License Server” screen including a product number.
This number should be sent to Geotechnical Research Center to obtain an
activation number. For activation, DYNA should be run as administrator.
Note: Before the activation DYNA may produce a different product numbers at
each run, however, since they all refer to the same product, you don’t need to resend the product number.
0.2.2 Network version
Network version allows to run multiple instances of DYNA at the same time;
number of instances depends on number of seats are purchased. For the network
version only License Server needs to be activated. Activation process is similar to
the standalone version (Item 0.2.1).
Clients should be connected to the license server by TCP/IP. After the activation
address or the name of the License Server should be provided to the clients.
Note : Although individual copies of DYNA prompt the Activation/”License Server”
screen, License Server option below in the box should be used. If the connect
automatically option is checked, after a successful connection, DYNA connects to
the License Server automatically.
0.2.2.1 License Server security levels
You can customize the security level of the License Server;
1 - Public: Anyone can login with an IP address.
2 - Password protected: License server asks a password you could define.
3 - Login required: License server asks user name and password you could
define. You could also define a date range for any user, enable or disable any
account.
1.0 PURPOSE OF THE PROGRAM
The DYNA 6 program returns the response of rigid foundations to all types of
dynamic loads. The rotation of centrifugal or reciprocating machines, shockproducing machines, earthquakes, traffic and other sources of dynamic forces can
produce these loads. The response to harmonic loading for a flexible, rectangular
mat on elastic half-space or on a group of piles can also be calculated. The
stiffness and damping constants of the foundation (needed for the analysis) are
evaluated within the program for surface foundations, embedded foundations and
piles, pile interaction in a group and other features. For rigid footings, all six
degrees of freedom are considered as coupled.
The foundation stiffness and damping constants (matrices) are also returned for
possible use in soil-structure interaction analysis. These constants are available
for rigid footings, flexible mats (caps) on piles, or piles without any connecting cap,
and also for flexible mats on elastic half-space.
2.0 TYPES OF FOUNDATIONS AND BACKGROUND THEORY
The types of foundation for which DYNA6 evaluates stiffness and damping
constants are shown schematically in Figure 2.1 to 2.6 and are described in the
following sections.
2.1 Footing on Piles (Pile)
The first option in the DYNA6 program is for a footing supported by a group of piles
that are embedded in a layered medium. Pile heads may be fixed or pinned. The
pile may be of stepwise variable cross-section. The cap connected to the pile may
be of stepwise variable cross-section. The cap connected to the piles may be rigid
or flexible. For flexible caps, only the axial pile stiffness, which dominates the
vertical and rocking response, is considered. Figure 2.2.1 shows some of the types
of piles, which can be analyzed. The analysis of this type of foundation is carried
out in the program in two steps. First, the complex stiffness of the single pile-soilpile interaction factors to evaluate the group stiffness. The effect of soil side layers,
if present, is then added separately and the response is calculated. There is also
a brief discussion of the assumptions employed in the analysis. It is recommended
that the user read this part in order to understand the capabilities and limitations
of the underlying theory and the program.
Figure 2 .1a: Pile Footing (Rigid Cap)
Figure 2 .1b: Pile Footing (Flexible Cap)
Figure 2.1.1: Types of Piles and Soil Profiles
Single Pile Analysis
Calculation of single pile stiffness and damping is based on the approach given in
Novak and Abou-Ella (10,11). In this approach, the dynamic soil reactions to the
displacements of a pile element are calculated assuming that the soil consists of
infinitely thin layers extending horizontally to infinity. This method is versatile and
has computational advantages over more rigorous methods of dynamic analysis
of piles, especially at high frequencies. Additional assumptions and features are
discussed next.
Low frequency range
The theory used for evaluating stiffness is best suited to accommodate high
frequencies. The soil stiffness in the vertical and horizontal directions approaches
zero, as the frequency tends to zero. The theory is modified to match more rigorous
solutions by choosing a minimum cutoff frequency below which the soil stiffness is
taken as constant and the damping is taken as linear. The dynamic soil reactions
are shown schematically in Figure 2.1.2 with S1 and S2 representing stiffness and
damping, respectively, and the dimensionless frequency a 0 = R/vs where  =
frequency is 0.3 for both stiffness and damping. The accuracy of the approach in
the low frequency range depends on the pile to soil, respectively). Figures 2.1.3
and Figure 2.1.4 show the vertical and horizontal pile stiffness compared to other
approaches.
Figure 2.1.2: Modification of Soil Reactions for Low Frequency Range
(a0 (min) shown for horizontal vibration)
Figure 2.1.3: Static Vertical Stiffness of a Single Pile (s = 0.5)
Floating
Endbearing
Figure 2.1.4: Comparison of Pile Dynamic Stiffness with that Obtained Using the
Kaynia and Kausel (1982) Approach (discrete points)
a) Kv’ = vertical normalized stiffness and damping
b) Kf’ = horizontal normalized fixed-head stiffness and damping
c) Kh’ = horizontal normalized pinned-head stiffness and damping
Pile tip condition
Pile tip condition may range from floating to endbearing and is automatically
accounted for by defining the stiffness of the soil layer under the tips (vb). The
theory, however, does not account for the vanishing of radiation (geometrical)
damping below the natural frequency of the soil deposit, a condition most
pronounced for endbearing piles in a shallow stratum. The program overcomes
this limitation by allowing the user, at his discretion, to specify a pile tip condition
(FLOATING or ENDBEARING). For endbearing condition, the program
approximately calculates the deposit's first natural frequency and eliminates
radiation damping, leaving only material damping, as shown schematically in figure
2.1.5 The specified tip condition does not affect single pile stiffness nor does it
affect damping above the natural frequency of the deposit. If ENDBEARING is not
specified the code used FLOATING as default.
Figure 2.1.5: Correction of Damping below Natural Frequency of Layer u (End
Bearing Option)
Figure 2.1.6: Notation for Weakened Zone
Weak zone
The piles may have a weakened zone around them (see Figure 2.1.6), which
makes it possible to approximately account for the effects of imperfect bond
between the pile and the soil, pile sleeves and pile slippage. It also takes into
account the reduction of soil stiffness and increase of soil material damping due to
high strain. The weakened zone effect is calculated using the theory due to Novak
and Sheta (8). The original theory assumes the weak zone to be massless to avoid
wave reflections at the artificial boundary between the weak zone and outside soil
(28). The program allows the use of a weak zone mass participation factor (M.P.F
= 0 to 1) that represents the fraction of the weak zone mass to be added to the pile
mass at each layer. The M.P.F. should increase with the decrease of weak zone
thickness and the increase of weak zone shear modulus ratio (Gm/G) the
recommended maximum value for the M.P.F. is 0.75, with 0.25 to 0.5 being typical.
The weak zone reduces damping much more than stiffness.
Free length
The pile head may protrude from the ground or complete pile-soil separation at the
first layer may be assumed. The free length is accounted for by considering the
topmost layer as void (G1= 0,R1= 0, see Figure 2.1.1, case A). A free length
reduces stiffness, damping and group effects and may be used to account for
gapping, which has similar effects (Figs. 2.1.7a,b).
Battered piles
The effect of batter is handled approximately by calculating the pile stiffnesses
referenced to its local axes using the projected pile length on a vertical plane.
These stiffnesses are then transformed pile length on a vertical plane. These
stiffnesses are then transformed to the global axes system. Such approximation is
valid for slightly battered piles.
Pile groups
No Interaction Option
If the no interaction option is specified, the piles are assumed to act independently
of one another. Vertical and horizontal forces are distributed equally on individual
piles. The group stiffness is calculated by summing pile stiffnesses using the
appropriate transformation to the C.G. of the system. The No Interaction option is
of interest only for comparison with the Interaction option and for academic
purposes.
Interaction Option
If pile-soil-pile interaction is considered, as it should be for closely spaced piles,
the group stiffness and damping are calculated using the superposition method
described in El Naggar and Novak (24). The interaction between each two piles is
used to formulate the group complex flexibility matrix from which the group
stiffnesses and damping are deduced. The group effect is considered separately
for the vertical translation, the horizontal translation in the XZ plane and the
horizontal translation in the YZ plane (Z being the vertical axis). The complex
ij 
dynamic displacement of pile i due to unit load on pile j
dynamic flexibilit y of pile i
interaction factor  is given by equation 2.1.1.
The program evaluates the dynamic interaction factors according to equation
2.1.2:
 (a0, s / d , l / d , Ep / Es, Eb / Es)  st (a  0, s / d , L / d , Ep / Es, Eb / Es) * f (a0, s / d )
Where s = pile spading, d = diameter, L = pile length, E = Young's modulus of
bearing stratum, st = static interaction factor and f represents the frequency
variation.
Static interaction factors
The vertical static interaction factors are based on fitting the charts of Poulos and
Davis (15). The limits of the fit are as follows: L/d = 10 to 100; s/d >= 2; E p/Es =
100 to 5000; Eb/Es >= 1. Outside of these limits the accuracy or the fit deteriorates.
An example of the group efficiency ratio (group stiffness with interaction)/(group
stiffness without interaction), in the vertical direction, is shown in Figure 2.1.7. The
horizontal static interaction factors are due to E1-Sharnouby and Novak (26). The
separation (gapping) at the pile top reduces interaction and is taken into account
using a straight line approximation to the reduction factors shown in Figure 17 of
(26) for Ep/Es = 1000. Soil layering is approximately accounted for in both vertical
and horizontal interaction factors.
Figure 2.1.7: Static Group Efficiency Ratio in the Vertical Direction for a Square
4X4 Pile Group (L/d = 50, s =0.5)
Figure 2.1.7a: Effect of Pile Free Length on Horizontal Group Stiffness and
Efficiency of 3X3 Group (L/d > 25, S/d = 3, Kr =EpIp/EsL4; El Sharnouby & Novak,
1985)
Figure 2.1.7b: Development of Gap Separating Pile from the Soil with Number of
Cycles for Different Load Amplitudes. Steel Tube Pile with 610mm O.D., Stiff
Clay (Swane & Poulos, 1984)
Frequency variation of interaction factors
The frequency variation of interaction factors is based on the charts of Kaynia and
Kausel (27). The charts are provided for floating piles with the following
parameters: s/d = 2, 10; L/d = 15; Ep/Es = 1000; a0 = 0 to 0.5. The program
interpolates and extrapolates along spacing. The changes in pile length, pile to soil
stiffness ratio, and stiffness of bearing stratum are assumed to be accounted for
by the static interaction factors. Such a correction provides adequate results for a 0
<= 0.25 and s/d <= 5. For a layered soil or piles with variable cross-section, the
dimensionless frequency is calculated using a weighted average of the shear wave
velocity along the pile length (or along the effective pile length for the horizontal
direction), and the radius at the top or the average radius at the top for noncircular
piles. If the endbearing pile tip condition is specified (see single pile discussion),
static interaction factors are used for frequencies lower than the natural frequency
of the soil deposit. The results may show an abrupt change in group stiffness and
damping at this frequency.
The group stiffness and damping display strong variations with frequency and
sharp peaks as opposed to the smooth variation of the corresponding single pile
values. Negative stiffness may occur depending on the frequency and the
fundamental pile spacing to diameter ratio. Figure 2.1.8 shows an example of
dynamic group stiffness and damping in the vertical and horizontal directions. (The
differences observed are not of great practical significance. Most practical cases
feature very small a0', 0.4 or less.) For soils with high vertical nonhomogeneity (e.g.
Gibson soil), the above mentioned approximations yield less accurate results for
the group stiffness in the horizontal direction.
Figure 2.1.8: Normalized Horizontal and Vertical Dynamic Stiffness of a 4X4 Pile
Group (a0’ = d/Vs, solid curve after Kaynia (27)) DYNA result shown may differ
slightly from those returned by the latest version of the code. (L/d = 15, Es/Ep =
10-3, s/p = 0.7)
Groups Containing Battered Piles
The interaction factors between battered piles are considered to be equal to those
between vertical piles at an equivalent spacing calculated at 1/3 pile length (or 1/3
effective pile length for the horizontal direction) from the top (see Ref. 15). In
addition, it is assumed that a vertical load on pile j causes only a vertical
displacement at pile i and similarly for horizontal load, coupling between the
horizontal and vertical directions is accounted for only in the single pile flexibility.
Such an assumption would not affect the stiffness of a symmetrically arranged pile
group.
Option for group stiffness output
The keyword MATRIX (see section 7) prints the stiffness and damping constants
for a rigid foundation of any type referred to C.G. To obtain stiffness and damping
contents of a single pile or a pile group referred to pile head level, introduce the
height of the Centre of Gravity Zc = 0.0. In addition, two other options are available
specifically for pile groups with the INTERACTION option.
The keyword DISTRIBUTION causes the printing of individual pile loads
corresponding to unit horizontal and vertical displacements to calculate the load
distribution on individual piles. It is noted that the output forces represent absolute
values (amplitudes). Due to phase shifts between forces on individual piles these
maxima do not occur exactly at the same time.
The keyword FLEXIBLE is used to print the group complex stiffness matrix in the
vertical direction, while the keyword LATERAL is used to print the group complex
stiffness terms are referenced to pile heads and may be used in the analysis of
flexible foundations (caps) or any flexible superstructure using the FEM (Fig.
2.1.9). Horizontal vibration modes and torsion can be analyzed as with rigid
footings.
Figure 2.1.9: Pile Group with Flexible Cap or No Cap. Stiffness and Flexibility
Matrices are Returned Referring to all Pile Heads
Flexible Caps
When the pile cap is thin relative to its plan dimensions, it may bend significantly
under vertical loads or moments in the vertical planes; however, the cap horizontal
and torsional response can still be calculated employing the rigid cap option,
CAPRIGID.
The flexible cap analysis for vertical loads and rocking moments can be conducted
in two ways:
(a) The user can calculate the complete stiffness matrix of the piles without
a cap using DYNA6 and introduce it into his own finite element
subroutine for the analysis of the superstructure (or flexible cap)
(b) The user can employ the DYNA6 option CAPFLEXIBLE that analyzes
the pile group together with a finite element model of the flexible cap.
The option CAPFLEXIBLE is limited by the following assumptions:

The loads are harmonic vertical forces or moments in the vertical planes

The pile cap is rectangular and subdivided into rectangular elements

The piles are located at the mesh nodes

Rigid blocks, pedestals, machines etc. resting on the cap are
represented by lumped masses located at the mesh nodes

Only vertical displacements of the mesh nodes are calculated and up to
five of these displacements are returned in one run

Forces on individual piles are not returned;

