PipeSOIL
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utoPIPE Reference Information
PipeSOIL
The following topics are available:
Model Discretization
Defining Soil Points in AutoPIPE
Soil Restraint Properties in AutoPIPE
Calculation of Soil Restraint Properties
Longitudinal Soil Properties
Vertical Soil Properties
Buried Pipeline Modeling Example
utoPIPE Reference Information
Model Discretization
The analysis of a buried piping system requires special modeling consideration. This is because the (support)
restraint provided by soil surrounding a buried pipe is continuous. Since an AutoPIPE analysis is based on
discretely defined points, an accurate model of the soil's restraint capabilities would require the definition of a
large number of closely spaced piping points. Each soil point would then require a set of support springs
which model the stiffness(es) provided by the soil at that point. The effort required to construct such a model
is logistically impractical. Therefore, a rational method is needed in order to determine the number and
distribution of soil points required to perform an analysis which produces reasonably accurate results.
When bends (i.e. elbows, miters, & field bends) or tees (including any other multi-pipe connections) are
present in a buried piping system, significant bending moments and axial forces can be generated in the
region of these geometric features under thermal, pressure, or seismic load applications. At some distance
away from the bend (or tee) the bending moment will become very small leaving the pipeline subjected to
axial force only. In order to obtain a cost/time effective yet accurate stress analysis, the spacing between soil
points near the bend should be small in order to simulate the pipe bending and transverse soil bearing
interaction. However, further away from the bend, the only effect to be modeled is the transfer of soil friction
to axial load in the pipe. The axial effect can be adequately modeled using longer spacings between soil
points.
Guidelines for choosing soil point spacings in an arbitrary buried pipeline have been developed from
considerations of the behavior of a flexible beam on an elastic foundation and pipe anchorage effects. Figure
D-1(A) shows a flexible beam on an continuous elastic foundation subject to a point load R. The distribution
of displacement (and bearing reaction), shown in Figure D-1(B), is given by
(D-1)
where
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(D-2)
For a buried pipe with a bend (or tee), the lateral bearing behavior of the soil will be similar to that for the
case of a flexible beam on a continuous elastic foundation. Figure D-1(C) shows a plan view of this situation,
where an axial force in one leg produces a lateral moment in the other leg.
Figure D-1: Comparison of a buried pipeline with a bend to an infinite beam on a continuous elastic
foundation.
The shape of the resulting displacement curve is as shown in Figure D-1(B), note that displacement decreases
with increasing distance from the bend. Thus, three basic zones of pipe-soil interaction can be identified.
Zone 1, nearest the bend, is the area of high bending effects which produce the major lateral displacement of
the pipe. Zone 2 is a transition region where bending effects have reduced to small levels, and as the distance
from the bend increases they go to zero, leaving only axial effects. Zone 3 is the region where the pipe and
soil displace identically (the pipe is effectively, or virtually anchored in the soil).
The length of Zone 1 (Lb) is identified as the point where the lateral displacement first becomes zero (closest
to the bend). This length is known as the bearing span, and is given by:
(D-3)
The length of Zone 1 plus Zone 2 is identified as the point where the axial frictional resistance provided by
the soil decreases to zero (no pipe displacement relative to the soil). This distance is known as the virtual
anchor length (La). The virtual anchor length cannot be quantified directly since its value depends on the type
of soil force-displacement response. However, it can be estimated fairly well based on another term known as
the maximum slippage length (Lm).
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Figure D-2
Consider a buried pipe, shown in Figure D-2, where the soil force vs. displacement response is rigid-plastic.
When the pipe is subjected to a thermal load (causing elongation), the longitudinal yield strength of the soil
(P1) is generated in order to restrain the pipe growth. The maximum slippage length can be determined by
equating the length of pipe over which the yield strength of the soil must act in order to resist the thermal pipe
load. Thus, in order to achieve a balance of force
(D-4)
hence,
(D-5)
where:
Lm
H
A
E
P1
=
=
=
=
=
Maximum slippage length (L).
