1-27-00, Immediate Settlement and Bearing Capacity
Ref:
Principles of Geotechnical Engineering, Braja M. Das, 1994
Coastal Engineering Handbook, J.B. Herbich, 1991
Topics:
Secondary Consolidation
Immediate Settlement
Total Settlement & Change of Settlement with Time
Mechanical Properties
Shear Strength
Degree of Permeability
Elastic Constants
Blow Count
Examples
Bearing Capacity Summary
--------------------------------------------------------------------------------------------------------------------Secondary Compression Settlement "Secondary (compression) settlement is more important in organic and highly compressible inorganic soils.
In overconsolidated inorganic clays, the secondary consolidation index is very small and of less practical
importance."
Braja M. Das
Principles of Geotechnical Engineering
**Marine soils are generally overconsolidated clays or sands
"Soil disturbance decreases the coefficient of secondary compression in the range of virgin compression.
Evaluation of settlement caused by secondary compression has often not been reliable."
USACE
Settlement Analysis
Secondary Compression Settlement is generally only a concern for highly organic
material (e.g. peat)
Calculation Method
 t 
et  C  log  
tp = time when primary consolidation is complete, C =
t 
 p
secondary compression index
et
H
1 ep
H = layer thickness
S st 
ep = void ratio when primary consolidation is complete,
Uniform C/Cc ratio (USACE)
Inorganic
0.025 - 0.065
Clay
0.025 - 0.085
Silt
0.030 - 0.075
Peat
0.030 - 0.085
Immediate Settlement  settlement that occurs at the instant of loading,
 mainly due to shear deformation,
 computed by applying the theory of elasticity
 not important for saturated clays (permeability is too low)
 effect is usually negated by the disturbance of the soil by the construction process
1 2
I ,
E
i = immediate settlement
 = surcharge (added load) at the surface
B = width or diameter of foundation
E = modulus of elasticity of soil
 = Poisson's ratio
I = nondimensional influence factor
 i  B
Tables from Das (1994)
Influence Factor (I) for rigid foundations
m = (length of foundation)/(width of foundation)
Circle
Rectangle
1
1.5
2
3
5
10
m
0.79
0.88 1.07 1.21 1.42 1.70 2.10
I
Modulus of Elasticity (E)
Modulus of Elasticity (E)
Type of Soil
(psi)
Soft clay
250-500
Hard clay
850-2000
Loose sand
1500-4000
Dense sand
5000-10,000
Poisson's ratio ()
Type of Soil
Loose sand
Medium sand
Dense sand
Silty sand
Soft clay
Medium clay
Poisson's ratio ()
0.2-0.4
0.25-0.4
0.3-0.45
0.2-0.4
0.15-0.25
0.2-0.5
20
2.46
50
3.0
Modulus of Elasticity (E)
(kN/m2)
1380-3450
5865-13,800
10,350-27,600
34,500-69,000
100
3.43
Total Settlement & Change of Settlement with Time
ST(t) = St + Sst + i , ST = total settlement, St = primary consolidation settlement (function
of time), Sst = secondary compression settlement, i = immediate settlement
*** For (most) marine soils and construction, neglect secondary compression settlement
and immediate settlement
Primary Consolidation Settlement as a function of time
St
 100 , U = degree of consolidation (%), S = ultimate primary
S
consolidation settlement, St = primary consolidation settlement at time t
Recall: U 
Mechanical Properties of Soil
Shear Strength - obtained from soil tests, formula for saturated soil
  c   tan 
 = shear strength
c = cohesion strength (undrained shear strength)
' = effective stress,     u   H
 = angle of internal friction (angle of repose)
from Das (1994)
Soil Type
Loose sand
Medium sand
Dense sand
Gravel with some sand
silt
 (degrees)
27-35
30-40
35-45
34-48
26-35
Cohesionless soil (80% or more sand), c = 0   f  ' tan 
Cohesive soil, assume  = 0,
Cohesion strength (c) for clays from unconfined compression strength,
(Das 1994)
Consistency
ton/ft2
kN/m2
Very soft
0 - 0.5
0 - 48
Soft
0.5 - 1
48 - 96
Medium
1-2
96 - 192
Stiff
2-4
192 - 384
Very stiff
4-8
384 - 766
hard
>8
> 766
Degree of Permeability
Degree of permeability
High
Medium
Low
Very low
Practically impermeable
k (cm/s)
> 10-1
10-3 - 10-1
10-5 - 10-3
10-7 - 10-5
< 10-7
Blow Count (N, blows/ft or blows/30 cm)
N is the average blows per foot in the stratum, number of blows of a 140-pound
hammer falling 30 inches to drive a standard sampler (1.42" I. D., 2.00" O. D.)
one foot. The sampler is driven 18 inches and blows counted the last 12 inches.