Cap contact with the soil and its embedment are not considered.
2.2 Footing on Homogeneous Half-Space (half-space)
In the option shown in figure 2.2, the footing rests on the surface of or is embedded
in a deep homogenous deposit considered as halfspace. A stratum whose depth
is greater than about five equivalent footing radii may be treated as halfspace using
this option.
The halfspace stiffness and damping constants are considered as frequency
dependent and are evaluated using the theory due to Veletsos et al. (1,2,3).
Embedment is accounted for as described by Novak et al. (4 to 7) and may include
a weakened zone or backfill around the foundation as formulated in (8). Soil
material damping (viscosity) is included and the properties of the side layer
overlying the halfspace zone mass participation made in the paragraph on piles
apply to the weak zone of embedment.
Figure 2.2: Footing on Homogeneous Half-Space (HALF_SPACE)
2.3 Footing on Homogeneous Layer (stratum)
For the option shown in Figure 2.3, the footing rests on the surface of or is
embedded in a shallow, homogeneous layer underlain by a rigid medium. The
layer stiffness and damping constants are calculated using the formulae due to
Kausel and Ushijima (9). The most prominent feature of this case is that the
geometric damping of the foundation can be considerably reduced if the dominant
frequency of the response is lower than the first natural frequency of the layer. The
range of problem parameters such as the ratio (embedment depth/layer depth) is
limited (see section 7.2.3). Material damping should be considered.)
Figure 2.3: Footing on Homogeneous Layer (STRATUM)
2.4 Footing on Layered Medium (rigid body)
This option is for a rather deep footing such as a caisson that may be embedded
in and underlain by a layered medium. The properties of the soil layers may be
different but constant within each layer except for the soil column under the footing
in which the soil properties may differ from those of the outer part of the layer. This
feature makes it possible to take an approximate account of the increased
confining pressure under the footing.
This option is treated in the program as a special case of a thick pile as shown in
Fig. 2.4.1 and outlined in (11) and should not be applied to shallow foundation with
E/r less than about 5 (E = embedment depth). Deformations of the footing due to
shear, bending and torsion are considered. Also included is the inertia effect of the
body, which can result in strong variation of stiffness with frequency and even in
negative stiffness constants. If this option is used just to obtain the stiffness and
damping of the body without the effect of its mass, the program can be run with a
very small, nominal, value of mass (i.e. with unit weight approaching zero). The
body may protrude from the ground. The free length is accounted for by
considering the natural frequency of the layer applies to the RIGID-BODY option.
The tip condition refers to the soil below the lowest layer. The stiffness and
damping constants returned refer to the top of the footing if the height of the center
of gravity is input as zero. For all options except RIGID-BODY, the height of the
center of gravity is measured from the base of the footing to the centre of gravity
(C.G.) of the whole machine-footing system and is positive if the C.G. lies above
the base. For the RIGID-BODY option, the height of the center of gravity is
measured from the top surface of the footing to the C.G. of the superstructure (see
example 11), as with piles.
Figure 2.4: Deep Footing in a Layered Medium (RIGID- BODY)
Figure 2.4.1: Deeply Embedded Foundation Treated as a Pile (RIGID-BODY
option)
2.5 Footing on Layer Overlaying Half-Space (composite medium)
For this option, the footing base rests on the surface of a shallow layer underlain
by a halfspace (Fig. 2.5a). The layer may be uniform (Fig. 2.5c) or non-uniform
with linearly varying shear wave velocity (Fig. 2.5d). The halfspace is
homogeneous. The footing can also be embedded in overlying layers as shown in
Fig. 2.5b. The properties of the embedded layers may vary independently. The
layer under the footing base and the halfspace should satisfy the conditions
mentioned later in section 7. The base soil reaction is calculated using equivalent
shapes, the impedances are evaluated approximately using equivalent dimensions
obtained by equating the geometric properties of the base area of the actual footing
with those of a square base. The effect of embedment is evaluated as in all other
options, i.e. by Refs. 4 and 8. The impedance functions may undulate as depicted
in Fig. 2.5.1
Figure 2.5: Rigid Footing Resting on Composite Medium Comprising a Layer
Overlying Halfspace and Embedded in Side Layers (COMPOSITE –MEDIUM)
a) Surface Footing
c) Uniform Layer Profile
b) Embedded Footing
d) Non-Uniform Profile
Figure 2.5.1: Example of Vertical Stiffness for COMPOSITE MEDIUM
2.6 Flexible Rectangular Mat on Half-Space (mat)
When the foundation block (mat) is thin relative to its plan dimensions, it may bend
under vertical loading and respond in a variety of flexural vibration modes. This
option, limited to vertical response of a rectangular mat on homogeneous
halfspace, provides the response at up to five specified nodes to several harmonic
vertical nodal loads and the complex stiffness matrix for a rectangular mesh of
nodal points. If the response is required at more than five nodes, more than one
run must be made. This complex stiffness matrix used in this option is the inverse
of the flexibility matrix, which is calculated using a function that fits the values of
Green's function published by Whittaker and Christiano (29). The frequency of the
fundamental mode of a flexible mat can be compared with the frequency of the
vertical vibration mode calculated assuming footing rigidity to appreciate the
possible effects of footing flexibility. A perfect agreement with option 2.2 (footing
on homogeneous halfspace) cannot be expected, as the assumptions of the two
analyses are somewhat different. The rocking response may be predicted as well
by inputting any acting couple as two equal but opposite vertical loads acting at
two closely spaced nodes. The overall footing rotation about an in-plane axis may
be calculated using the vertical displacements of the different nodes. (In horizontal
and torsional response, the mat behaves as if it was rigid.) A lumped mass model
is used to represent the footing mass. Other masses, e.g. machine, pedestals, etc.,
may be input and included in the analysis as additional lumped masses.
Figure 2.6: Flexible Rectangular Footing on Homogeneous Halfspace and its
Response to Vertical Load (Mat Foundation) (MAT)
2.7 Soil nonlinearity
The analysis is linear. An approximate account of nonlinearity can be taken by
means of the weakened zone around the footing or pile and by adjusting the values
of soil shear modulus and internal damping according to the level of stress. (See
e.g. Ref.18)
2.8 Soil material Damping
Soil properties enter the calculation in term of shear wave velocity V s:
Vs  Gs / s
Where Gs is shear modulus and s is mass density, unit weight R, and material
damping. In DYNA6, material damping is defined as D = tan = 2 where  is the
loss angle and  is the damping ratio. Hysteretic, frequency independent material
damping is assumed, as it is more realistic than viscous damping. This results in
strong growths of equivalent viscous damping with frequency approaching zero as
is schematically depicted in Fig. 2.8.1. Thus, the role of material damping can be
dominant in the low frequency range, particularly for soil strata and endbearing
piles, vibrating with frequencies lower than the fundamental frequency of the soil
layer (Fig. 2.8.1a), a situation where no geometric damping exists.
Figure 2.8.1: Effect of Hysteretic Material Soil Damping on Foundation
Impedances for a) – Stratum and b) –Halfspace (Deep Deposit)
a) Stratum
b) Halfspace
3.0 TYPES OF DYNAMIC LOADING
A rigid body such as a footing, a machine foundation, or a silo, etc. can be
supported by any of the above types of foundation and be analyzed for three types
of loading indicated in Fig 3.1. These are transient, random and harmonic loading.
All loads are referred to the reference point, usually the center of gravity of the
whole system (including the machine if present), and can act in all six degrees of
freedom.
A fourth type of loading, shock loading, is available for foundations of shock
producing machines such as hammers. These foundations may consist of one or
two masses (block) and are analyzed for vertical response in two degrees of
freedom (Figure 3.2).
3.1 Loading Type 1: Transient
Transient loading is characterized by an irregular but specific time history of limited
duration (Figure 3.1 , Type 1). Some machines such as crushers, pumps, hammers
or presses and can cause such a loading also by earthquakes, blasts or
explosions.
The response to transient loading is also transient and is calculated using the Fast
Fourier Transform (FFT). Information on this method can be found, e.g. in Refs.
19 and 20.
Transient loading is described by a number of discrete data points. The data points
must be equidistant; their total number must be even and sufficiently high to yield
adequate accuracy. It is recommended that the number of points be a power of 2.
If not, the program automatically completes the load time history with zero load
terms to the nearest power of 2. A number of zero points (zero loading) should be
added to the end of the transient time history to alleviate the problems associated
with the periodicity implied in the Fast Fourier Transform. The zero points are
needed particularly with a short impulse. The maximum number of points allowed
is 1024.
The program returns the complete time history of the response in six degrees of
freedom as well as its maxima.
Figure 3.1: Types of Loading for One-Mass Footings
Type 1 – Transient Loading
Type 2 – Stationary Random Loading
Type 3 – Harmonic Loading
3.2 Loading Type 2: Random
Random loading is characterized by an irregular time history (Figure 3.1, Type 2)
that is best described by the corresponding power spectral density (power
spectrum) (Fig 3.1, Type 2,b). (For the definition of the power spectrum and the
analysis of response to random loading, see, e.g. Ref. 19.) The random excitation
included in DYNA6 is assumed to be stationary, i.e. its statistical characteristics do
not vary with time. This type of loading may stem, for example, from crushers,
pumps, traffic, and wind approximately from earthquakes.
The excitation is described by its power spectral density given for a number of
points (frequencies). The maximum number of data points is 200.
These data points are to be equidistant. The minimum frequency must be greater
than zero and together with the maximum frequency define respectively the lower
and upper bounds of the frequency contents of the process (Fig. 3.1, Type 2,b).
The program returns the mean peak values of the response expected to occur
during the period of observation T. This peak value of the response is expressed
by:
uˆi  g *u
3.1
In which g is the peak factor and Su is the standard deviation (root-mean-square
value) of the response. The peak factor is calculated from the spectra. The period
T may typically be 20 to 60 seconds for earthquakes and 600 to 3600
seconds for machine or wind loading.
3.3 Loading Type 3: Harmonic
Harmonic loading is caused by unbalanced masses of rotating and reciprocating
machines such as turbines, generators, compressors, fans, diesel engines and
many others. It is the most common type of excitation. This excitation may have
one harmonic component and consequently, a sinusoidal time history (Fig. 3.1,
Type,a) or more harmonic components(case b). If there are harmonic components
the response has to be calculated for each component separately and the results
added.
In DYNA6, the harmonic excitation can be of two types: the constant amplitude
excitation and the frequency dependent or quadratic excitation. The constant
amplitude excitation is defined as:
P(t )  P0 * sin(t )
3.2
In which P0 is the excitation force amplitude,  the circular frequency of excitation
and t is time. (P0 cost results in the same response.) The constant amplitude
excitation can also be used when calculating transfer function.
The quadratic excitation is more often present and is usually caused by centrifugal
forces of rotating unbalanced masses and is defined as:
P(t )  me * e * 2 * sin(t )
3.3
In which, me = unbalanced mass, e = its eccentricity and  = circular frequency.
mee and the frequency range define this type of excitation. Eq. 3.1 can also be
used to evaluate quadratic excitation at a certain frequency if the force amplitude
is calculated by:
P0  me * e * 2
3.4
Conversely, Eq. 3.4 can be used to evaluate the excitation product m ee if the force
amplitude, P0, is given for a certain operating frequency. The difference between
the two types of harmonic excitation is further clarified in section 7.4.1.
3.4 Loading Type 4: Shock (IMPACT Option)
Shock loading is generated by shock producing machines such as hammers or
presses. This option of DYNA6 facilitates the analysis of response to shock loading
for two types of hammer foundation with an inertial foundation block, anvil and an
anvil pad; case (b) exemplifies a hammer with a directly sprung anvil without the
inertial block but with springs and dampers and a protection trough.
When the blows are centric, both of these types of hammer foundations can be
represented by a two mass model with two degrees of freedom as shown in Fig.
3.3a. The vertical displacements v1(t) and v2(t) are return by DYNA6. For the
foundation with the inertial block (Fig. 3.2a), they describe the motion of the anvil
(v1) and the block (v2) respectively. For the directly sprung hammer (Fig. 3.2b),
v1(t) is the motion of the anvil and v2(t) the motion of the trough.
For a hammer with the inertial block, the anvil pad is described by its area,
thickness, Young’s modulus and material damping ratio, which is presumed to be
hysteretic; constants k1 and c1 are evaluated in the program. For the directly
sprung hammer (Fig. 3.2b), total stiffness constant of the springs, k1, and the
damping constant of the dampers, c1, have to be provided. Constants k2, c2
describe the soil or pile properties and are calculated for both types of hammers
within DYNA6 for any of the foundation types shown in Figs. 2.1 to 2.5.
Two types of shock loading are available. For a shock whose duration t is much
shorter than the fundamental period of the foundation, the response is treated as
vibration due to initial velocity issued to the anvil by the blow of the head (Fig.
3.4a). The initial velocity C of the anvil is to be established by (23):
C  (1  kr ) *
m0
*C0
m0  m1
3.5
In which kr = collision (restitution) coefficient such as 0.5, m0 = mass of the hammer
head (tup), m1= mass of the anvil and C0 = impact velocity of the head best
obtained from hammer manufacturers.
For a shock whose duration is not much shorter than the foundation fundamental
period, the blow of the head is represented as half sine pulse acting on the anvil;
the energy of the blow is described by the pulse amplitude, p 0, and its duration, tp
(Fig. 3.4b). If the assumed pulse is not sinusoidal, an equivalent sinusoidal pulse
may be established from the equality of areas, i.e. S0 t p(t) dt.
For both types of shock loading, the response is computed using the complex
eigenvalue analysis (21 and 22). Damping is accounted for accurately with
constants k and c determined for the dominant frequencies of the anvil and the
block.
One mass foundations
When the foundation of a shock producing machine can be represented by one
mass as shown in Fig. 3.3b and when the shock is described as a pulse of a given
shape and duration, the response can be computed as loading type 1 (Fig. 3.1). In
this case blow may act with eccentricity, vertically or horizontally and can be
associated with moments. This may facilitate the analysis of presses and other
equipment. Response in six degrees of freedom is provided.
Figure 3.2: Hammer Foundations: a) – With Inertial Foundation Block and Anvil
Pad and b) - Directly Sprung Hammer
a)
b)
Figure 3.3: Mathematical Models of Hammer Foundations
a) 2 DOF
b) 3 or 6 DOF
Figure 3.4: Types of Shock Loading: a) – A Very Short Shock Treated as an
Initial Velocity Loading, and b) – Half Sine Pulse of Any Duration
a) Short Shock
b) Half Sine
4.0 UNITS
Any units can be used but they must be consistent. The output will come out in the
same units in which the input is provided. For the English system, the units are lb,
slug, ft, s with mass in slug = weight/gravity (lb/ft/s2) and gravity = 32.2 ft/s2. For
the SI system, the units are N (for force), kg (for mass), m, s or kN, Mg = 1000 kg
(tonne), m, s; gravity = 9.81 m/s2.
For random loading, the power spectrum is read in as (force)2 at circular
frequencies  in rad/sec.
When the excitation is due to ground motion xg(t) , the force is defined as mass(m)
x ground acceleration (xg) for harmonic or transient loading: for random loading,
the load power spectrum is m2S
xg()
is the power spectrum of ground
acceleration.
Basic Units for DYNA
SI System
Imperial System
Time
s (second)
s (seconds)
Length, distance
m
ft
Gravity constant
9.81 m/s2
32.2 ft/s2
Mass
kg
slug = lb/32.2
Mass moment of inertia
kg.m2
slug.ft2
Unit weight
N/m3
lb/ft3
Shear wave velocity
m/s
ft/s
Frequency
rad/s
rad/s
Forces
N
lb
Moments
N.m
lb.ft
Displacements (output)
m
ft
In DYNA6.1, 4 sets of consistent units are offered or user specified units can be
chosen individually. The optional sets of units are:
SI: m,N, kg or m, kN, Mg (= 1,000 kg = tonne)
English (Imperial): ft, lb, slug or ft, kip (= 1,000 lb), kslg (= 1,000 slug) with these
options the compatible gravity acceleration is entered automatically as either 9.81
m/s2 for SI or 32.2 ft/s2 for the English system. With the user-selected units, it has
to be entered separately.
5.0 NOTATION
For loading types 1 to 3, the input forces and moments and the response
components follow the sequence of labels shown in Fig. 5.1. For example, labels
1 and 2 indicate horizontal directions along the X and Y-axis. The force and
moments are defined with regard to the C.G. of the system.
The forces and translations are positive if they follow the positive direction of the
corresponding axis. Moments and rotations are positive if they act in the clockwise
direction when watched from the origin in the positive direction of the pertinent
axis. Thus, e.g., two positive horizontal forces p 1, p2 acting above the C.G. in the
directions +X, +Y result in moments M4 < 0 and M5> 0. Stiffness constants, being
by definition external forces, follow the same sign convention; consequently, the
cross-stiffness constants of symmetrical foundations differ in signs.
For the two mass foundations (Fig. 3.3a), the vertical displacements are positive
when they act downward.
Figure 5.1: Notations and Sign Conventions
6.0 DATA INPUT
6.1 General Keywords
Data are input into the DYNA6 System using a keyword-oriented procedure. A
keyword is used to indicate that a particular collection of data is being input. The
user selects the keyword by clicking on the appropriate box then inputs the data
associated with the keyword.
The only limitation on the input that exponential format must not have a blank
space between the ‘E’ and exponent.
Examples:
1.0E9
correct
1.0E09
correct
1.0E 9
incorrect
Problem Description:
The following pages outline the various keywords used to describe the problem to
the DYNA6 system.
Problem Title:
The problem may be given a title by clicking on the Title on the menu bar. The title
can be a maximum of 80 characters long. The title is used on the all the printed
output of DYNA6.
The limitations on the title are:
(1) The first character of the title must be alphabetic (i.e. no digits)
(2) The title must not contain equals (=), commas (.) or dollar sign ($).
Settings:
Next to the Title menu is the Settings menu. Under this menu the user can set the
following options:
1) Output Flags
2) Analysis Constants
3) Units
4) Frequency Units
1) Output Flags:
Data Echo:
DYNA6 will generate an echo indicating the interpretation of the input data.
Clicking on the Echo Input Data box may enable this echo.
Dimensionless Results:
The response amplitudes calculated for Harmonic Loading may be nondimensioned by clicking on the Dimensionless Results box.
Note: This command will produce dimensionless amplitudes that are equal to
dynamic amplification factors and are defined by the following formulae:
Constant force amplitude excitation:
Dimensionless translations:
A
u 0( )
u 0( min)
Dimensionless rotations:
Quadratic excitation:
F 0( )
F 0( min )
m
u 0( )
A
* u0 
mee
u 0 ( )
A
Dimensionless translations:
Dimensionless rotations:
In the above formulae u0, F0 indicate true amplitudes of translation and rotation,
respectively and min is the minimum frequency for which the response is
calculated.
A
I
Mi
mee * ( )
Pi
*F0
For constant amplitude harmonic excitation, a zero frequency should be entered
as the minimum in order to get the static displacements and the correct dynamic
amplifications.
For the flexible mat (option MAT) and the flexible cap (option CAPFLEXIBLE), the
dimensionless vertical translations returned are calculated as the actual dynamic
displacements divided by the static displacement of the circular rigid mat due to
the sum of the vertical loads, Pi:
ustat 
P
i
4*G * r0
(1   )
where r 0 
area