Thermal pipe strain (dimensionless).
Cross sectional area of the buried pipe (L ).
Modulus of elasticity of the buried pipe (F/L ).
Longitudinal yield strength of the soil (F/L). Refer to
the Longitudal Soil Properties help topic for
determining values of this variable.
Equation D-5 is valid regardless of the source of strain since the pipe-soil slip is relative. Thus, H represents
the total relative strain, which can be due to thermal pipe loads, or a seismic wave (or a combination of
both).As noted, the basis for Equation D-5 is a rigid-plastic response. However, a correlation to the virtual
anchor length can be made by evaluating a typical soil force vs. distance plot, as shown in Figure D-3. Note
that if the soil response is rigid-plastic, the length of the elastic strain region shrinks to zero. Thus, Lm will
equal the length of the plastic strain region, and its also equal to La.
Figure D-3
Figure D-3 shows a typical elastic-plastic distribution of longitudinal soil restraint force as a function of the
distance from a bend (or tee). The hatched area represents the total soil restraint force, as calculated by
Equation D-5, and equals the actual soil restraint force represented by the area under the curve. The position
of the maximum slippage length (Lm) relative to the plastic strain region depends on the shape of the soil
force vs. displacement response curve. However, the calculated value of Lm will always be less than the
virtual anchor length (La) for elastic-plastic, and elastic response curves. Therefore, the following formula
(based on past studies) should be used to estimate La regardless of the type of soil force-displacement
response.
(D-6)
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where
co = Dimensionless constant which lies in the range from 1.0 ("stiff" soils) to about 2 (soft soils).
The magnitude of co can be greater than 2.0 if the longitudinal yield strength (P1 ) is not achieved by the
soil.Comparison of analysis results for similar system models with various virtual anchor lengths indicate that
estimated values of co should be limited to the following range (unless a larger value can be justified):
1.5 d co d 2.0
The system model can be terminated and anchored at a distance away from a bend (or tee) equal to the virtual
anchor length (La) without any loss of accuracy to the analyzed results. Depending on the overall
configuration of the piping system and the type of analysis to be performed, the inclusion of Zone 3 in the
system model may or may not be necessary or desirable. This decision is left to the judgement of the
Engineer/modeler.
Table D-1 can serve as a guide for determining the number of soil points, and buried piping elements required
in each of the three zones. It is emphasized that these are guidelines only and may not be appropriate for all
situations.
utoPIPE Reference Information
Defining Soil Points in AutoPIPE
The process of defining a buried piping system is a combination of user defined piping points, and internally
generated (by AutoPIPE) soil points. The user only needs to define piping points for identifying the following
critical parts of a buried piping system:
1.
As required by changes in the system geometry.
2.
For specification of piping components (e.g. valves, reducers, flanges, anchors, etc.).
3.
Where soil properties change.
4.
Where the maximum spacing (between the internally generated soil points) defined for the current soil identifier is to be changed.
The first and second items in this list are straight forward. Thus, the following discussion concentrates on the
piping points required for defining the critical points related to the soil. Different soil types are often
encountered along the length of a buried piping system. A piping point must be defined at the intersection of
the pipeline and the plane which divides dissimilar soils. This allows a set of soil properties to be linked with
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a specific range of piping (between the specified piping points). Where a new soil type is encountered, a soil
identifier and its set of properties must be defined and applied from that point on in the system. In addition, if
a buried pipe has a vertical orientation new soil properties must also be defined. This is because the
orientation of transverse horizontal, up, and down are relative to the local coordinate system for a straight
pipe element (refer to Soil Restraint Properties). However, if only the maximum spacing is to be changed a
new soil identifier is not required. Simply modify the spacing value to be associated with the marked portion
of the buried pipeline (within the region defined for that soil identifier).
A piping point must also be defined at each location where the maximum spacing of a soil is to be changed.