Indicates soil strength***
Sand
Density
N
N
Very loose
Loose
Medium
Dense
Very dense
0-4
4-10
10-30
30-50
>50
<2
2-4
4-8
8-15
15-30
>30
Clay
Undrained Compressive
strength (T/m2)
<2.5
Very soft
2.5-5.0
Soft
5.0-10.0
Medium
10-20
Stiff
20-40
Very stiff
>40
hard
1 T/m2 = 0.1 tons/ft2
*** Blow Count or the Standard Penetration Test is standard in the U.S., but should only
be used in sandy soil (NOT clays). Clays tend to have erroneously high blow counts
when tested in place due to the inability of water to drain out (i.e. the test is on water
pressure, not soil strength.
A better test is the Static Cone Test in which an instrumented sensor is continuously
driven into the soil and sends data back to a computer.
Examples
Units: 1 t ~ 1000 kgf ~ 10 kN,
1 lb/ft2 = 47.88 N/m2
1 psi = 6.9 kN/m2
(t = metric ton)
for unsaturated soil with S=40%, '= 1.8 t/m3
for saturated soils, = 2.0 t/m3
for quartz sand, G = 2.65, n = 38% = 0.38
for water, w = 1.0 t/m3
Ultimate Bearing Capacity of the Soil
Two aspects for design:
Settlement
Bearing Capacity
Bearing Capacity (definition): ability of the soil to safely carry the pressure placed on the soil by
any engineered structure without undergoing a shear failure with accompanying large
settlements. A safe bearing pressure with respect to failure does not ensure that settlement will be
within acceptable limits. Must conduct settlement analysis.
Procedure (USACE)
1. Evaluate the ultimate bearing capacity pressure qu
2. Determine a reasonable factor of safety (FS) based on available subsurface surface
information, variability of the soil, soil layering and strengths, type and importance of the
structure and past experience. FS will typically be between 2 and 4. (marine applications
1.5-2.5)
3. Evaluate allowable bearing capacity qa by dividing qu by FS; i.e., qa = qu /FS
4. Perform settlement analysis when possible and adjust the bearing pressure until
settlements are within tolerable limits. The resulting design bearing pressure qd may be
less than qa . Settlement analysis is particularly needed when compressible layers are
present beneath the depth of the zone of a potential bearing failure. Settlement analysis
must be performed on important structures and those sensitive to settlement.
Ultimate Bearing Capacity (qu) Calculation (Terzaghi's Ultimate Bearing Capacity Equation)
For saturated, submerged soils
1
qu  qc  qq  q   cN c  qN q   BN 
2
qu  qc  qq  q  cN c  qN q  0.3 BN 
for strip foundations
for circular or square foundations
qc, qq, q = load contributions from cohesion, soil weight and surcharge
Nc, Nq, N = bearing capacity factors for cohesion, soil weight and surcharge
c = cohesion strength of soil
q = soil weight
G 1
w )
 ' = effective bulk density of soil (       w 
1 e
B = width of the foundation
Soil weight is calculated as q   D , where D is the depth of penetration of the
foundation
NOTE:  ' is used only for the portion of the soil that is submerged, otherwise the
W  Ww
bulk density (   s
) is used (neither is a dry weight!)
Vtotal
From Handbook of Coastal Engineering, vol 2, ch 7 (A. G. Young), 1991
For shallow foundations (Vesic, A.S., "Bearing Capacity of Shallow
Foundations", Foundation Engineering Handbook, 1975)
N q  e  tan  tan 2 45   2
N   2N q  1tan 
N c  N q  1cot  ,  > 0
N c    2  5.14 ,  = 0, clay
for deep foundations Nc  9
Allowable bearing capacity (qa)
qa 
qu
, essentially the allowable load of the structure
FS
Layered profiles will require calculating an effective B for each layer and ultimate
and allowable bearing capacities for each layer
(more later)