(For the Flexible Cap option, G and  are the value at the pile tip.)
Note: If the dimensionless amplitude cannot be evaluated because Ust is zero, true
amplitude cannot be evaluated because Ust is zero, true amplitudes are
returned.
Stiffness and Damping Matrices:
The stiffness and damping constants are intermediate items in the DYNA6 solution
of the response of rigid bodies but can be useful for separate analysis of elastic
superstructures such as buildings supported by any of the foundations shown in
Figs.1 to 4. A printout of the footing stiffness and damping constants is possible
when the user clicks on the Stiffness/Damping Matrices box.
This keyword will instruct the DYNA6 system to output the constants stored in the
Foundation Stiffness and Damping Matrices. These constants are referred to the
C.G. of the footing specified in the input and incorporate the mass of soil and piles.
Because of the inertia effect of these masses, the stiffness constants can be
negative, particularly for higher frequencies, soil Poison’s ratio ->0.5 and massive
piles. For the option RIGID-BODY, the mass of the embedded footing is also
incorporated in the stiffness and damping constants.
NOTE: For the flexible mat (MAT option) and the flexible cap (CAPFLEXIBLE
option), the keyword MATRIX is not applicable.
2) Analysis Constants:
Damping Safety Factor:
If the applied frequency is close to the resonant frequency of the foundation or, in
the case of foundations supporting a superstructure, close to the superstructure
resonant frequency, the response strongly depends on the magnitude of the
damping constants. To reduce the possibility of damping overestimation and thus
response underestimation, an optional user specified safety factor may be applied
to the damping constants by entering a value in the
Damping Safety Factor box. Where Damping Safety Factor (S) is any positive
number greater than 1.0 defined by:
S
c(calculated )
c(used )
C (calculated) is the damping constant calculated from theory and C (used) is the
damping constant given in the output and used in response calculation. The default
value for S is 1.0.
Example:
Damping Safety Factor = 2.0
This will divide the damping constant by 2.0. A value of S between 1.0 and 2.0 is
recommended, with 2.0 suitable especially for pile foundations and deeply
embedded foundations.
Notes:
1. The damping safety factor is not applicable to the flexible mat (MAT) and
the CAPFLEXIBLE options.
2. The damping safety factor is not incorporated in the pile group stiffness
matrices at the pile heads printed using the keywords FLEXIBLE,
DYNFLEX, LATERAL OR DYNLAT (see Section 8.2.1). It is incorporated in
the rigid pile cap matrix printed using keywords MATRIX, TABULATE and
DYNSTIF.
Gravitational Constant:
The gravitational constant is automatically selected when a set of units is chosen,
for the SI units the value is 9.81 m/s2 and for the Imperial system the value is 32.2
ft/sec2. However, a different value may be entered by the user in the Gravity
Acceleration box. The dimension of the gravitational constant must be consistent
with the dimensions of the other input data and determines the dimensions of the
output. For example with gravity = 32.2 ft/sec2, the displacement amplitudes of the
response are returned in ft; with gravity = 9.81 m/s2 the displacement amplitudes
are returned in m. Amplitudes of rotations are always in radians.
3) Units:
By default, DYNA6 does not include any units in the echo of the input data or the
results. To indicate that a given set of units is to be used in the output file the user
clicks on either the SI Units or Imperial Units button. If it becomes necessary to
use other alternate units, click on the Other button. Once this option is selected, a
set of four boxes becomes available so that the user may choose:
1) Force Units
2) Length Units
3) Mass Units
4) Frequency Units (see next section)
The user is given the option to choose either the standard SI or Imperial unit for
that particular parameter, or to input a new one.
Maximum lengths:
Length: 2 characters (example m or ft)
Force: 3 characters (example N or lb)
Mass: 4 characters (example kg or slug)
Note: The inclusion of units specification for output purposes has no effect on the
numerical values of the results which are governed by the gravity constant.
The user must ensure that the input units are consistent and that they
correspond to the chosen value for the gravity constant.
4) Frequency Units:
The default units for frequency are rad/s. The program also supports the use of
input and output frequencies in Hertz (cycles per second) and rpm (revolutions per
minute.
Notes:
1. The LOAD option RANDOM (SEE SECTION 7.4.3) IS ONLY ALLOWED UNITS
OF rad/s.
2. The plots of the stiffness and damping constants that are produced by the
GRAPH utility would always use RAD/S for the frequency axis, irrespective of
the units used in input and output. The program handles such transformation of
units internally.
6.2 Foundation Description (general)
Once the project has been titled, the user clicks on the Foundation menu and then
on Choose Foundation Type. The user is then offered a choice of six options that
may be selected and described to the system. These options are illustrated in Figs.
2.1 to 2.6 and are called PILE, HALF-SPACE, STRATUM, RIGID-BODY,
COMPOSITE-MEDIUM and MAT. The procedure will be described in great detail
for the Pile Foundation case (section 8.2.1). The following sections (sections 8.2.2
to 8.2.6) will highlight specific features and limitations for the respective foundation
type.
6.2.1 Pile Foundation
The Foundation window allows for three options to be inputted by the user. The
first option in the Foundation window is to select the Embedment type, described
as either a Surface foundation or an Embedded one. The second option in this
window is the footing shape, described as either Circular or Rectangular. The third
option is the Footing Flexibility; the footing can either be Rigid or Flexible. The Skid
option is shown onscreen but it is not currently available in the program. Once
these options have been selected, the user clicks on the OK box.
The Pile Data window then appears and the user has the opportunity to enter all
the relevant information with regards to the soil and the piles.
Figure 6.1: Notations for Pile Foundation Option with Rigid Cap (CAPRIGID)
1) PILE CAP
If the Flexible Cap option is selected, clicking on the Pile Cap button will bring up
the Mat Foundation information window. Clicking on the Data button opens up the
Flexible Mat Data window. There are a number of parameters to be entered by the
user:
1) Mat Properties
a) Length LX
b) Length LY
c) Thickness
d) Mass Density
e) Poisson’s Ratio
f) Young’s Modulus
2) Response at Nodes (maximum of 5)
3) Output Options
a) FLEXIBLE
b) DYNFLEX
4) Number Of Nodes
a) In the X direction NX
b) In the Y direction NY
5) Node Spacing in X
a) Equal
b) Unequal (click on the Edit button to edit to the spacing
between nodes)
6) Node Spacing in Y
a) Equal
b) Unequal (click on the Edit button to edit to the spacing
between nodes)
Click OK to return to the Data window. Clicking on the Masses button allows the
user in input the magnitude and location of loads on the mat. Clicking on the Figure
button will cause the program to formulate a diagram of the inputted mat. The Piles
button allows the user to enter the number and location of piles on the mat.
Notes:
1) The total number of nodes (NX.NY) allowed by the program is 1650. The
actual number that may be analyzed depends on the available free memory.
Refer to section 8 for more details.
2) The static load on pile is the dead load the pile carries. It can be estimated
because its effect is weak but increases with pile slenderness.
3) Material damping (tan) of piles ranges from 0.02 to 0.10.
4) The coefficient of rigidity in shear, k’, as used here, is associated with
shear modulus G and cross-sectional area A as k’/GA and derives from the
effect of shear on beam vibration. Suitable values of the shear rigidity
coefficient are 1.11 for a solid circular cross-section and 1.2 for a
rectangular cross-section. The elementary beam theory suggests the
values of 1.334 and 1.5 for the circular and rectangular cross-sections,
respectively. (See Harris & Creede “Shock and Vibration Handbook”, 2nd
ED., McGraw-Hill, 1976,pp. 7-16.) For slender piles, this coefficient is not
important. The effect of shear is significant only for sturdy (rather rigid) piles
and rigid bodies.
If the Rigid Cap option is selected, then clicking the Pile Cap button opens the
Footing Base Dimensions and Data window. There are three parameters one can
input in this window. For a circular foundation, the radius is entered and for a
rectangular foundation, the lengths in the x and y directions (Lx,Ly) are entered.
The coordinates of the base centre (Xc,Yc,Zc) are also entered. The mass moments
of inertia (Ixx,Iyy,Izz,Ixy,Ixz,Iyz) can be entered by the user if they have been previously
calculated or the user can click on the Calculate box and use the 3DVIEW utility to
calculate them (see ch.9) Once all the data has been entered, click on the OK box.
Notes:
a) If the foundation is not rectangular (or oddly shaped) then a
representative length, Lx or Ly, should be selected and then the other
length should be calculated so that the area of the rectangular footing
would be equal to the area of the actual footing.
b) The coordinates of the base centre should be calculated after the
determination of the coordinates of the C.G. of the system, either by the
user or through the 3DVIEW utility.
c) The last three items in mass (Ixy,Ixz,Iyz ) are products of inertia. They are
important only for grossly asymmetrical foundations; in normal cases,
they can be taken as zeroes.
d) For rigid-body option the masses and mass moments of inertia are those
of the foundation itself are accounted for through the unit weight of the
rigid body.
2) SIDE LAYERS
This option is only available if the Embedded option is chosen and is
unavailable for the Flexible Cap pile foundation and mat foundation option. Clicking
on the Side Layers button brings up the Data for Cap/Footing Side Layers window.
By default, the weak zone around a footing is not considered, but can be
incorporated into the calculations by selecting Weak Zone in this window. The user
can enter the following side layer parameters in this window:
1) Side Layer Thickness
2) Side Layer Shear Wave Velocity
3) Side Layer Unit Weight
4) Poisson’s Ratio
5) Damping
Once all the data has been entered click OK to return to the Pile Data window.
3) PILES
Clicking this button brings up the Pile Head Arrangement for Rigid Pile Cap
window. In this window, the user can input the following parameters by clicking on
the appropriate box:
1) Pile Head Condition
a) Fixed
b) Pinned
Note: Pinned head piles are not allowed to carry moments about X
or Y-axes.
2) Pile Tip Condition
a) Floating Tip
b) Endbearing
3) Pile Properties:
a) Pile Length
b) Pile Unit Weight
c) Static Load
4) Pile Material Properties:
a) Young’s Modulus
b) Poisson’s Ratio
c) Damping
d) Rigidity Coefficient
The user can manually input all the pile coordinates by clicking on Individual on
the menu bar and typing in the coordinates (or pasting an outside file) in the
Coordinates for Individual Piles window. By clicking on the menu bar Mesh, the
Mesh Generation window appears and the user can simply type in the coordinates
of the two opposite corners in the appropriate boxes and the program will formulate
the proper pile mesh. The mesh can be titled and saved for later use. The user has
the following options when developing the mesh:
1) Shape of the Mesh
a) Rectangular
b) Circular
2) Total Number of Piles
a) in X,Y Directions (rectangular mesh)
b) In R,  Directions (circular mesh)
3) Pile Spacing (in X,Y or R,  directions)
a) Equal (default)
b) Unequal (the user can manually set the spacing by
clicking on the Edit button)
4) Generation Direction
-
Click on this box so that the numbering of the piles
follows the X direction instead of the Y (default)
direction.
Figure 7.2: Generation of Pile Numbering
Once all the information about the mesh has been entered, click on the Apply box
to return to the Pile Head Arrangement window. If necessary, more individual piles
can be added to the newly created mesh by using the Individual window, these
piles will be added to the end of the list of piles.
Note: The maximum number of piles allowed by the program is 86 for the PC
version operating within the conventional memory (640 KB), and 1000 for
the extended/virtual memory version. The actual number that may be
analyzed depends on the available free memory. Refer to Section 8 for more
details.
If the Flexible cap option has been chosen, clicking on the Piles button will open
the Pile Head Arrangement for Flexible Cap window. The user does not need to
input the locations of the piles but only the material properties for the piles as
follows:
5) Pile Head Condition
a) Fixed
b) Pinned
Note: Pinned head piles are not allowed to carry moments about X
or Y-axes.
6) Pile Tip Condition
a) Floating Tip
b) Endbearing
7) Pile Properties:
a) Pile Length
b) Pile Unit Weight
c) Static Load
8) Pile Material Properties:
a) Young’s Modulus
b) Poisson’s Ratio
c) Damping
d) Rigidity Coefficient
If any of the piles in the mesh are battered, click on the menu bar Batter to bring
up the Data for Battered Piles window. In this window the user can input the
following information:
1) Pile Number (from mesh)
2) Angle 
3) Angle 
Click OK to return to the Pile Head Arrangement window.
Clicking Figure on the menu bar brings up a graphical representation of the mesh.
Holding the mouse pointer over one the piles will highlight it and bring up its
coordinates; this diagram can also be printed out. Clicking on the menu bar Print
Coord. will allow the user to print out the pile list along with their respective
coordinates.
4) PILE SOIL
Clicking on the Pile Soil button opens the Data for Pile-Soil System window. In this
window the user inputs information about the pile and soil elements. The user has
the option of choosing:
1) Soil Medium Type
a) Layered
b) Parabolic
2) Pile-Soil-Pile Interaction
a) No Interaction
b) Interaction
3) Weak Zone Interaction (default is no interaction)
For a layered soil (maximum of 30 layers), the user needs to calculate and input
the following parameters:
1) Layer Depth
2) Pile X-radius
3) Pile Y-Radius
4) Pile Area
5) Pile Y Inertia
6) Pile X Inertia
7) Pile Z Inertia
If the Parabolic option is chosen, then the parameters need only be entered for
one layer. The user then clicks on the Soil Elements tab at the bottom of the
window and enters the following information into the spreadsheet:
1) Soil Shear Wave Velocity
2) Soil Unit Weight
3) Poisson’s Ratio
4) Damping (material damping of soil is defined here as D = tan=
2 where  = loss angle and  = damping ratio)
5) SOIL BELOW
Clicking on the Soil Below button allows the user to enter the soil properties below
the pile. The following parameters are then typed in the appropriate boxes:
1) Soil Shear Wave Velocity
2) Soil Unit Weight
3) Poisson’s Ratio
4) Damping (material damping of soil is defined here as D = tan=
2 where  = loss angle and  = damping ratio)
6) OUTPUT
Clicking on the Output button opens up the Output Options for Pile Foundation
window. The user can select the following output options:
1) Print Piles Forces Due to:
a) Unit Displacements (selecting this box opens up the Data
for Applied Unit Displacements window)
b) Actual Loads (selecting this box opens up the Data for
Applied Actual Loads window)
2) Piles Vertical Stiffness
a) Print in Output File
b) Print in DYNFLEX File
3) Piles Lateral Stiffness
a) Print in Output File
b) Print in DYNLAT File
4) Print Forces Distribution (returns the distribution of the forces on
individual piles connected by a rigid cap. This keyword is not
allowed for flexible caps).
Notes: 1) The keyword FLEXIBLE prompts the printout of the vertical complex
stiffness matrix, n X n, of the group of piles, referred to the individual pile
heads, for the analysis of flexible caps or superstructures. The keyword
DYNFLEX places the same stiffness matrix into a separate file called
DYNFLEX in the current directory. This file is not a part of the output file.
The vertical stiffness matrix is relevant for flexible cap vibration modes
such as the one depicted in Fig.2.6.
2) The keyword LATERAL prompts the printout of the 2n X 2n group
complex stiffness matrix, referred to individual pile heads, pertinent to the
response in the lateral XZ plane (horizontal, rocking and coupling terms),
followed by the corresponding matrix for the YZ plane.
3) The keyword DYNLAT places the same matrices in a separate file called
DYNLAT in the current directory. If the piles are numbered 1,2,3,...n and
the horizontal translation and the rotation at the pile head of pile number i
are denoted by Ui and Fi, respectively, the arrangement of the degrees of
freedom in the lateral stiffness matrices is as follows:
{U1x,F1y,U2x,F2y,...,Uix,Fiy,...,Unx,Fny}
for the XZ plane, with each item having a real and an imaginary part, and
{U1y,F1x,U2y,F2x,...,Uiy,Fix,...,Uny,Fnx}
for the YZ plane
4) The keywords FLEXIBLE, DYNFLEX, LATERAL and DYNLAT should be
used with caution because for a large pile group and a large number of
frequencies, the size of the files and printouts may become excessive.
Clicking on the Resultants button allows the user to input the coordinates of up to
10 points other than the C.G. The program then calculates the translations of the
these points and places them in the output file.
6.2.2 Half-Space Foundation
The input parameters needed for this type of foundation are similar to the Pile
Foundation (see Section 6.2.1) except that the Flexible cap option is not available.
Clicking on the Foundation Type window, the user selects Half-Space and goes
through the same process as described in the preceding section. The Soil
Properties as described in section 6.2.2 are also the same for the Half-Space
Foundation.
Figure 6.3: Notations for Half Space Option
a) Surface
b) Embedded
6.2.3 Stratum Foundation
When the Stratum Foundation option is selected, the Stratum Foundation data
window is opened. Here the user can input the data by clicking on the following
buttons:
1) Footing (this is inputted in the same manner as the Pile
Foundation (Section 6.2.1) but the Flexible option is not available)
2) Stratum
i) Geometry
a) depth from ground surface to base of foundation (h)
b) depth from ground surface to rigid underlying layer (H)
ii) Soil
a) Shear Wave Velocity
b) Soil Unit Weight
c) Poisson’s ratio
d) Material Damping
3) Resultants (as described in Section 6.2.1, this allows the user to
track the translation of up to 10 points, other than the C.G.)
Figure 6.4: Notations for Stratum Option
a) Surface
b) Embedded
Notes:
1) The stratum option is valid for these limits:
a) h/H<0.75
b) h/R0<1.5
c) R0/H<0.5
Where R0 is the equivalent footing radius.
2) If preprocessing subroutines 3DVIEW and DATAPREP are used,
coordinates Xc,Yc and Zc are entered automatically.
3) For the determination of the validity limits, DYNA calculates the
average equivalent radius from those for the translations, rocking
and torsion, i.e.
R0= (Rh,v X2+Rrx +Rry +Rt)/5
6.2.4 Rigid Body Foundation
Selecting the Rigid Body Foundation option opens the Rigid Body Foundation data
window. The flexible cap option is not available because it would be subject to
bending deformations. The data is entered into the data windows in the same way
as described in Section 7.2.1. Clicking on the Structure button opens up the
Structure and Foundation Data window, this window is quite similar to the Footing
Base Dimensions and Data window. The user can input the following information
into the data window:
1) Structure Mass and Inertia
a) Total Mass
b) Moments of Inertia (Ixx,Iyy,Izz,Ixy,Ixz,Iyz)