First, the lengths Lb and Lm must be calculated by hand for each buried bend (or tee). Then, the locations of
the required piping points can be identified by applying rational guidelines for the spacing of soil points in the
three zones. Since AutoPIPE does not have the ability to specify a linearization of spacings in the transition
zone (Zone 2), guidelines are required in addition to those provided in Section D.1. The Figure below shows
one approach for modeling spacings in the three zones.
Figure D-4
Note that only point A02 is required by the geometry of the system. Points A01 and A03 are defined at a
distance of Lb from the bend in order to mark the bearing span region in each direction. Point A06 is defined
and rigidly anchored at a distance of La (= 1.5˜Lm) since pipe-soil interaction beyond this point (Zone 3) is
minimal. Points A04 and A05 are each placed at distances away from the bend so that soil point spacings can
be specified by marking the applicable range of piping points. The dimensions at the bottom of Figure D-4
(above) represent the maximum spacing (expressed as multiples of the pipe diameter) to be specified between
each set of piping points.
The maximum spacing defined on the ‘Soil’ dialog is used by AutoPIPE as an increment for determining the
number of soil points that will be generated between any two adjacent piping points, regardless of what spans
those points (e.g. a run, bend, valve, etc.). Where the distance between adjacent piping points does not equal a
whole number of max. spacings, AutoPIPE calculates a smaller spacing value based on the total number of
spacings it finds between the piping points.
Figure D-5, below, shows a run of buried pipe where the distance from A05 to A06 is L. If "L" is not wholly
divisible by the specified maximum spacing (S), the last spacing interval length will be less than "S" (it will
be the length c˜S, where "c" is a constant in the range 0 < c < 1).
Figure D-5
AutoPIPE compares the length of the last spacing interval (number 6 in Figure D-5) with the specified max.
spacing value. If the length of the last interval is less than the max. spacing value, the soil point spacing is
recalculated per the following equation:
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(D-7)
where:
Sc
=
L
n
=
=
Actual spacing length used by AutoPIPE for
generating soil points (L).
Length between adjacent piping points (L).
Total number of soil point spacing intervals, based
on the maximum spacing "S" (dimensionless).
On the other hand, if the specified spacing value (S) is greater than the distance between adjacent piping
points (L), only a single soil point will be generated halfway between the piping points. Again, this is
regardless of what connects those points.
AutoPIPE calculates the soil point spacings, and generates the actual soil points whenever the Global
Consistency Check is executed. It should also be noted that the soil point spacings used by AutoPIPE (Sc) do
not replace the maximum spacing values specified for each defined soil identifier.
The user should be aware that soil points are transparent (automatically generated) in AutoPIPE. Each
defined soil point adds to the overall size of the system model. Thus, more disk space is consumed and
analyses require more time to complete a run. Therefore, short spacings over long lengths between piping
points should be avoided, or else a large number of soil points will be created.
Analysis results are produced for soil points in the same manner as piping (and framing) points are listed. The
naming convention for soil points is the same for every interval between piping points. An example of this
convention is shown in Figure D-6.
Figure D-6
For every span between adjacent piping points, generated soil points are named "+1", "+2", "+3", and so on.
Soil point numbers increase in the forward direction of each piping segment. Numeric results for soil points
are organized such that the soil point data is inserted between the piping point listings which surround them.
Note: Refer to the Pipe Soil Example in the AutoPIPE Workbook for a detailed example of the development
of a buried piping system.
utoPIPE Reference Information
Soil Restraint Properties in AutoPIPE
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The Soil Properties dialog allows specification of simplified soil restraint force vs. displacement relationships
for each direction relative to the orientation of a buried pipe. This allows consideration of the restraint
nonlinearities inherent to a buried pipe resting at the bottom of an excavated trench. Figure D-7, below,
shows a typical force-displacement diagram with the input variables required by AutoPIPE identified
Note: Refer to Static Analysis discussion for details related to the bi-directional displacement assumptions in
nonlinear analyses.
Figure D-7
This input format provides flexibility in the method used to model soil stiffnesses. It allows definitions
ranging from rigid-plastic response to approximation of the actual shape of the stiffness curve (in the range of
small displacements). Note that if the value of K2 is zero, P becomes the ultimate soil restraint force for any
1
displacement that is greater than the corresponding yield displacement. Conversely, if K2 is not zero, large
displacements could cause less accurate calculations for the soil restraint force (since there is no cutoff point
for the upper end of the K2 region).
Differences in soil resistance may be expected to occur from point to point along a buried pipe due to
variations in the properties of the backfill soils. Inevitably, there is also some uncertainty concerning the most
representative values of K1, P1, and K2 for design. Under such conditions, it is often desirable to perform
parameter studies in order to determine the effect which variations in the assumed values have on the
behavior of the buried piping system. A range of values which produces an upper and lower bound like that
shown in Figure D-8 is suitable for such parameter studies.
If variations in soil resistance are found to have an important effect on the behavior of the pipe, the range of
uncertainty can be narrowed by site-specific investigations of the soil properties. If variations of soil
resistance do not have a significant effect on pipe behavior, detailed parameter studies are not warranted.
Figure D-8
It should be clarified that the orientations of Trans Horizontal, Longitudinal, Trans Vertical Up and Trans
Vertical Dn (soil parameter categories on the Soil Properties dialog) are all relative to the local coordinate
system convention used for straight pipe elements (refer to Straight Pipe Forces and Moments ). Thus,
longitudinal soil parameters resist axial pipe movement (along the local x axis), while Trans Horizontal
parameters resist pipe movement along the local z axis. Pipe movement in the direction of the local +y axis is
resisted by the Trans Vertical Up parameters, and pipe movement in the direction of the local -y axis is
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resisted by the Trans Vertical Dn parameters.
This convention is consistent for modeling buried pipes which are placed at the bottom of an excavated
trench. However, if a section of buried pipe lies in a vertical orientation, the up and down categories on the
Soil dialog no longer correspond to the physical up and down directions (as defined by gravity). Thus, a new
soil must be defined in order to shift the directional property orientations as compared to a horizontally laid
pipe.
utoPIPE Reference Information
Calculation of Soil Restraint Properties
Ideally, a geotechnical engineer should evaluate the specific soils to be modeled in AutoPIPE, and supply
design values for the required input variables (K1, P1, & K2). However, these variables are not always
included in a soil report. Therefore, this section has been provided in order to offer the piping designer
guidelines for estimating (ranges of) the required input data. Remember, these are guidelines only, soil
conditions can vary greatly and each situation should be reviewed by a geotechnical engineer (e.g. frozen
soils will require additional consideration).
Note: Users modeling the PipeSOIL transition model should not construe any estimated or assumed soil
properties contained herein as being appropriate for modeling specific soil sites unless the published values
are corroborated by a geotechnical engineer familiar with the soil types involved.
Typically, laboratory tests and field studies can provide the following soil property data:
z
unit weight (J)
z
water content
z
relative compaction
z
undrained shear strength (Su)
z
cohesion (c)
z
angle of internal friction (I)
z
angle of friction of soil against pipe face (G)
Together, these properties can be used to construct a restraint force-displacement relationship for the soil
surrounding a buried pipe. Where some of this data is not available through testing, tables are provided which
give "ball park" estimates. The user should be aware that estimates generally require parameter studies in
order to bound the soil response as discussed in the Soil Restraint Properties in AutoPIPE topic.
An elastic-plastic response (K2 = 0) will be assumed for the determination of the soil restraint force vs.
displacement relationship. This is an assumption which is consistent with accepted practice, and provides
some conservatism of design. Also, any surcharges (e.g. a foundation load at ground level) effecting soil
properties must be considered in addition to the methods defined in the following sub-sections.
First, the soil(s) should be identified according to a standard system of classification. Where applicable, the
Unified Soil Classification System (see Table D-2, and Figure D-9) will be referred to for defining soil types.
Once a soil is classified, equations can be selected for determining the soil properties required by AutoPIPE.