2) Rigid Body Top Surface
a) Length Lx
b) Length Ly
3) Top Surface Centre (Xc,Yc,Zc)
Next, the user clicks on the Rigid Body button to bring up the Rigid Body
Foundation Data window. The following data is entered in this window:
1) Rigid Body Properties
a) Total Depth (depth of footing plus soil column underneath)
b) Unit Weight
c) Static Load (approximate)
2) Rigid Body Material
a) Young’s Modulus
b) Poisson’s Ratio
c) Damping Coefficient
d) Rigidity Coefficient (See footnote 3 in section 6.2.1)
3) End Condition
a) Floating (default)
b) Endbearing
Figure 6.5: Notations for Rigid Body Option
The rigid-body must be described at different levels throughout the soil media. In
order to do this, the user clicks on the Elements button to bring up the Rigid Body
Foundation/Soil Elements Data window. The user can click on the Weak Zone box
if the weak zone is to be taken into account in the calculations. Clicking on the
Rigid Body Elements tab, the user can input:
1) Rigid Body Elements
a) Layer Depth
b) Rigid Body X Radius
c) Rigid Body Y Radius
d) Cross Sectional Area
e) Cross Section Y Inertia
f) Cross Section X Inertia
g) Cross Section Z Inertia
Clicking on the Elements for Side Soil Layers tab, the user can input the following:
2) Soil Elements
a) Soil Shear Wave Velocity
b) Soil Unit Weight
c) Poisson’s Ratio
d) Material Damping
Clicking on the Elements for Soil Layers Below tab, the user can input the following:
3) Soil Layers Below
a) Shear Wave Velocity
b) Unit Weight
c) Poisson’s ratio
d) Damping
e) Shear Modulus Ratio (Gin/Gout)
f) Material Damping Ratio
The Below and Resultants buttons are used in the same fashion as described in
Section 6.2.1.
6.2.5 Composite Medium Foundation
Selecting the Composite Medium Foundation opens the Composite Medium
Foundation window. The Footing, Side Layers, and Resultant buttons all bring up
data windows identical to those found in the Pile Foundation Option (see Section
6.2.1). The Below button brings up the Properties of Soil Layer Below Foundation
window and the user can input the following parameters:
1) Layer Height (H)
2) Layer Shear Wave Velocity
3) Layer Soil Unit Weight
4) Layer Poisson’s Ratio
5) Layer-Half Space Shear Wave Velocity Ratio
Figure 6.6a: Notations for Composite Medium
i) Surface
ii) Embedded
Figure 6.6b: Soil Profile and Notations for Composite Medium
i) Uniform Layer
ii) Non-uniform Layer
Note On Limitations:
The impedance functions are exact for the radio of layer thickness to halfwidth of
the square footing (H/a) equal to 0.5, 1,2,3 and 4 for uniform layers (Fig. 6.6b(i))
and equal to 2,3,4,5 and 10 for non-uniform layers (Fig. 6.6b(ii)). If the ratio (H/a)
doesn’t coincide with one of the above values the program chooses the closest
(H/a) ratio available (interpolation is not implemented because of the strong nonmonotonic variations at high frequencies).
In the composite-medium option, accurate values of stiffness and damping are
used at frequencies equal to 0.10, 0.25,0.50..., 4.75 and 5.0 times (Vs ‘/a) where
Vs’ is the shear wave velocity at footing base level and a is halfwidth of the square
base(or the equivalent square base). For a frequency less than 0.10 Vs’/a, the
program uses the minimum value (0.10 Vs’/a) and for frequencies in the range
(0.10-5.0) Vs’/a, a linear interpolation is implemented. If the frequency is greater
than 5 (Vs’/a) the program uses the maximum value of 5 (Vs’/a).
The response phase shift, F, relative to the excitation force may be printed using
the optional keyword
Notes on Soils:
1) Poisson's ratio of the half-space is assumed 0.33 in this option.
2) Material damping of soil is assumed 0.03 and 0.05 for the layer and the halfspace, respectively.
3) Two values for Poisson's ratio of the layer are available 0.33 and 0.45. If a
different value is entered the program sets it to the closest one. (Interpolation is
not implemented in the program because of non-monotonic variations)
4) Vs' is the layer shear wave velocity at footing base level. (Fig. 7.6b)
5) Three values for the shear wave velocity ratio are available 0.8, 0.6, and 0.3. If
a different value is entered the program sets it to the closest one.
6) The ratio of unit weight of the half-space to that of the layer (p/p') is assumed
1.13.
6.2.6 Mat Foundation
Selecting the Mat Foundation Option brings up the Mat Foundation window, similar
to one used by the Pile Foundation (flexible cap option). The Data, Masses, and
Figure buttons all function in the same manner as described in Section 6.2.1The
user then clicks on the Soil button, which opens the Properties of Soil Below
Foundation, to enter the soil properties of the layer:
1) Soil Properties
a) Shear Wave Velocity
b) Soil Unit Weight
c) Poisson’s Ratio
Figure 6.7: Notations for Flexible Mat on Halfspace (Option MAT) and Pile
Foundation with Flexible Cap (CAPFLEXIBLE Option)
a) Elevation
Plan
Notes:
1) The nodes should be labeled from left to fight and from bottom to
top as shown in Fig. 6.7. If the response is required at more than five
nodes, more than one run must be used.
2) The response has real and imaginary parts. Returned are the
absolute value and the phase (optional) from which both the real and
imaginary parts may be obtained.
3) The total number of nodes (NX.NY) allowed by the program is 144
for the PC version operating within the conventional memory (640
KB), and 1650 for the extended/virtual memory version. The actual
number that may be analyzed depends on the available free
memory.
4) The keywords DYNFLEX and FLEXIBLE should be used with
caution as they may produce an excessive amount of data.
5) Material damping is not considered in this option because it is very
small compared to the geometric damping generated by the
halfspace.
6.3 Load Description (general)
In order to indicate that the load information is to be input the user clicks on the
menu bar Loads and selects Choose Load on the pull-down menu. The remainder
of the load description is divided into four parts depending upon which load type is
selected.
To finish inputting the required data, please go to the appropriate
subsection. Refer to Figures 3.1 and 3.4 for the different load types available.
6.3.1 Harmonic Load
Selecting the Harmonic load type from the Loads menu will bring up the Harmonic
Load Data window. The user then inputs the following parameters:
1) Output Phase Angle (click to enable)
2) Quadratic (i.e. its amplitudes are proportional to 2) or Non
Quadratic (i.e. its amplitudes are constant)
3) Frequency (in rad/s, Hertz, or RPM)
a) Maximum Frequency
b) Minimum Frequency
c) Step Frequency
4) Amplitude of Forces
a) Force in X Direction
b) Force in Y Direction
c) Force in Z Direction
5) Amplitude of Moments
a) Moment about X Direction
b) Moment about Y Direction
c) Moment about Z Direction
6) Applied Loads Phase
a) In Phase (default)
b) Out of Phase (click on the Phase Shift button to edit the
phase shift)
Notes :
(a) A minimum frequency of zero is not recommended. The program
will change it to a value of 0.001 to avoid errors.
(b) If the excitation is assumed to be of the quadratic type, i.e. its
amplitudes vary with frequency by Eq. 3.3, it is input by the following
values, with circular frequency in rad/s:
forcei  (mee)i 
pi
op
where i  x, y, z
In which pi = the excitation force amplitude acting in direction i at
momenti  (meer  mi ) 
Mi
op
frequency op, MI = the excitation moment about axis i at frequency
op. Usually, the magnitudes of pi and Mi are given for the operating
frequency op and have to be divided by op to get the input. Finally,
r = the respective arm of the excitation force with regard to the centre
of gravity of the system and mi is the unbalanced moment
independent of pi. (Often, there are no unbalanced forces; pi but
there is unbalanced moments mi.)
c) All the phase sifts are entered in degrees. For the quadratic case,
the vertical forces are usually 90 degrees out of phase from the
horizontal forces.
d) This option to specify input forces phase shifts is available only for
harmonic loads and rigid footings or rigid caps.
e) Due to numerical round off errors, some phase shifts that should
be zero show random fluctuations in sign and value; these phase
shifts should ignored. The phase shifts are returned in the range 0
to 2or 0 to -2 as shown in the figure.
f) The number of frequencies should not exceed 1024.The resultant
translation at any point on the machine-foundation system is due to
a combination of both translations and rotations, at the system's
centre of gravity.
g) If the option Dimensionless is used, the resultant translations are
not returned in dimensionless form but are given in actual values.
The option Resultants does not apply to flexible mats and caps (Mat,
Capflexible).
All output displacement amplitudes are "single
amplitudes," i.e. displacement amplitudes from the mean position,
not peak-to-peak values.
6.3.2 Transient Load
Selecting the Transient load type from the menu brings up the Transient Load Data
window; this load type is described using equidistant data points. The user then
inputs the following data.
1) Data Points Properties
a) Number of Data Points (maximum 1024, preferably a
power of 2)
b) Time Interval Between Points
2) Amplitude of Forces
a) Force in X Direction (click on the Time History button to
edit)
b) Force in Y Direction (click on the Time History button to
edit)
c) Force in Z Direction (click on the Time History button to
edit)
3) Amplitude of Moments
a) Moment about X Direction (click on the Time History button
to edit)
b) Moment about Y Direction (click on the Time History button
to edit)
c) Moment about Z Direction (click on the Time History button
to edit)
4) Output of FFT for Load
a) Graph (default)
b) All
5) Output of FFT for Response
a) Graph (default)
b) All
In the above, if you choose the option GRAPH, only the files required by the Plot2D
utility would be generated. If you choose the option ALL, then, in addition to the
GRAPH files, the Fourier transforms would be included in the output file. The
contents of the generated plotting files are as follows:
FTFORCE.DGR: data for plotting the Fourier transforms of applied forces
FTMOMENT.DGR: data for plotting the Fourier transforms of applied moments
FTTRANS.DGR: data for plotting the Fourier transforms of response translations
FTROTAT.DGR: data for plotting the Fourier transforms of response rotations
Each of the above files has an associated text file with the same name but with an
extension .DTX that is also used by the GRAPH utility. Use the keyword ALL with
care; the length of the output file may be increased by up to 1300 lines.
Note: a) If the number of points is a power of 2 (e.g. 256 or 512 or 1024), the
trailing zero load values that are needed to alleviate the problems
associated with the periodicity implied in the Fourier Transform approach,
should be included in the data provided by the user. Otherwise add an extra
zero point (e.g. number of points = 257 or 513 etc.) and the program would
automatically add zeros until the number of points is equal to the next power
of 2.
b) If there is a significant static (DC) component in the transient input force,
as for example in the short moments of a power generator, it should be
separated from the signal for the sake of FFT accuracy and treated
separately as a static or very low frequency harmonic effect.
6.3.3 Random Load
Clicking on the Random load type brings up the Random Load data window. The
user then inputs the following data:
1) Number of Data Points
2) Observation Time (sec)
3) Minimum Frequency (rad/s and must be greater than zero)
4) Maximum Frequency (rad/s)
5) Spectrum Data (autospectra and cross-spectra may be input, up
to a total of 36)
a) Location of Spectra
b) Spectrum Ordinates
Note: a) Location of spectra indicates the correlation of forces in any two
directions and thus could be any of 36 alternatives, i.e., 1 1, 1 2, . . . . , 1 6,
2 2, .. . . ., 2 6, . . . ., 6 1, . . . ., 6 6 . . . ( leave a space between the two
relevant integers).
b) Spectrum ordinates are the values of the spectrum for individual
frequencies.
c) The Random load option is not allowed frequency units other than rad/s.
6.3.4 Impact Load
Selecting the Hammer load type form the menu brings up the Type of Hammer
Load data window. The user has two options to choose from in this window:
1) Supporting System
a) Pad
b) Spring
2) Hammer Load Type
a) Short Duration Pulse
b) Long Duration Half-Sine Pulse
NOTE:
(a) Keyword PAD is used for two mass foundations with anvil pad
(Fig. 3.2a); Keyword SPRING is used for directly sprung hammers
with anvil springs and dampers (Fig. 3.2b).
(b) Initial velocity of anvil is calculated from Eq. 3.5. This is the natural
frequency of the foundation
7.0 FOUNDATION BLOCK CALCULATIONS
3DVIEW
A Program For Machine - Foundation Block Calculation for Use in DYNA6
3DVIEW INTRODUCTION
In DYNA foundations are assumed to be rigid bodies. A single, rigid body replaces
the machine, its foundations, and other attached components with the reference
point being the centre of gravity of the whole system. The excitation forces, which
may act at any point, must be transferred to the system centre of gravity.
This subroutine 3DVIEW calculates the system mass, mass moments of inertia,
including products of inertia, and transfers all excitation forces and couples to the
centre of gravity, whose position is also calculated. All these items are needed as
input for DYNA and are returned with the signs and the format required by DYNA.
SYSTEM OF AXES
The system of axes chosen in this subroutine is shown in Fig. 7.1. It is parallel to
that used in DYNA (Fig. 5.1) except that the z-axis is taken positive upward to be
more convenient in preparing the data for 3DVIEW. There is no limitation on the
location of the origin.
UNITS:
Any system of units can be used but it must be consistent and the same as in the
program, i.e. force, mass, and length in SI units N, kg, m or in Imperial units lb,
slug (weight/g, lb/ft/s2, with 9 = 32.2 ft/s2), ft.
Figure 8.1 : General Layout and System Axes for 3DView
CALCULATION OF SYSTEM MASS, MASS MOMENTS OF INERTIA AND THE
POSITION OF CENTRE OF GRAVITY
Bodies of complex shapes can be subdivided into various components defined as
follows:
Rectangular Blocks: Each rectangular block is defined by its three side lengths,
three coordinates of its centre of mass, and its density. The
sides of a rectangular block should be parallel to the three
coordinate axes.
Circular Cylinders: Each circular cylinder is defined by its diameter, length, three
coordinates of its centre of mass, density, and the direction of
its axis. The axis of the cylinder should be parallel to one of
the coordinate axes X, Y, Z.
Lumped Masses:
These are other bodies, e.g. machines, which cannot be
represented by the above elements. Each lumped mass is
defined by its mass, three coordinates of its centre of mass,
and six moments of mass about three axes parallel to the
coordinate axes and passing through its centre of mass.
Accounting for Holes: To account for holes for both lumped masses and complex
bodies, the mass is entered with a negative sign. For blocks
and cylinders the density is entered with a negative sign.
Excitation Forces: Each excitation force system is defined by three coordinates
of its point of application, one force in direction of each
coordinate axis, and one couple about each coordinate axis.
The sign convention for the forces shown in Fig. 9.1 is the same as that used in
the main program, i.e. the right hand rule controls the moments. Automatic change
in some signs accompanies the transformation from 3DVIEW axes to DYNA axes
accomplished by 3DVIEW.
Rectangular Blocks, 7 numbers for each block: Input data for rectangular blocks.
The format is:
Lxi Lyi Lzi Xi Yi Zi p; for i = 1,NB (No. of rectangular blocks)
where
Lxi Lyi, Lzi = lengths of rectangular block sides parallel to the X,Y and Z axes,
respectively;
xi, yi, zi = X, Y, and Z coordinates of the block centre of mass.
 = mass density of block material.
- Each block data should be entered on a separate line.
- If NB = 0 skip this data block.
Cylindrical Blocks, 6 real numbers and one integer for each cylinder: Input data for
circular cylinders. The format is di li pi xi yi zi NA
where
di, li, pi = diameter, length, and mass density of the circular cylinder, respectively.
xi, yi, zi = X, Y, and Z coordinates of the cylinder centre of mass.
NA = Axis code = 1 cylinder axis is parallel to X - axis.
= 2 cylinder axis is parallel to Y - axis.
= 3 cylinder axis is parallel to Z - axis.
-Each cylinder data should be entered on a separate line.
- If NY = 0 skip this data block.
Figure 7.1a: Relation between IDC Coordinates and DYNA Coordinates
Lumped Masses, 10 real numbers: Input data for lumped masses. The
format is:
mi xi Yi zi Ixxi Iyyi Izzi Ixyi Ixzi
where
mi = mass
xi, yi, zi = X, Y and Z-coordinates of the body centre of mass.
Ixxi , Iyyi , Izzi = mass moments of inertia about X, Y and Z-axes, respectively.
Ixyi, Ixzi, Iyzi= mass products of inertia about XY, XZ, and YZ-axes respectively.
- Each body data should be entered on a separate line.
- If NC = 0, skip this data block.
Forces and Moments, 9 numbers: Input data for excitation forces.
The format is:
Fxi Fyi Fzi Mxi Myi Mzi Xi Yi Zi
where
Fxi, Fyi , Fzi = forces acting at point i in the X, Y and Z-directions, respectively.
Mxi , Myi , Mzi = moments acting at point i about the X, Y and Z-axes, respectively.
xi, yi, zi = X, Y, and Z-coordinates of point I.
- Each point input forces should be entered on a separate line.
- If NP = O, skip this data block.
3 DVIEW OUTPUT
The output of 3DVIEW includes:
The total mass and mass coordinates of the system mass centre (C.G.) in the
3DVIEW coordinates.
The mass moments of inertia and product of inertia relative to DYNA6 axes.
Resultant excitation forces (including moments relative to DYNA6 axes).
The total mass, mass moments of inertia, and excitation force are input directly
into DYNA6 without any changes in magnitude or signs.
The user is required to calculate the coordinates of the foundation base centre in
the DYNA6 axes system, Xc, Yc and Zc, relative to C.G., as shown in figures 8.1
and 8.1a.
Example
Using the 3DVIEW subroutine, calculate the total mass, position of the centre of
gravity and mass moments of inertia for the whole foundation system shown in Fig.
8.2. The system comprises four lumped masses, one body that can be subdivided
into rectangular blocks and one cylinder. The specific mass is 2500 kg.
The auxiliary 3DVIEW axes are placed at the base level as shown in Fig. 8.2. The
body is subdivided in three rectangular blocks. Block 3 represents a hole
(depression) and is input as a rectangular block with negative mass.
Figure 8.2
8.0 RUNNING THE PROGRAM MANAGER AND OTHER UTILITIES
This section describes the use of the program DYNA6 and other utilities included
in the DYNA6 Package.
8.1 Contents of the DYNA Package
DYNA 6 User Interface: This is the program manager that allows the user to
interactively prepare the input data file required by the main program. It also allows
the user to invoke the DYNA6 program and all utilities from one screen menu
3Dview; this utility assists the user to evaluate the properties of the combined
foundation equipment system, required as input by the main program. The
evaluated properties include the position of the center of gravity, the total mass,
the mass moments of inertia and the resultant excitation forces and moments
relative to the center of gravity.
DYNA6:
This is the main program, which calculates the stiffness and dumping constants of
the foundation as well as the system response to various load types.
Plot 2D:
This is the post processor. It allows the user to graphically depict the results of
DYNA6 on the screen and to print them.
8.2 DYNA 6 User Interface 3DVIEW
To invoke the user interface click on the DYNA6 icon. The main screen shown in
Fig. 10.1 will be displayed