Knowledge of the soil type also helps when property values must be estimated. Table D-3 has been supplied
in order to provide comparative values for J, c, and I.
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NOTES
1.
Atterberg limits plotting in the hatched area (see Figure D-9) are borderline classifications requiring use of dual Group Symbols. The
equation of the "A-line" is as follows: Ip = 0.73(WL - 20)
2.
For soils having 5 to 12% of fines passing through a No. 200 sieve, use dual Group Symbols (e.g. GW-GC).
3.
Variable Definitions:
Cu
Ip
Cz
wL
=
=
=
=
uniformity coefficient
plasticity index (%)
coefficient of curvature
liquid limit (%)
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Figure D-9
The properties for soil backfill around a buried pipe can vary greatly depending on the type of soil, and the
degree of backfill compaction. General guidelines for estimating soil properties based on these factors are
summarized in Table D-4.
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Click on a button below to display more related soil property information.
Transverse Horizontal Soil Properties
Longitudal Soil Properties
Vertical Soil Properties
utoPIPE Reference Information
Transverse Horizontal Soil Properties
The resistance to transverse deflections of buried pipelines can be estimated using information derived from
studies of the behavior of laterally loaded piles and the passive resistance of anchor plates. Studies have
shown that the value of K increases approximately linearly with depth in both sandy and clayey soils. Thus
1
the value of K1 can be expressed in the form:
(D-8)
where
K1
=
Z
ki
=
=
initial slope of the transverse resistance-displacement
curve (F/L2).
depth from ground surface to center of pipe (L).
soil stiffness parameter (F/L3), see Table D-5 for
clays or Table D-6 for sands.
Typical values of the soil stiffness parameter (ki) are given in Table D-5 for clay, and in Table D-6 for sand.
For both clay and sand, the resistance to transverse deflection depends strongly on whether the backfill is
compacted or not. Uncompacted backfill offers little resistance to pipe displacement, and would be
characterized by values on the order of 10 lb/in . Compaction increases the strength of clays and the relative
density of sands. Well compacted backfills of either sandy or clayey soils would be characterized by values
on the order of 100 lb/in3.
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The ultimate resistance (P1) of a backfill soil to a transverse pipe displacement is governed by the strength of
the soil. An estimate of P1 may be based on passive earth pressure theories for anchor blocks. The following
sub-sections describe equations for P1 where the backfill soil is clay based, and sand based respectively.
Clay Based Soils
For buried pipes backfilled with clay, the value of P1 can be calculated from the expression:
(D-9)
where:
P1
=
Rc
=
Su
d
=
=
ultimate soil resistance to transverse pipe displacement,
assuming K2 equals zero (F/L).
coefficient whose value varies with the depth of
embedment (dimensionless). Refer to Table D-7.
undrained shear strength (F/L2).
outside diameter of pipe (L).
Sand Based Soils
For buried pipes backfilled with sand, the value of P1 can be calculated from the expression:
(D-10)
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where
P1
=
Rs
=
d
Z
Jc
=
=
=
=
=
ultimate soil resistance to transverse pipe displacement,
assuming K2 equals zero (F/L).
coefficient whose value varies with the depth of embedment
and the relative density of sand (dimensionless). Refer to
Table D-8 below.
outside diameter of pipe (L).
depth from ground surface to center of pipe (L).
effective unit weight of the soil (F/L ).
Jsat - JH2O for depths below the water table.
Jdry + w(Jsat - Jdry) for depths above the water table.
utoPIPE Reference Information
Longitudinal Soil Properties
Based on studies of pile behavior under conditions of axial load, a relationship between skin friction (or
adhesion) and longitudinal displacement of a pipe has been developed. Values for K1 and P1 are dependant
upon the diameter of the buried pipe, the depth of burial, and the properties of the backfill soil. The following
sub-sections describe equations for K1 and P1 where the backfill soil is clay based, and sand based
respectively.