To invoke any option in the screen, click on its icon.

The option are:

FILE: By clicking on this option, a menu appears, listing the following file
options.

New: to start a new data file

Open: to open an existing data file (created by DYNA6)

Save: to save the current data to the existing data file.

Save as: to save the current data to a new file

Import Dyna5 File: to import a data file generated by the older version
(DYNA5)

Print input data: to print the input data file.

Utilities: This option has 3 utilities.
1. Window File Manager (click Windows Explorer) to search for a
data file.
2. Plotting utility to graph the results from existing or previously
saved output files
3. Complex Footing 3Dview utility to calculate the properties of the
machine-foundation block and the force and moments due to
machines.

Exit: to exit the DYNA6 user interface.
Title: This option allows the user to enter the program title (maximum of 80
characters)
Settings: This option allows the user to input the settings including the units of the
problem, the output format and the damping safety factor
Foundation: This option allows the user to select the foundation type. There are 6
foundation types available to choose from as described in Sec 2.1 listed here.

Pile: This option is for piled foundation. It allows the user to specify the footing
conditions (embedment, shape to input the piles, pile cap properties. It also
allows the user to input the properties of the soil along the pile (Pile-Soil), below
the pile tip (soil below) and adjacent to the pile cap for embedded footing (side
layers). Finally it allows the user to input the output options including the
coordinates for points where the resultant translations are required to be
calculated.

Half-Space: This option is for rigid foundation on a homogeneous soil (halfSpace). It allows the user to input the footing properties (Footing) or calculate
them (using 3Dview by clicking on “Calculate”). It also allows the user to input
the properties of the half-space (Below) and the adjacent embed footing (Side
Layers) Finally, It allows the user t input the coordinates of the points where the
resultant translations are required (Resultants).

Stratum Foundation: This option is for footing sitting on a layer under lain by
bedrock. It allows the user to input the properties (Footing) or calculate them
using 3Dview (by clicking on “calculate”) It allows the user to input the
properties of the soil layer (Stratum). Finally, it allows the user to input the
coordinate of the points where the resultant translations are required
(resultants).

Composite: This option is for footing sitting on a layer underlain by a half-space
(deep homogeneous soil deposit). It allows the user to input the footing
properties (Footing) or calculate them using 3Dview (by clicking “calculate”). It
also allows the user to input the properties of the soil layer and half-space
(Below) and the soil adjacent to the embedded footing (Side Layers). Finally it
allows the user to input the coordinates of the points where the resultant
translations are required (Resultants).

Rigid: This option is for rigid foundations (i.e. piers or caissons). It allows the
user to input the properties of rigid super structure (Structure). It also allows the
user to input the variation of the pier cross-section and soil along the pier and
below its tip (Elements), this includes the geometrical properties of the pier
(Rigid body elements). The properties of the soil along the shaft (Elements for
side Soil Layers) and the properties of soil below the tip of the pier (Elements
for soil Layers Below). And the properties of the soil layer below the foundation
to the bedrock (Below). Finally, it allows the user to input the coordinates of the
points where the resultant translations are required (Resultants)

Mat: This option is for flexible raft foundations. It allows the user to input the
mat data (Data) and the masses of the machines and their Pedestals (Masses)
and the soil properties below the foundation (Soil). It also allows the user to
view the mesh representing the foundation and the lumped masses locations
(Figure). After selecting one of the foundation options, the icons for “Loads”
and “Run” will be activated.

Loads: Allows the user to choose one from the following four potions

Harmonic: This option is for harmonic loading (centrifugal or reciprocating
machines). Details of the harmonic loading are given in section 3.3.

Transient: this option allows the user to input the characteristics of the
transient load (Transient) where the numbers of data points and time
interval as well as the force amplitudes are required. This option allows the
user to define the format of the FFT of the output load and response. Details
of transient loading are given in Section 3.1.

Random: This option allows the user to input the characteristics of a random
load (Random) including the number of data points observation time and
the minimum and maximum frequency required. Details of random loading
are given in Sec. 3.2.

Impact (Hammer): This option allows the user to input the properties of the
supporting system of the hammer block which could be a pad (Pad) for
which Young’s modulus, material dumping, thickness and plan dimensions
are required, or could be a spring system (Spring), where the stiffness and
damping constants of the spring are required. It also allows the user to
model the hammer impact as a very short pulse (short duration pulse) where
the initial velocity and mass of the awning and the estimated natural
frequency of the footing are required. Alternatively, the hammer impact
could be modeled as a half-sine pulse (long duration Half-Sine Pulse) where
the duration and peek value of the pulse is required. Details of Hammer
Loading are given in section 3.4.

Run: After the input process is complete, this option allows the user to run
Dyna6 (Execute Dyna6). After the run is completed successfully the user is
prompted to input the name of the output file. When the user inputs the name
of the output file, the control is returned to the main screen and the Post
Processor option is active.

Post Processor: This option activates the utility Plot 3D where the user can
depict the output graphically or in a spreadsheet. The output depends on the
problem and the format required. This output may include

Translational Response: This may include translational response of C.G. or
at any point specified by the user using the option (Resultants).

Rotational Response at C.G. (please disregard other menu items)

Vertical Stiffness: This option allows the user to view and print the variation
of the vertical stiffness with frequency.

Vertical Damping: This option allows the user to view and print the variation
of the vertical damping with frequency.

Horizontal stiffness: This option allows the user to view and print the
variation of the vertical damping with frequency

Horizontal Damping: This option allows the user to view and print the
variation of the horizontal damping with frequency

Rocking Stiffness: This option allows the user to view and print the variation
of the Rocking stiffness with frequency.

Rocking Damping: This option allows the user to view and print the variation
of the rocking damping with frequency.

Coupled Hill Rocking Damping: This option allows the user to view and print
the variation of the Coupled Hill Rocking Damping with frequency.

Torsional Stiffness: This option allows the user to view and print the
variation of the torsional stiffness with frequency.

Torsional Damping: This option allows the user to view and print the
variation of the torsional damping with frequency.

Fourier Transform for Translations: It allows the user to view and print the
absolute value of the complex FFT of translation at C.G. (available for
transient loading option only).

Fourier transform for Rotation: It allows the user to view and print the
absolute value of the complex FFT of rotation at C.G. (available for transient
loading option only)

Fourier transform for Forces: It allows the user to view and print the absolute
value of the complex FFT of forces at C.G. (available for transient loading
option only)

Fourier Transform for Moments: It allows the user to view and print the
absolute value of the complex FFT of the moment, for positive frequencies
only (available for transient loading option only).
8.3 View and Print Results of DYNA 6
The output files generated
1
by DYNA6 may be treated as any Dos ASCII file,
i.e., it may be print or edited using any editor. This can be done from the file option
0
and then using the Windows file manager to find the file and open it using NotePad
and WordPad.
.
3
V
8.4 Graphic Depiction of DYNA 6 Results
i
1
This option is invoked through the post processor menu or through the Plotting
e
0
utility (PostProcessor in the File option).
w
.
a
4
n
G
d
r
P
a
PostProcessor utility allows the used to view, edit and/or print the data and graphs
for the output
It has the following options:

File: This option allows the user to open a new file (New) open an existing chart
(Open Chart), save an existing chart (Save chart), import data for plotting from
Excel or Formula one files, or print preview and print data and /or chart.

Edit: This option allows the user to edit the data.

Data: This option allows the user to change the format of data.

Plots: This option allows the user to edit or create plots.

Chart: This option allows the user to edit the chart (title, footnote, legend, exit,
ect.)

View: This option allows the user to change the format for the Tool Bar.

Window: This option allows the user to change the format for the screen
(Cascade, File Horizontal, title, vertical and Arrange icons)
9.0 FREQUENTLY ASKED QUESTIONS
In this section, some of the questions DYNA users often ask are briefly addressed.
9.1 Negative Stiffness Constants
At certain frequencies the main (diagonal) stiffness constants, k ii, can be negative
which seems to suggest that the elementary formula for the natural frequency of a
one-degree-of-freedom system, i.e. w = (kii/m)
1/2
cannot work. Is this correct?
Negative diagonal stiffnesses may indeed occur under some conditions; they are
correct and cause no problems. They are most likely to be returned for higher
frequencies, rigid footings vibrating in the vertical direction particularly with soil
Poisson's ratio close to 0.5 (see Ref.2 and Fig. 2.5.1), heavy single piles in weak
soil or pile groups (Fig. 1.1.8). Negative stiffnesses pose no problems in response
calculations because the total soil resistance is a resultant of its real part,
depending on stiffness, and imaginary part, depending on damping.
At low
frequencies, the diagonal stiffness constants are always positive.
9.2 Natural Frequencies Are Not Returned by DYNA
System natural frequencies are not explicitly evaluated by DYNA because the
foundation stiffness and damping constants are in general strongly frequency
dependent and the damping is often very high, even super-critical. They are,
however, readily available from the response curves calculated for harmonic loads
over a broad range of frequencies. The peaks of such response curves indicate
the resonance regions and hence, the natural frequencies. To emphasize the
peaks and make them more pronounced a damping safety factor such as 2 could
be implemented for the purpose of resonance frequency identification.
9.3 Very Low Efficient of Pile Groups
The efficiency of a pile group can be assessed by evaluating the efficiency ratio,
which is defined as:
Group stiffness with interaction considered
Group stiffness with interaction neglected
The one in the nominator accounts for dynamic pile-soil-pile interaction and is
calculated by DYNA6 by the default option; the one in the denominator is
calculated with the keyword NO-INTERACTION which instructs the program to
neglect pile-soil-pile interaction (the group effect) and calculates the group
properties by superimposing the properties of single piles considered in isolation.
Examples of such ratios are displayed in Fig. 2.1.8. For group stiffness of closely
spaced piles the efficiency ratio is often much smaller than 1, particularly at low
frequencies. This is a typical effect of group action and is quite similar to static
group behaviour (see Ref. 15 and others). To increase group efficiency, one may
opt for a smaller number of larger piles with larger separation.
Under large
displacements, pile-soil-pile interaction can be reduced due to nonlinearity. With
DYNA this can be accounted for approximately by allowing for pile free length
(separation), a primary source of nonlinearity.
For damping the efficiency ratio can be evaluated in an analogues fashion and it
usually is greater than 1 indicating a favorable effect of group action.
9.4 Sharp Peaks in Pile Groups Stiffness
Sometimes, sharp peaks occur in the plot of pile group stiffness versus frequency.
Such peaks or valleys occur because under dynamic loads, soil motions travel
from pile to pile in the form of travelling waves. As a result, and depending on
frequency (wave length) and pile spacing, the pile may tend to vibrate in phase in
which case the group stiffness is reduced, or in anti-phase, which increases the
stiffness and leads to marked peaks, peaks such as those visible in Fig. 2.1.8. All
theories available (e.g. Refs. 17, 27) indicate such peaks.
Under nonlinear
conditions they may be reduced but not eliminated (Ref. 17).
9.5 The effect of the Keyword ENDBEARING
The pile tip conditions can be specified as either FLOATING (default) or ENDBEARING. Some users observed that changing this keyword did not change the
results.
The pile tip condition is taken care of primarily and automatically by the
specification of soil properties below the pile tip. The keyword END-BEARING
produces only two effects:
(1)
For pile bearing on a stiff stratum, it generates the calculation of the
fundamental natural frequency of the soil stratum and eliminates radiation
(geometric) damping in the frequency range below this natural frequency (see Fig.
2.1.5);
(2)
It replaces the dynamic interaction factors in this low frequency range by
the essentially static interaction, as it is appropriate, because in that region no
travelling waves exist.
9.6 Mass Participation Factor
Some users wonder what is the role of the mass participation factor and how it
should be chosen. Around the piles and around embedded rigid footings a weak
zone is allowed (keywords WEAK or ISOLATION) to account in an approximate
fashion for nonlinearity in the immediate vicinity of the embedded body and lack of
bond between the body and soil. In the theory, the mass of the weak zone is
neglected to prevent wave reflection from the artificial interface between the weak
zone and the outer region (see Refs. 8 and 28). The mass participation factor
accounts for the mass of the weak zone. Not to exaggerate its effect it should be
chosen as less than 1, increasingly so for thicker weak zones. The mass
introduced by the participation factor may cause small irregularities in stiffness or
pile displacement and internal forces.
9.7 Validation of DYNA Results
The theories employed in DYNA were validated by comparing their results with
those of other theories and with experiments. For rigid bodies, such comparisons
were reported in Refs. 5, 6 and 32, for pile foundations in Refs. 32 to 35 and a few
others. Some comparisons of DYNA with other theories are also described in
Chapter 2. More experimental validation is, of course, desirable but in this regard
the theories incorporated in DYNA are no less validated than most other theories
used in practice.
10.0 EXAMPLE PROBLEMS
This volume contains examples of problems that may be analyzed by the DYNA6
program. The examples illustrate all of the information and load options and most
of the other non-default options. The heading for each problem gives a description
of the function and soil properties as well as the requested output. The heading is
followed by a listing of the input file to be processed by DYNA6 and the resulting
output file. Where appropriate, examples of the plots produced using the Plot2D
utility are included. The following table gives a summary of the options and
requested output for all the examples.
Table 10.1 Summary of examples
Example Foundation
No
1
Type
Load
Options & Requested Output
Type
Pile
Harmonic
(Single)
(Nonquadratic)
Pile (Single,
Battered)
Harmonic
3
Half-Space
Transient
4
Half-Space Hammer (Initial
(Embedded) Velocity)
Response, Peak Stresses
5
Half-Space Harmonic
(Embedded/
(Quadrat
Weak)
Ic)
Response Amplitude & Phase Shift,
Resultant Translations, Tabulate
Stiffness & Damping
6
Pile
Harmonic
Response Amplitude And Phase Shift
(Group)
(Quadratic)
2
Stiffness Constants (Matrix), Damping
Safety Factor (Safety), Displacement
Distribution
Stiffness Constants (Matrix)
(Quadratic)
Response, Fourier Transforms
Schematic
7
Pile
Harmonic
Stiffness Constants (Matrix), Vertical
Group Stiffness (Flexible), Distribution
Of Forces
(Group)
8
Half-Space
Random
Peak Factor, Maximum Response,
Power Spectra
9
Stratum
Random
Peak Factor, Maximum Response,
Power Spectra
10
Pile
Harmonic
Stiffness Constants (Matrix), Response
(Parabolic
(Quadratic)
Soil)
11
Rigid-Body
Transient
Response
12
Composite-
Harmonic
Response Amplitude & Phase Shift
Medium
(Quadratic)
Pile
Harmonic
(Group,
(Quadratic)
13
Response
Battered,
Embedded)
14
Matf
Harmonic
(Mat
(Quadratic)
Response At 5 Different Points
Foundation)
15
Pile
Harmonic
(Battered,
(Nonquadratic)
General)
Vertical Group Stiffness (Flexible),
Lateral Group Stiffness (Lateral)
8.1
Example 1: Single Vertical Pile Under Constant Amplitude Harmonic Load
(a)
Evaluate stiffness and damping constants of a single fixed head, vertical
pile with constant cross-section, embedded in a layered soil medium comprising
ten layers adjacent to the pile; consider the soil properties and the weakened zone
with properties given in the Figure below.
(b)
Calculate the response of the pile to harmonic excitation which has constant
amplitudes equal to 1, 1, 1, 1, -1, 1 acting in all six directions and whose frequency
is ω = 100 rad/s. (The signs of forces and moments have to be consistent with the
sign convention shown in Figure 5.1.)
Units to use: lb, slug, ft.; mp = weak zone mass participation.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. You will now be brought to a screen with several options, only one of which, you can
currently select. Click on “Edit Settings” under the ‘Project Control’ header to proceed.
3. On the project settings menu, select the “Imperial Units”, check off “Echo Input Data”
and “Stiffness/Damping Matrices” and adjust the “Damping Safety Factor” to 2. Click
“OK”.
4. Next, select “Edit Foundation” from the Project properties menu and a selection of
foundations will appear in a new window. Select “Pile” and under Footing Shape click
“Rectangle” and “OK”
5. Now a window titled “Pile Foundation” will open up. To begin, select the “Pile Cap”
button to set the values for the pile cap.
6. Input the data for the footing and base dimensions and click “OK”.
7. Next select the “Piles” button and input the Pile Head Condition, Pile Material
Properties, Pile Tip Condition, and Pile Properties. Then select the option “Individual”
from the top of the menu and input the X and Y coordinates of the pile. Click “OK” twice
to return to the Pile Foundation menu.
8. Select the “Pile-Soil” button and proceed to input the data for Layer Depth and Pile XRadius. Then click “Calculate geometrical data” and the rest of the table should fill out.
Check off “Weak Zone” under Soil Medium Type and click on the tab at the bottom of the
Data for Pile-Soil System window, labeled “Soil Elements” to proceed.
9. Input all of the soil data and click “OK” to return to the Pile Foundation menu.
10. Select “Soil Below” on the Pile Foundation menu and input the requested values. Click
“OK”.
11. Select “Output” on the Pile Foundation menu and proceed to check off Unit
displacements and input the frequency labels and pile numbers then check off Actual
Displacements and do the same. Click “OK” three times to return to the main menu and
select “Edit Load”.
12. On the Load Type Choice menu, select “Harmonic” and click “OK”.
13. Select “Non-Quadratic” from the drop down menu and input all of the other values
accordingly. Click “OK” when finished to return to the main menu.
14. Finally, click “Run Project” to view the results.
Example 2: Single Battered Pile Under Constant Amplitude Harmonic Load
(a)
Evaluate stiffness and damping constants of a single pile battered in the xz - plane
whose angle to the vertical is α = 10o. The pile is embedded in a layered soil medium
comprising ten layers adjacent to the pile;
(b)
Calculate the response of the pile to quadratic harmonic excitation of amplitudes
equal to 0.0001, 0.0001, 0.0001, 0.0001, -0.0001, 0.0001 acting in all six directions and
whose frequency is ω = 100 rad/s.
Units: lb, slug, ft.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. You will now be brought to a screen with several options, only one of which, you can
currently select. Click on “Edit Settings” under the Project Control header to proceed.
3. On the project settings menu, select “Imperial Units”, check off “Echo Input Data” and
“Stiffness/Damping Matrices”. Click “OK”.
4. Next, select “Edit Foundation” from the Project properties menu and a selection of
foundations will appear in a new window. Select “Pile” and under Footing Shape click
“Rectangle” and “OK”
5. Now a window titled “Pile Foundation” will open up. To begin, select the “Pile Cap”
button to set the values for the pile cap.
6. Input the values for the Footing Base and Dimensions of the base and click “OK”.
7. Next, select “Piles” and proceed to input the values for Pile Head/Tip Condition and
Pile/Material Properties. Then, click Individual and input the coordinates for the single
pile. Click “OK”.
8. On the same menu select “Batter” and input the batter angle Alpha. Click “OK” twice to
return to the “Pile Foundation” menu.
9. Now click the “Pile-Soil” button and check off Weak Zone and input the Layer Depth
and Pile X-Radius information and click the “Calculate” button to fill in the rest of the
table. Then click the “Soil Elements” tab at the bottom of the window.
10. Input all of the required data (Soil Layer Shear Wave Velocity, Soil Unit Wt.,
Poisson’s Ratio, etc.) Click “OK” to return to the previous menu.
11. On the Pile Foundation menu, select “Soil Below” and input the values in the empty
spaces. Click “OK” twice to return to the project properties menu.
12. Now select the “Edit Load” button to proceed to the Loading Type Choice menu. Select
the “Harmonic” load type and click “OK” to proceed to the next menu.
13. Input the values for the Frequency and Force and Moment Amplitudes. Click “OK”.
14. Finally, select “Run Project” to process the inputs and receive the output values. Click
the “Enter” bar on the keyboard two times to view the Output File or select Output File
from the Project Properties menu.
Example 3: Transient Load Applied to Rigid Body on Half-Space (Surface
Footing)
The transient response of a 22 m high rigid silo (Figure 8.1) is calculated for horizontal
excitation due to the San Fernando Earthquake, 1971, component S90W with peak
acceleration of 0.11 g (Figure 8.2) acting in the x-direction.
The silo is supported by a 10.5 m diameter foundation resting on a half-space.
Use SI units: kN, Mg = 1000 kg, m.
Note: Better plots than those returned by DYNA can be obtained by generating the output
file DYNAPLT and using it together with the user's plotting subroutine. (See example 12,
p. 8.109.)
9.1 m
C.G.
0.2 m
C.G.
R.C.
silage
zC = 10.63
10.5 m
0.9 m
Half-space
VS = 152 m/sec
γ = 19.2 kN/m3
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. You will now be brought to a screen with several options, only one of which, you can
currently select. Click on “Edit Settings” under the Project Control header to proceed.
3. On the “Project Settings” window check off Other. Under Frequency Units select
“Hertz”. Under Force Units, check off “Other” and input ‘kN’ in the blank space. Under
Mass Units, check off “Other” and input ‘Mg’ in the blank space. Finally, under Length
Units check off “Meter” and click “OK”.
4. Now select “Edit Load” on the Project Properties menu and the Foundation Type
Choice window will appear. On this window, select “Half Space” and under the heading
Footing Shape check off “Circle”. Click “Ok”.
5. Open now is the Half-Space Foundation window. Select “Footing” to proceed.
6. Input the Footing Mass & Inertia, the Dimensions of Base, and Coord. Of Base Center
values. Click “OK” to return to the previous menu.
7. Back on the Half-Space Foundation window; select “Below” to proceed. Input the
appropriate values in the empty spaces as labeled. Click “OK” twice to return to the Project
Properties window.
8. Now select the “Edit Load” option to proceed. The Loading Type Choice window will
appear, select “Transient” and click “OK”.
9. Now on the Transient Load Data menu, input the values under Data Points Properties
and check off “ALL” under Output of FFT for Load and Output of FFT for Response.
Under Amplitude of Forces click the “Time History” button.
10. The Time History window should be open. Input the adjacent values next to the
appropriate time in the empty space under the Value header. Click “OK” twice to return to
the Project Properties menu.
11. Finally, select the “RUN PROJECT” button to run the analysis. Click the “Enter” key a
few times until the analysis window closes. The Output File window should open up. If it
does not or the Output File was accidentally closed, click the Output File button under the
Project control label.
Example 4: Two Mass Hammer Foundation on Half-Space (Embedded)
(a)
Evaluate the stiffness and damping constants of a symmetrical two mass hammer
foundation with an anvil pad. The foundation analyzed is described in detail in Ref. 23 and
is shown in Figure 5. It is assumed that separation between the soil and footing sides may
occur due to heavy vibration of the hammer. Consequently, an effective embedment depth
of 5.2 ft (smaller than the actual embedment depth of 8.2 ft) is used in the analysis. The
initial estimate of the first natural frequency of the two mass system is 58 rad/s.
(b)
Calculate the response of this foundation to the impact of the hammer head assuming
initial velocity of the anvil equal to 1.52 ft/s.
(c)
Calculate the maximum stresses on the anvil pad and the soil.
separation
Anvil (mass = 1863 slug)
(0.15)
3.28
(1.00)
4.92
(m)
13.12
(4.00)
4.92
(1.50)
4.10
(1.25)
γ = 90 lb/ft3
5.2
4.92
6.56
(1.50)
(2.00)
16.40
(5.00)
4.10
(1.25)
VS = 408 ft/s
0.5
(1.50)
ft
ℓ = 5.2 ft
(E = 216 x 104 lb/ft2, D = 0.1)
C.G.
8.20
(2.50)
PAD
4.92
VS = 500 ft/s
(1.50)
γ = 120 lb/ft3
ν = 0.25
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should now be open. Click the Edit settings option to
proceed.
3. Check off Imperial Units, Stiffness/Damping Matrices, and Output Draft Plots.
Click “OK”.
4. Select the “Edit Foundation” option to proceed. The Foundation Type Choice window
should open up. Check off “Embedded” under Embedment. Click “OK”.
5. On the Half-Space Foundation window click the button labeled “Footing” to proceed.
6. Input the values in the empty spaces indicated under “Footing Mass & Inertia” and
“Dimensions of Base”. Click “OK”.
7. Select “Side Layers” on the Half-Space Foundation menu and the Side Layer window
should open up. Input the side layer properties in the allotted space and click “OK” to
proceed.
8. Select “Below” on the Half-Space Foundation menu and the Properties of Soil Below
window should open up. Input the values for the soil properties in the appropriate spaces.
Click “OK” twice to return to the Project Properties window.
9. On the Project Properties window, select “Edit Load” and the Loading Type Choice
window should appear. Select “Hammer” and click “OK”.
10. The Type of Hammer Load window should be open. Under Supporting System,
select “Pad” and under Hammer Load Type, select “Short Duration”. Click “OK”.