Clay Based Soils
For saturated clay soils (I = 0), the ultimate longitudinal soil resistance (P1) can be calculated from the
expression:
(D-11)
where:
P1
=
d
D
Su
=
=
=
ultimate soil resistance to longitudinal pipe
displacement, assuming K2 equals zero (F/L).
outside diameter of pipe (L).
adhesion factor (dimensionless).
undrained shear strength (F/L2).
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Figure D-10 shows values of D which have been suggested by various investigators. Also, see Table D-9 for
estimates of the adhesion (D˜Su) of cohesive soils in contact with various piping materials.
Figure D-10
For piles, the displacement required to mobilize the full adhesion resistance is on the order of 0.2 to 0.5
inches for 12 inch diameter piles. On this basis, the displacement which corresponds to P1 can be expressed
as a function of the pipe diameter, and it lies in the following range:
(D-12)
Therefore, the value of K1 can be estimated to be in the range:
(D-13)
Sand Based Soils
In sandy soil, the value of P1 can be expressed in terms of the angle of frictional resistance between the pipe
and the backfill (G). Values of G, suggested by two investigators, are given in Tables D-9 and D-10.
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As shown in Table D-9, the recommended values of G depend only on the type of pipe material in contact
with the soil. Table D-10 shows the variation in values of G for several granular soil types.
For sandy soils, the ultimate longitudinal soil resistance (P1) can be calculated from the expression:
(D-14)
where:
P1
=
d
ks
=
=
Z
Jc
=
=
=
=
G
=
ultimate soil resistance to longitudinal pipe
displacement, assuming K2 equals zero (F/L).
outside diameter of pipe (L).
coefficient of lateral earth pressure
(dimensionless).
depth from ground surface to center of pipe (L).
effective unit weight of the soil (F/L3).
Jsat - JH2O for depths below the water table.
Jdry + w(Jsat - Jdry) for depths above the water
table.
angle of friction of soil against pipe face (q).
Values of ks may vary widely depending upon the relative density or compaction of the backfill soil. For
loose sands, ks may be as low as 0.25; while for compacted backfill, ks may range from 0.5 - 1.0. The
magnitude of the displacement which corresponds to P1 is about the same as it is for clays (see Equation D12). Thus, the value of k1 can be estimated to be in the range defined by Equation D-13. Considering possible
variations and uncertainties in the estimated values of the contributing soil parameters, a range of the soil
resistance variables (K1, and P1) should be determined, as discussed in the Soil Restraint Properties in
AutoPIPE topic.
utoPIPE Reference Information
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Vertical Soil Properties
Since most buried piping systems are constructed by placing the pipe in an excavated trench, soil restraint
characteristics can be very different for pipe movements which bear against the bottom of the trench (in-situ)
compared to pipe movements which bear against the top of the trench (backfill). Therefore, AutoPIPE allows
the specification of soil strength parameters for the up and down directions individually (refer to the Soil
Restraint Properties in AutoPIPE topic for details related to these directions and the spatial orientation of the
pipe).
Click a button below to display more information on each of these vertical soil properties.
Downward Pipe Movement
Upward Pipe Movement
utoPIPE Reference Information
Downward Pipe Movement
(D-15)
The vertical support provided by a soil against downward movement of a buried pipe may be expressed in
terms of conventional bearing capacity theory. The pipeline is assumed to act as a cylindrically shaped
continuous strip footing. Thus, the ultimate soil reaction (P1) for all soil types can be determined from the
expression:
where
P1
=
d
c
H
Jc
=
=
=
=
ultimate soil resistance to downward pipe
displacement, assuming K2 equals zero (F/L).
outside diameter of pipe (L).
cohesion (or Su) of soil below pipe (F/L2).
depth from ground surface to bottom of pipe (L).
effective unit weight of the soil, not the backfill
(F/L3).
Refer to Table D-11 below for the proper effective unit weight equation relative to the location of the water
table.
Ng,
Nc,
Nq = bearing capacity factors (dimensionless). Refer to Figure D-11.