11. The Pad System Data window should now be open. Input the values for Hammer
Foundation Properties, Short Duration Pulse data and Pad Supporting System. Click
“OK”.
12. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 5: Half-Space With Weak Zone and Harmonic Load (resultant
translations and stiffness tabulation are required)
For the rectangular foundation (10 ft x 16 ft) shown in Figure:
(a)
Calculate the response to quadratic harmonic load of amplitudes (0.0055, 0.0055,
0.0055, -0.04, 0.04, 0.04) whose frequency ranges from 0.25 Hertz to 12.5 Hertz. The
vertical force is 90 ͦ out of phase from the horizontal forces. The response phase shift is to
be printed.
(b)
Calculate the resultant translations at a point on the foundation surface with
coordinates (5.0, 8.0, and 1.25) relative to the centre of gravity.
(c)
Tabulate the stiffness and damping constants vs. frequency.
The foundation is embedded in halfspace with Vs = 220 ft/s, γ = 100 lb/ft3, ν = .25, D = 10%
and is backfilled with weaker soil (side layer: depth = 2 ft, Vs = 180 ft/s, γ = 75 lb/ft3, ν =
.25, D = .1); weak zone ratios: Gin/Gout = .25, ν in = .25, Din = 20%, t/Ro = 0.2, M.P.F. = 0.25.
X
Y
Side Layer
10 ft
Z
VS = 180ft/s
C.G
Weak Zone:
γ = 75 lb/ft3
Gin/Gout = 0.25
ν = 0.25
t/Ro = 0.2
D = 0.1
2 ft
Half Space: VS = 220 ft/s
ν = 0.25
γ = 100 lb/ft3 D = 0.1
Point 1
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The Project Properties window should now be open. Select “Edit Settings” under the
Project Control heading to continue.
3. In the “Project Settings” window, select Imperial Units under the “Units” heading. Also,
under the “Frequency Units” heading, select Hertz. Finally, under “Output Flags” check off
Echo Input Data and Output Draft Plots and click OK to proceed.
4. Select “Edit Load” on the “Project Properties” window and the “Foundation Type
Choice” window should open up. Now, select Half-Space, Embedded under
“Embedment”, and Rectangle under “Footing Shape”. Click OK to proceed.
5. The “Half-Space Foundation” window should now be open. To continue select the
Footing button.
6. The “Footing Base Dimensions and Data” window should open up. Fill out the missing
data beneath the headings Footing Mass & Inertia, Dimensions of Base, Coord. Of Base
Center and Coord. Of CG. Click OK to return to the “Half-Space Foundation” menu.
7. On the “Half-Space Foundation” menu select Side Layers to continue to the “Data for
Cap/Footing Side layers” window. Check off Weak Zone below the “Side Layers
Properties” header and fill out the data in the chart accordingly. Click OK.
8. Back on the “Half-Space Foundation” menu click Below to proceed. Fill in the blank data
and click OK.
9. Back on the “Half-Space Foundation” menu, select Resultant to continue. A window
titled “Locations for Resultant Translations from Origin” should open up. Input the resultant
X,Y, and Z data and click OK to continue.
10. Back on the “Project Properties” menu select Edit Load to open up the “Loading Type
Choice” window. Select Harmonic and click OK to proceed.
11.Input the data under the Frequency and Amplitude of Forces/Moments headings and
check off out of phase below Applied Loads Phase.
12. The “Form Load Harmonic Phase Shift” window should open up. Input the Phase Shift
data in the allotted space and click OK.
13. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 6: 8-pile Foundation With Pile Interaction and Stiffness Printout
Analyze the response of a machine foundation resting on 8 concrete piles 12 m in length.
All other properties are shown in Figure 10. Interaction between piles is accounted for
(default option).
Evaluate the stiffness and damping constants of the pile group referred to C.G. of system at
frequencies of 10 rad/s and 100 rad/s. Print the pile group vertical stiffness matrix at pile
heads. Print the distribution of dynamic forces on individual piles.
The units to use are N, kg, m.
Given:
The Machine
Total mass = 9600 kg
Exciting forces are due to rotor unbalances (quadratic) and act in vertical as well as
2,
is given by mee = 4.0 kgm and moment
meer = 10 kgm2.
The height of the horizontal excitation = 3.66 which is also the height of the machine
centroid.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. The “Project Settings” window should open up. Under “Units”, check off SI Units. Under
“Output Flags” check off Echo Input Data and Output Draft Plots and click “OK” to
continue.
4. On the “Project Properties” window select Edit Load below the “Project Control”
heading. The “Foundation Type Choice” window will open up. Click Pile, check off
Rectangle blow the Footing shape header and click OK to continue.
5. The “Pile Foundation” menu should now be open. To continue, click the Pile Cap button.
6. . The “Footing Base Dimensions and Data” window should open up. Fill out the missing
data beneath the headings Footing Mass & Inertia, Dimensions of Base, Coord. Of Base
Center and Coord. Of CG. Click OK to return to the “Pile Foundation” menu.
7. In the “Pile Foundation” menu click Piles to proceed. The “Pile Head Arrangements for
Rigid Piles” window will now be open. Check End-Bearing Tip below the Pile Tip
Condition header. Also, input the properties for the steel.
8. Next select Mesh in the tabs to open the “Mesh Generation” window. Check off
Rectangular Mesh. Input all of the remaining missing data. Click Apply to move on.
Finally, click OK to return to the “Pile Foundation” menu.
9. Click Pile-Soil to proceed. The “Data for Pile-Soil System” window will open up. Fill
out the blank windows with the correct data. Click “Soil Elements” at the bottom of the
window to continue.
10. In the window, fill in the missing data and click OK to proceed.
11. Finally, on the “Pile Foundation” menu select Soil Below to open the “Properties of
Soil Below the Foundation” window. Fill out the blank data and click OK to continue.
12. The “Project Properties” window should open up. Select Edit Load beneath the “Project
Control” heading. The “Loading Type Choice” window should open up. Select Harmonic
and click OK to proceed.
13. The “Harmonic Load Data” window should open up. Check off Output Phase Angle.
Also fill in the Frequency data, the Amplitude of Forces/Moments data, and check off
out of phase below the Applied Loads Phase heading. Finally, click Phase Shift to
proceed.
14. The “Form Load Harmonic Phase Shift” window should open up. Fill in the Phase Shift
data and click OK to finish.
15. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 7: 8-pile Foundation With Pile Interaction and Stiffness Printout
Analyze the response of a machine foundation resting on 8 concrete piles 12 m in length.
All other properties are shown in Figure 10. Interaction between piles is accounted for
(default option).
Evaluate the stiffness and damping constants of the pile group referred to C.G. of system at
frequencies of 10 rad/s and 100 rad/s. Print the pile group vertical stiffness matrix at pile
heads. Print the distribution of dynamic forces on individual piles.
(b)
Calculate the response of this foundation to a quadratic harmonic load of amplitudes
4.0, 0., 4.0, 0., 10.0, 0. for frequencies ranging from 5 rad/s to 185 rad/s with a frequency
increment of 5 rad/s.
The units to use are N, kg, m.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. The “Project Settings” window will now be open. Under Units, check off SI Units. Also,
check off Echo Input Data, Stiffness/Damping Matrices, and Output Draft Plots under
the Output Flags heading. Click OK. Click Edit Foundation under the “Project Settings”
header.
4. The “Foundation Type Choice” window will open. Click Pile and Rectangle below the
heading Footing Shape. Click OK.
5. The “Pile Foundation” window will open. First, click Pile Cap to proceed.
6. . The “Footing Base Dimensions and Data” window should open up. Fill out the missing
data beneath the headings Footing Mass & Inertia, Dimensions of Base, Coord. Of Base
Center and Coord. Of CG. Click OK to return to the “Pile Foundation” menu.
7. Back on the “Pile Foundation” window, select Piles to proceed. The “Pile Head
Arrangements for Rigid Piles” window will open up. Fill in the blank data and check off
End-Bearing Tip. Click Mesh to continue.
8. The “Mesh Generation” window will open up. Check off Rectangular Mesh and Xdirection below the header “Generation Direction”. Fill in the blank data spots and click
APPLY to proceed. Return to the “Pile Foundation” menu.
9. From the “Pile Foundation” menu, select Pile-Soil to open the “Data for Pile-Soil
System” window. Fill in the blank spaces on the “Pile Elements” data set and click “Soil
Elements”.
10. Fill in the “Soil Elements” data set and click OK to return to the “Pile Foundation”
window.
11. The “Properties of Soil Below the Foundation” window will open. Fill in all of the
missing blanks. Click OK to return to the “Pile Foundation” window. Click Output to
continue.
12. The “Output Options for Pile Foundation” window will open up. Check off Unit
Displacements, Actual Loads, Print in Output File and Print Distribution. Check off
OK to proceed.
13. The “Loading Type Choice” window will open. Select Harmonic and click OK to
proceed.
14. The “Harmonic Load Data” window will open up. Check off out of phase below the
Applied Loads Phase header and fill in the missing data beneath the Frequency and
Amplitude of Forces/Moments headers. Click Phase Shift to continue.
15. The “Form Load Harmonic Phase Shift” window should open up. Fill in the Phase Shift
data in the empty blanks and click OK to proceed.
16. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 8: Random Load Applied to Rigid Body on Half-Space (Surface
Footing)
Using the random vibration approach, calculate the expected peak response of the rigid silo
shown in Figure 8.1 to horizontal earthquake excitation given the spectrum m2 S Åg 1 (Figure
8.5) applied in x-direction. The silo rests on half-space. (A smoothed spectrum is
preferable.)
The units used are kN, Mg = 1000 kg, m.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. The “Project Settings” window should be open. Check off Other beneath the “Units”
header. Check off Other beneath the “Mass Units” and “Force Units” headers and fill in the
blanks. Also, check off Meter below the “Length Units” header. Finally, check of Echo
Input Data and Output Draft Plots below the “Output Flags” headers. Click OK.
4. On the “Project Properties” window click Edit Foundation to open up the “Foundation
Type Choice” window. Ensure that Surface, Circle and Rigid are checked off. Also click
Half Space and OK to continue to the “Half-Space Foundation” window.
5. Click Footing to proceed.
6. The “Footing Base Dimensions and Data” window will open up. Fill in the missing data
and click OK to return to the “Half-Space Foundation” window.
7. Click Below to open the “Properties of Soil Below the Foundation” window. Fill in the
blank data and click OK till you reach the “Project Properties Menu”. Click Edit Load
below the “Project Control” header.
8. The “Loading Type Choice” window will open up. Click Random and OK to proceed.
9. The “Form Load Random” window will open. Fill in all of the blank data including the
chart with the “Frequencies” and corresponding “Values”. Click OK to return to the
“Project Properties” menu.
10. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 9 : Random Load Applied to Rigid Body on Stratum
Using the random vibration approach, calculate the expected peak response of the silo
shown in Figure 8.1 to the horizontal earthquake excitation given by Figure 8.5; in this case
the silo is supported by a stratum of limited depth of 20 m (Figure 8.6). (For shallow strata
nonzero damping should be used.)
The units used are kN, Mg = 1000 kg, m.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. The “Project Settings” window will open up. Check off Other beneath the “Units”,
“Force Units” and “Mass Units” headers. Fill in the empty blanks. Check off Echo Input
Data beneath the “Output Flags” header. Click OK to return to the “Project Properties”
window.
4. Under the “Project Control” header, click Edit Foundation. The “Foundation Type
Choice” window will open up. Click Stratum and check off Surface, Circle, and Rigid.
Click OK.
5. The “Stratum Foundation” window will open. Click Footing to proceed.
6. The “Footing Base Dimensions and Data” window will open. Fill in the blank data spots
and click OK to return to the “Stratum Foundation” window.
7. Click Stratum to open the “Form Footing Stratum Data” window. Fill in the blanks with
the appropriate data and click OK to return to the “Project Properties” window.
8. Under the “Project Control” header click Edit Load to open the “Loading Type Choice”
window. Click Random and OK to continue.
9. The “Form Load Random” window will open up. Input the missing data and fill out the
Frequencies and Values in the empty table. Click OK to return to the “Project Properties”
window.
10. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 10: One Pile Foundation With Parabolic Soil Shear Modulus
Distribution and Harmonic Load
(a)
Evaluate the stiffness and damping constants of a circular foundation (R-5 ft) on one
pile (length = 30 ft). The pile is embedded in parabolic soil medium whose properties are
shown in Figure 8.7.
(b)
Calculate the response of the foundation to quadratic excitation with amplitudes
1,1,1,1,1,1 in all six degrees of freedom for two frequencies, 99 and 100 rad/s.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. Check off Imperial Units under the “Units” header. Also check off Echo Input Data
and Stiffness/Damping Matrices under the “Output Flags” header. Click OK to return to
the “Project Properties” window.
4. Under the “Project Control” header click Edit Foundation to proceed to the “Foundation
Type Choice” window. Click Pile and check off Surface, Circle, and Rigid. Click OK.
5. The “Pile Foundation” window will open up. First click Pile Cap to continue.
6. The “Footing Base Dimensions and Data” window will open up. Fill in the blanks and
click OK to return to the “Pile Foundation” window. Click Piles to continue.
7. The “Pile Head Arrangements for Rigid Piles” window will open up. Fill in the blank
spaces and then click Individual to proceed.
8. The “Coordinates for Individual Piles” window will open up. Fill in the X-Coord and
and Y-Coord data and click OK to continue.
9. The “Data for Pile Soil System” window will open up. Check off Parabolic and Weak
Zone below the “Soil Medium Type” and Other below “Calculating Pile Geometrical
Data”. Fill in the data and click Soil Elements at the bottom of the window.
10. Fill in the missing data for the Soil Elements and click OK to return to the “Pile
Foundation” window.
11. Fill in the missing data. Click OK to return to the “Project Properties” window. Click
Soil Below to open up the “Properties of Soil Below the Foundation” window. Fill in the
data and click OK to return to the “Project Properties” window.
12. Below the “Project Control” header on the “Project Properties” window, click Edit
Load. The “Loading Type Choice” window should open up. Click Harmonic and OK to
continue.
13. The “Harmonic Load Data” window will open up. Fill in the data below all of the
headers. Click OK to return to the “Project Properties” window.
14. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 11: Transient Load Applied to Silo Supported by Embedded Rigid
Body
Calculate the transient response of a silo supported by a deep reinforced concrete block
(RIGID-BODY option) (Figure 8.8). The load acts in the x-direction and its amplitudes are
shown in Figure 8.9. All properties of soil and dimensions are shown in Figure 8.8.
The units are kN, kg x 103, m.
(The RIGID-BODY option is not recommended for embedment less than 5 radii. This
example is given to illustrate input and output of option.)
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. The “Project Settings” window will open up. Check off Other under the “Units”, “Force
Units”, and “Mass Units” headers and fill in the empty blanks with the correct units. Ensure
that Meter is checked off beneath “Length Units”. Below “Output Flags”, check off Echo
Input Data, Stiffness/Damping Matrices, and Output Draft Plots. Click OK
4. In the “Project Properties” window, click Edit Foundation below the “Project Control”
header to open the “Foundation Type Choice” window. Select Rigid foundation type and
ensure Surface and Circle are checked off. Click OK.
5. The “Rigid Body Foundation” window will open up. Click Structure to proceed.
6. The “Structure and Foundation Data” window will open up. Input the appropriate data in
the spaces and click OK to return to the “Rigid Body Foundation” window. Next, click
Rigid Body.
7. The “Rigid Body Foundation Data” window should open up. Input the rigid-body data
and check off Floating below the “End Conditions” header. Click OK to return to the “Rigid
Body Foundation” menu. Click Elements.
8. The “Rigid Body Foundation/Soil Elements Data” window should open up. Check off
Weak Zone below the “Side Layers Properties” header. Fill in the table and click Elements
for Side Soil Layers to proceed.
9. The “Elements for Side Soil Layers” section should be open. Fill in the table with the
appropriate data. Click Elements for Soil Layers Below.
10. The “Elements for Soil Layers Below” section should be open. Enter the data into table
and click OK to return to the “Rigid Body Foundation” menu. Now, click Below.
11. The “Properties of Soil Below the Foundation” window will open up. Fill in the empty
boxes and click OK to return to the “Project Properties” menu.
12. Click Edit Load below the “Project Control” header. The “Loading Type Choice”
window will open up. Click Transient and click OK to proceed.
13. The “Transient Load Data” window will open up. Input the number of Data Points and
time interval. Check off Graph beneath the headers labeled “Output of FFT for Load” and
“Output of FFT for Response”. Finally, click Time History beneath the “Amplitude of
Forces” header.
14. The “Time History” window will open up. Input the Values for each Time. Click OK
to return to the “Project Properties” menu.
15. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 12: Composite-Medium With Uniform Layer and Harmonic Load
(Dimensionless Amplitudes)
Calculate the dimensionless response (see section 7.1) of a square foundation (13 ft x 13 ft)
to quadratic harmonic load of amplitudes (.0055, .0055, .0055, .04, .04, .04) whose
frequency ranges from 1 rad/s to 101 rad/s. The foundation rests on a 26 ft thick soil layer
3
, Vs
3
, Vs
(The contents of output file DYNAPLT are used to produce the response curves sown in
Figure 8.10).
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. The “Project Settings” window should open up. Check off Imperial Units beneath the
“Units” header. Also, check off Echo Input Data and Output Draft Plots. Click OK to
return to the “Project Properties” menu.
4. Click Edit Foundation and the “Foundation Type Choice” window will open up. Click
Composite and check off Rectangle below the “Footing Shape” header. Click OK.
5. The “Composite-Medium Foundation” window will open up. Click Footing to proceed.
6. The “Footing Base Dimensions and Data” window will open up. Input the Footing data,
Dimensions, and Coordinate data. Click OK to return to the “Composite-Medium
Foundation menu.
7. Click Below to open the “Properties of Soil Layer Below Foundation”. Input the Layer
data and click OK to return to the “Project Properties” menu.
8. Click Edit Load below the “Project Control” header to open the “Loading Type Choice”
window. Click Harmonic in the “Loading Type Choice” window and click OK.
9. The “Harmonic Load Data” window will open. Fill the blank boxes and check off out of
phase below the “Applied Loads Phase” header. Click Phase Shift.
10. The “Form Load Harmonic Phase Shift” window will open. Fill the boxes in with the
given data. Click OK to return to the “Project Properties” window.
11. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 13: Embedded Pile Foundation With Battered Piles and Harmonic
Load
Calculate the response of an embedded machine foundation supported by 8 battered
concrete piles. The piles are battered in the XZ plane at an angle of 10o to the vertical. The
properties of the foundation and the piles are the same as those of Example 7. The shear
wave velocity of the backfill soil is shown in Figure 8.11. Foundation-soil separation is
assumed for the top 0.84 m of embedment. The response to quadratic harmonic load of
amplitudes 4.0, 0., 4.0, 0., 10.0, 0. is to be calculated for frequencies ranging from 5 rad/s
to 185 rad/s with a frequency increment of 5 rad/s.
The units to use are N, kg, m.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. The “Project Settings” window will open up. Check off SI Units below the “Units”
window. Also, check off Echo Input Data and Output Draft Plots below the “Output
Flags” header. Click OK to return to the “Project Properties” window.
4. In the “Project Properties” window click Edit Foundation below the “Project Control”
header. The “Foundation Type Choice” window will open up. Click Pile and check off
Embedded, Rectangle and Rigid. Click OK.
5. The “Pile Foundation” window will open up. Click Pile Cap to proceed.
6. The “Footing Base Dimensions and Data” window will open up. Input the Footing,
Dimensions, and Coordinates data. Click OK to return to the “Pile Foundation” menu.
Click Side Layers.
7. The “Data for Cap/Footing Side Layers” window will open up. Fill in the data missing in
the table and click OK to return to the “Pile Foundation” window. Click Piles.
8. The “Pile Head Arrangements for Rigid Piles” window will open up. Check off EndBearing Tip below the “Pile Tip Condition” header. Input the Pile Properties and Pile
Material Properties. Click Mesh and the “Mesh Generation” window will open up. Check
off Rectangular Mesh and X-direction below “Generation Direction”. Input all of the
missing data and click Apply. Then click Batter.
9. The “Data for Battered Piles” window will open up. Input the Alpha and Phi values and
click OK twice to return to the “Pile Foundations” menu. Click Pile-Soil to proceed.
10. The “Data for Pile-Soil system” window will open up. Check off Circular Solid below
the “Calculating Pile Geometrical Data” header. Input the data in the table and click Soil
Elements at the bottom of the window.
11. The “Soil Elements” table will open up. Fill in the table and click OK to return to the
“Pile Foundation” window. Click “Soil Below” to continue.
12. The “Properties of Soil Below the Foundation” window will open up. Input the Shear
Wave Velocity, Unit Weight, Poisson’s Ratio, and Material Damping. Click OK to
return to the “Project Properties” window.
13. Click Edit Load below the “Project Control” header. The “Loading Type Choice”
window will open up. Click Harmonic and OK to proceed.
14. The “Harmonic Load Data” window will open up. Input the Frequency and Amplitude
of Forces/Moments data. Check off out of phase below the “Applied Loads Phase” header.
Click Phase Shift to proceed.
15. The “Form Load Harmonic Phase Shift” window will open up. Fill in the empty boxes
and click OK to return to the “Project Properties” window.
16. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 14: Flexible Mat Foundation (MATF) Under Vertical Harmonic Load
and a Couple
Calculate the vertical response amplitudes and phase shifts of a square flexible mat on an
elastic halfspace.
The mat is 3.0 x 3.0 m in plan, 0.25 m in thickness and has E = 2.06 x 107 kN/m2
kg/m3
3
, Vs
s
=
0.3. The excitation comprises a vertical harmonic force with an amplitude equal to 900. KN
acting at the mat centre and a couple with an amplitude of 6.0 kNm acting in a vertical
plane passing through the mat centre and parallel to the plate side. The mass of the pedestal
and the machine resting on it are represented by three lumped masses, m1, m2 and m3, shown
in the Figure.
The Procedure:
a)
The plate is subdivided in 36 elements featuring 49 nodes, to be numbered as shown.
(Other element outline can be chosen.)
b)
The vertical couple is replaced by two equal but opposite vertical loads, placed 1.0
m apart at nodes 24 and 26,
P = couple/distance = 6.0/1.0 = 6.0 KN.
c)
The mass of the mat is accounted for in the program while the keyword MASS in
the input enters the additional lumped masses only. (If there are no additional lumped
masses the input data should read MASS=0.)
d)
The keyword DYNFLEX places the soil stiffness matrix referring to the nodes, 49
x 49 in this example, into a file of the same name for further use. This file is not a part of
the output file but it can be printed and is shown here for illustration. (For a large number
of nodes, this file can be very large and impractical to print.)
If the printout of the stiffness matrix of the soil is desired it can be printed within the output
file using the command FLEXIBLE. (This is demonstrated in the Example on p. 8.63.)
8.128
The elements of the soil stiffness matrix are, as in other cases,
K(I,J) = K1 + iK2
where K1 = real stiffness, and K2 = imaginary part of the stiffness yielding the equivalent
viscous damping constant
c(I,J) = K2
NOTES:
a)
In this example, both the mat and the finite elements used are square. Rectangular
mats with any aspect ratio (length to width ratio) can be analyzed by DYNA3, however.
The program would operate for any aspect ratio for the finite elements but it is recommended
that this ratio be kept between 1.0 and 2.0 (0.5 and 1.0) for better accuracy.
b)
The MATF option may require a long computing time, especially when it is run for
many elements and frequencies on a PC. Example 14 takes 25 to 60 minutes on a PC
depending on the system. Therefore, if the user wishes to run this example just for a check,
the number of frequencies may be reduced.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. The “Project Settings” window will open up. Click SI Units below the “Units” header.
Check off Echo Input Data and Output Draft Plots below the Output Flags. Click OK to
return to the “Project Properties” menu. Click Edit Foundation below the “Project Control”
window.
4. The “Foundation Type Choice” window will open up. Click Mat and click OK.
5. The “Mat Foundation” window will open up. Click Data to proceed.
6. The “Flexible Mat Data” window will open up. Input the Mat Properties, Response, and
Number of Nodes data. Check off DYNAFLEX. Click OK to return to the “Mat
Foundation” window. Click Masses.
7. The “Flexible Cap Lumped Masses” window will open up. Input the Node and Mass
data. Click OK to return to the “Mat Foundation” menu. Click Soil.
8. The “Properties of Soil Below the Foundation” window will open up. Input the Shear
Wave Velocity, Unit Weight and Poisson’s Ratio. Click OK to return to the “Project
Properties” window. Click Edit Load below the “Project Control” header.
9. The “Loading Type Choice” window will open up. Click Harmonic and click OK to
proceed.
10. The “Mat Harmonic Load Data” window will open up. On the drop down menu, select
Non Quadratic. Input the Frequency data and check off the Output Displacement Phase
Shift option. Finally, click Loads.
11. The “Vertical Harmonic Loads” window will open up. Input the Node and Load data
and click OK to return to the “Project Properties” window.
12. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
Example 15: Piles Battered in a General Plane with Printing of Group
Stiffness Matrix in Vertical and Lateral Directions
Analyze the stiffness and damping properties of a group of 6 steel piles used to support an
offshore structure. The piles are battered in a general plane (i.e. not contained in a plane
parallel to one of the two major planes, XZ and YZ). The required input properties are given
below and in Figure 24. Consider complete pile-soil separation for the top 0.5 m.
Print the vertical and coupled horizontal (lateral) group stiffness matrices referred to the pile
heads whose level is defined at 1.0 m above the mud line. The frequencies to consider are
0.2 Hertz and 1.0 Hertz. The units to use are kN, Mg = 1000 kg, m.
Pile properties: Density = 77 kN/m3; Pile length (includes 1 m free length) = 31.0 m
Outside radius = 0.5 m, Inside radius = 0.46 m (A = 0.12 m2, I = 0.0139 m4)
Young’s modulus Ep = 2x108 kN/m2; Static load on pile = 4000 kN
Soil properties: Poisson’s ratio = 0.45; Damping, D=0.05. For soil below tips, Va = 300 m/s
and γ= 21 kN/m3. Other properties are given in the table below.
1. First, open the program DYNA and click on the icon labeled “New”. A window will pop
up prompting you to enter the name of the project and specific case. Click “Okay” to
continue.
2. The “Project Properties” window should open up. Click Edit Settings under “Project
Control” to proceed.
3. The “Project Settings” window will open up. Check off Other beneath the “Units”,
“Force Units”, and “Mass Units” headers. Fill in the appropriate boxes with the type of unit.
Check off Hertz below the “Frequency Unit” header. Also, check off Echo Input Data
below the “Output Flags” window and click OK to return to the “Project Properties”
window.
4. Click Edit Foundation below the “Project Control” header. The “Foundation Type
Choice” window will open up. Click Pile. Check off Rectangle below the “Footing Shape”
header. Click OK to proceed.
5. The “Pile Foundation” window will open up. Click Pile Cap to continue.
6. The “Footing Base Dimensions and Data window will open up. Input the Footing,
Dimensions, and Coordinates. Click OK to return to the “Pile Foundation” window. Click
Piles.
7. The “Pile Head Arrangements for Rigid Piles’ window will open up. Fill in the Pile and
Material Properties. Click Individual.
8. The “Coordinates for Individual Piles” window will open up. Input the X-Coord and YCoord data and click OK. Click Batter.
9. The “Data for Battered Piles” window will open up. Input the Alpha and Phi values for
the piles and click OK twice to return to the “Pile Foundation” window. Click Pile-Soil.
10. The “Data for Pile-Soil System” window will open up. Check off Other under
“Calculating Pile Geometrical Data” and Weak Zone under “Soil Medium Type”. Fill in
the Pile Elements data in the table. Click Soil Elements.
11. The “Soil Elements” section should now be open. Input the required data to complete
the table. Click OK to return to the “Pile Foundation” window and click Soil Below.
12. The “Properties of Soil Below the Foundation” window is now open. Input the required
data. Click OK to return to the “Pile Foundation” window. Click Output.
13. The “Output Options for Pile Foundation” window should be open. Check off Print in
Output file below both the “Piles Vertical Stiffness” header and “Piles Lateral Stiffness”.
Click OK to return to the “Project Properties” window.
14. Click Edit Load below the “Project Control” header. The “Loading Type Choice”
window should open up. Click Harmonic and click OK to proceed.
15. The “Harmonic Load Data” window should open up. In the drop down menu, select
Non-Quadratic. Input the data for Frequency, Amplitude of Forces/Moments, and make
sure in phase is checked off below the “Applied Loads Phase” header. Click OK to return
to the “Project Properties” window.
16. Finally, click “RUN PROJECT” to run the analysis. Click the “Enter” button several
times to advance the windows. The Output File should open up, but if it does not, select
“Output File” from beneath the Project Control heading.
11.0 REFERENCES
1. Veletsos, A.S. and Wei, Y.T. (1971) - “Lateral and Rocking Vibration of
Footings,” J. Soil Mech. And Found. Div., ASCE, SM9, September, pp. 1227- 1248.
2. Veletsos, A.S. and Verbic, B. (1973) - “Vibration of Viscoelastic Foundation,” J.
Earthquake Engrg. And Struct. Dyn., Vol. 2, pp. 87-102.
3. Veletsos, A.S. and Nair, V. V. D.(1974) - “Torsional of Vibration of Viscoelastic
Foundaation,” J. Geotech. Div., ASCE, Vol. 100, No. GT3, March, pp. 225-246.
4. Novak, M. And Beredugo, Y.O. (1972) - “Vertical Vibration of Embedded
Footings, ‘ J. Soil Mechanics and Foundation Division, ASCE , SM12, December,
pp.1291-1310.
5.Beredugo,Y.O. and Novak, M. (1972) - “coupled Horizontal and Rocking
Vibration of Embedded Footings,” Canadian Geotechnical Journal, Vol. 9, No. 4,
pp. 477-97.
6. Novak, M. And Sachs, K. (1973) - “Torsional and Coupled Vibrations of
Embedded Footings,” Inter. J. Earthquake Engrg. And Struct. Dyn., Vol.2 No.11,
p.33.
7. Novak, M. (1974) - “Effect of Soil on Structural Response to Wind and
Earthquake,” Inter. J. Earthquake Engineering and Struct. Dyn., Vol. 3, No.1, pp.
79-96.
8. Novak, M. And Sheata, M. (1980) - “Approximate Approach to Contact Problems
of Piles,” Proc. Geotech. Engrg. Div. ASCE National Convention “Dynamic
Response of Pile Foundations: Analytical Aspects,” Florida, October, pp. 53-79.
9.
Kausel, E. And Ushijima, R. (1979) - “Vertical and Torsional Stiffness of
cylindrical
Footing,”
Civil
Eng.
Dept.
Report
R79-6,
MIT,
Cambridge,
Massachusetts.
10 Novak, M and Aboul-Ella, F. (1978a) - “Impedance Functions of Piles in
Layered Media,” Journal of the Engineering Mechanics Division, ASCE, Vol. 104,
No EM6, Proc. Paper 13847, June, pp. 643-661.
11. Novak, M. And Aboul-Ella, F. (1978b) - “Stiffness and Damping of Piles in
Layered Media,” Proc. Earthq. Engrg. And Soil Dyn., ASCE Specialty Conf.,
Pasadena, California, June 19-21, pp. 704-719.
12. Poulos, H.G. (1971) - “Behaviour of Laterally Loaded Piles. II - Pile Groups,” J.
Soil Mech. Foundations Div., ASCE, 97 (SM5), pp. 733-751.
13. Poulos, H.G. (1974) - Technical Note, J. Geotech . Engrg. Div., ASCE, Vol
100, No GT2, Feb., pp. 185-190.
14. Poulos, H.G. (1979) - Group Factors for Pile-Deflection Estimation,” J.Geotech.
Engrg. Div., ASCE, GT12, pp. 1489-1509.
15. Poulos, H.G. and Davies, E.H. (1980) = “Pile Foundations Analysis and
Design,” John Wiley and Sons, p. 397.
16. Wong, H.L. and lUco, J.E. (1985), “Tables of Impedance Functions for Square
Foundations on Layered Media,” International Journal of Soil Dynamics and
Earthquake Engineering, Vol. 4, No. 2, pp. 64-81.
17. Sheta, M. And Novak, M (1982) - Vertical Vibration of Pile Groups,” Journal of
the Geotechnical Engineering Div., ASCE, Vol. 108, No GT$, April, pp. 570-590.
18. Kim, T.C. and Novak, M. (1981) - Dynamic Properties of Some Cohesive Soils
in Ontario,” Canadian Geotechnical Journal, 18, pp. 371-389.
19. Clough, R.W. and Penzien, J. (1975) - “Dynamic of Structures,” McGraw-Hill
Book co. Inc., New York, 634 p.
20. Brigham, E.O (1974) - The Fast Fourier Transform,” Prentice-Hall Inc., 252 p.
21 Novak, M. And El-Hifnawy, L. (1983) - “Vibration of Hammer Foundations,:”
International Journal of Soil Dynamics and Earthquake Engineering, Vol. 2, No. 1,
pp. 43-53.
22. El-Hifnawy, L. And Novak, M. (1984( - :Response of Hammer Foundations to
Pulse Loading, “ International Journal of Soil Dynamics and Earthquake
Engineering, Vol. 3, No. 3, pp. 124-132.
23. Novak, M (1983) - Foundations for Shock-Producing Machines,” Canadian
Geotechnical Journal, Vol. 20, No.1. pp. 141-158.
24. El Naggar, M.H. and Novak, M., 1996. Nonlinear analysis for dynamic lateral
pile response. J. of Soil Dynamics and Earthquake Engineering, Vol. 15, No. 4,
pp. 233-244.
25 Randolph, M.F. and Poulos, H.G. (1982). “Estimating the Flexibility of Offshore
Pile Groups,” Numerical Methods in Offshore Piling Proceedings of the 2nd
International Conference, University of Texas, Austin, TX.
26. El Sharnouby, H. and Novak M. (1986). “Flexibility coefficients and Interaction
Factors for Pile Group Analysis,” Canadian Geotechnical Journal, Vol. 23, No. 4,
pp. 441-450.
27. Kaynia, A.M. and Kausel, E. (1982). “Dynamic Behaviour of Pile Groups,”
Conference on Numerical Methods in Offshore Piling. Univ. of Texas, Austin, TX,
pp. 509-532.
28. Novak, M. And Han, Y. (1990). “Impedance of Soil Layer With Boundary Zone,”
Journal of Geotechnical Engineering, Vol. 116, No. 6, June, pp. 1008-1014.
29. Whittaker, W.L. and Christiano, P. “Dynamic Response of Flexible Plates
Bearing on An Elastic Half-Space,” RP-125-9-79, Dept. Of Civil Eng., CarnegieMellon University.
30. El Sharnouby, B. and Novak, M. (1985). “Static and Low Frequency Response
of Pile Groups,” Canadian Geotechnical Journal, vol. 22, No. 1, pp. 79-94.
31. Swane, I.C. and Poulos, H.G. (1984). “Shakedown Analysis of Laterally
Loaded Pile Tested in Stiff Clay,” Proc. 4th Australian-New Zealand Conf. On
Gemech., Perth, Vol. I, pp. 165-169.
32 Novak, M. (1985) “Experiments With Shallow and Deep Foundations,” Proc. Of
ASCE Symposium on Vibration Problems in Geotechnical Engineering, Detroit,
Mich., pp. 1-26.
33. Crouse, C.B., Price, T. And Mitchell, R., (1992). Evalutaion of Methods to
Estimate Pile Foundations Stiffnesses for Bridges,” Proc. 8th U.S.-Japan Bridge
Engineering Workshop, Chicago, Illinois, pp.14.
34. Han, Y and Vaziri, H. (1992). “Dynamic response of Pile Groups under Lateral
Loading,” Journal of Soil Dynamics and Earthquake Engineering 11, pp. 87-99.
35 El-Marsafawi, Han, Y. And Novak, M., (1992). “Dynamic Experiments on Two
Pile Groups,” Journal of Geotechnical Engineering, Vol. 118, No. 4, pp. 576-592.