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Figure D-11
Figure D-11 was taken from Leonards, Foundation Engineering, McGraw-Hill, 1962 (after Terzaghi and
Meyerhof). Either the Meyerhof or the Terzaghi curves can be used for dense, stiff soils. Whereas the
Terzaghi local shear curves should be used for loose, compressible soils.
If the angle of internal friction (I) is zero, as for saturated clay in undrained shear, the first and third terms in
Equation D-15 become very small and only the cohesion contributes materially to the bearing capacity. Thus,
for all practical purposes in a saturated clay:
(D-16)
For this case, values of Nc with respect to the depth of embedment and pipe diameter have been developed as
shown in Figure D-12. In this chart, the breadth (B) is equal to the outside diameter of the pipe (d). Figure D12 is after Skempton (1951), and was taken from Poulos and Davis' Pile Foundation Analysis and Design,
Wiley, 1980.
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Figure D-12
The displacement required to mobilize the full soil resistance is generally considered to be on the order of
10% to 15% of the outside diameter of the pipe. On this basis, the displacement which corresponds to P1 can
be expressed as a function of the pipe diameter, and it lies in the following range:
(D-17)
Therefore, the value of K1 can be estimated to be in the range:
(D-18)
utoPIPE Reference Information
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Upward Pipe Movement
Design approximations for this type of movement are based on studies of earth anchors subjected to vertical
uplift forces. The uplift resistance consists of two parts: the weight of the soil wedge (Ws) above the anchor;
and the shear resistance of the soil wedge being moved upwards.
The shape of the soil wedge is a major factor in the total uplift resistance. Figure D-13 shows several possible
shapes of breakout wedges which have been observed in tests on various types of soils. Figure D-13(A)
indicates the condition for a wedge of uniform width, which produces the lower bound value of uplift
resistance. Figure D-13(B) shows a tapered wedge which produces higher uplift resistance; the angle of the
taper has been found to be related to the angle of internal friction (I). The shape shown in Figure D-13(C) has
been observed in tests involving deep embedment in dense sands or clays. For weak soils or remolded soils,
as is the case for uncompacted backfill, the shape of the breakout wedge will likely correspond to Figure D13(A). It is recommended that this shape of wedge be used for design.
Figure D-13: Possible shapes of breakout wedge
Thus, the ultimate soil resistance (P1), for all soil types, can be determined from the expression:
(D-19)
where:
P1
=
Ws
=
d
c
Jc
=
=
=
=
=
=
D
Fc,
Fq
=
ultimate soil resistance to upward pipe displacement,
assumes K2=0 (F/L).
effective weight of soil wedge per unit length (F/L). Use
the equations for Jc(shown below) when considering the
water content of the backfill.
outside diameter of pipe (L).
cohesion (or Su) of soil above pipe (F/L2).
effective unit weight of the soil (F/L3).
Jsat - JH2O for depths below the water table.
Jdry + w(Jsat - Jdry) for depths above the water table.
depth from ground surface to top of pipe (L).
breakout factors (dimensionless) see Figure D-14 and
Figure D-15.
The curves for Fc and Fq, shown in Figures D-14 and D-15, are expressed as functions of the ratio of depth of
burial to pipe diameter (D/d), and the angle of internal friction (I).
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Figure D-14: Breakout factor (fc)
Figure D-15: Breakout factor (fq)
Clay Based Soils
Tests indicate that relatively large displacements, on the order of 10% to 20% of the depth to the top of the
pipe (D), are required to mobilize the full uplift resistance. On this basis, the displacement which corresponds
to P1 can be expressed as a function of the depth "D", and it lies in the following range:
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(D-20)
Therefore, the value of K1 can be estimated to be in the range:
(D-21)
Sand Based Soils
Tests indicate that relatively small displacements, on the order of 1% to 2% of the depth to the top of the pipe
(D), are required to mobilize the full uplift resistance for dense to loose sands. On this basis, the displacement
which corresponds to P1 can be expressed as a function of the depth "D", and it lies in the following range:
(D-22)
Therefore, the value of K1 can be estimated to be in the range:
(D-23)
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