Appropriate values, as a function of the footing location relative to the slope may be
found on p. 7.2-136 in DM 7. The case of a two layer cohesive soil is covered on pp.
7.2-137,138 in DM 7.2.
For purposes of this discussion, we will consider foundations on granular soils and
cohesive soils separately.
Most structures founded on granular soils have settlement tolerance limits that come
into play well before potential bearing capacity failure becomes an issue. Therefore, the
design of foundations on granular soils is focused primarily on settlement.
In order to evaluate the settlement potential of granular soils, we need to give some
thought to what type of data we can obtain from the field and laboratory
investigations. The first thing to realize, in this regard, is that it is extremely difficult
(and expensive) to obtain anything approaching an undisturbed sample of granular soil.
This means that meaningful laboratory tests to evaluate settlement parameters are
usually out of the question. Consequently, the evaluation of settlement of foundations
on granular soil is typically based on field data. What type of field data? By far the
most common field test for this purpose is the SPT. Since the SPT does not directly
measure settlement parameters, correlations are used to relate the SPT N-values to
settlement potential. One way this is accomplished is as follows. SPT tests are
performed during the field investigation, settlements are measured and, knowing the
loads applied to the foundations, a correlation can be found, between N-value, bearing
pressure and settlement. Another approach is to correlate SPT N-values with a
fundamental soil property such as “elastic” modulus and compute settlements based
on Theory of Elasticity.
The first approach was proposed by Terzaghi and Peck, in the 1940’s. They presented
charts relating bearing pressure for one inch of settlement to N-value, footing size and
depth. [Note: As mentioned in Chapter 3, 1-inch settlement has long been accepted as
the allowable total settlement for spread footings. If the allowable settlement is less
than 1 inch, the bearing pressures are reduced in direct proportion.] A more recent,
revised version of their chart is given in Figure 4.2. The values obtained from these
charts are intended to be design, or allowable, values corresponding to one inch of
settlement. Notice that three charts are provided for three different embedment ratios
( D f / B ) . Notice also that the allowable soil pressure decreases linearly below a
certain footing width. This accounts for the fact that bearing capacity (rather than
settlement) controls in that range of footing sizes. The only difference in the three
charts is the footing width at which the allowable pressure becomes constant for a
given N-value. Finally, these charts do not explicitly deal with “size effect”; i.e., the
well known phenomenon that settlement increases with footing size.
- 30 -
Figure 4.2. Design Chart for Proportioning Shallow Footings on Sand
Modified Meyerhof Method A similar approach which was originally presented by Meyerhof in 1956 and revised in
1965 may be expressed in equation form. In current form, it is usually known as the
Modified Meyerhof Method.
0.44q ' Br
For footings less than 4 ft wide: δ = (4.13)
N 60σ r' K d
0.68q ' Br ⎛ B ⎞
For footings greater than 4ft wide: δ = ⎜ ⎟ (4.14)
N 60σ r' K d ⎝ B + Br ⎠
δ = settlement
Br = reference width = 1 ft = 0.3 m = 12 inches = 300 mm
q ' = net bearing pressure
σ r = reference stress = 1 tsf = 100 kPa, etc.
N 60 = average SPT N 60 -value between bottom of footing
and depth 2B below the footing.
B = footing width
K d = depth factor = 1+0.33 ≤ 1.33
The N 60 values are not to be corrected for overburden. Groundwater effects are
considered to be accounted for in the N-values, provided the water table does not
change appreciably after the borings are drilled. To account for potentially falsely high
- 31 -
N-values in dense silty sand below the water table, it is suggested to correct the N-
values as follows.
N 60 corrected = 15 + 0.5 ( N 60 field − 15 ) for N 60 > 15 (4.15)
Even though the Modified Meyerhof Method is 50% less conservative than his original
version, studies have shown that it still overestimates settlements 75% of the time.
Note that eqn (4.14) does contain a size effect factor.
Burland and Burbidge
(Burland, 1985) collected more than 200 records of structures founded on sands and
gravels. They started with the premise that the settlement could be represented by an
equation of the form:
δ = z I mv q '
where, δ = settlement
z I = depth of influence, below which the vertical
strains are negligible (4.16)
mv = average coefficient of vertical compression
within the depth of influence
q ' = average net bearing pressure of foundation
B&B found the zone of influence to be:
Z I = B 0.75 (meters) (4.17)
Interpretation of the depth of influence based on measurement of settlements beneath
a few foundations is shown in Figure 4.3a.
Although the data points are few, they do tend to follow equation(4.17).
B&B also examined the trend of δ / q versus B , as shown in Figure 4.3b. This
trend line also confirms equation (4.17). [Note that, in the graph, the settlement is
designated sc instead of δ as is used in this study guide.]
It should be noted that the actual thickness of compressible granular soil should
be used if it is less than B 0.75 . Statistical analysis of the settlement records, as
shown in Figure 4.4, resulted in the coefficient of vertical compression:
mv = 1.4
( MPa −1 ) (4.18)
- 32 -
Figure 4.3a. Thickness of granular soil beneath foundation contributing to
settlement, interpreted from settlement profiles [after (Burland, 1985)].
This value is intended for normally consolidated sands. B&B suggest reducing this
value by a factor of 3 for over-consolidated sands. This reduction should be used with
caution. In any case, it is often difficult to know if a sand deposit is over-consolidated.
The following correction factor for shape is recommended when the footing is not
square. Note that the value of C s varies from 1.0 for a square or circular footing
to 1.56 for a strip footing.
⎡ 1.25( L / B) ⎤
Cs = ⎢ ⎥
⎣ ( L / B) + 0.25 ⎦ (4.19)
where, ( L / B ) = of footing
Combining(4.16), (4.17) ,(4.18) and (4.19), the settlement is calculated from:
δ = Cs B 0.75 1.4
q' [δ = mm, B = m, q ' = kPa ]
δ = 1.62 ⋅ Cs B 0.75 1.4
q' [δ = in, B = ft , q ' = tsf ]
- 33 -
Figure 4.3b. Relation between settlement on sand and width of footing, for sands
having N-values between 26 and 40 [after (Burland, 1985)] .
Figure 4.4 Relation between compressibility of sand and SPT N-values [after
- 34 -
Elastic Theory Although soils, especially granular soils, are not truly elastic materials, they behave like
elastic materials at small strains. Therefore, the solutions of theory of elasticity may be
used for estimating foundation settlement.
The solution for settlement beneath a flexible load on an isotropic homogeneous
elastic medium can be written as:
Notice the similarity
δ= I 0 I1
between eqn. (4.21)
and the Burland and
Burbich formulation where, Es = Young's Modulus and (in our case, for soil)
I 0 , I1 = Influence factors for shape and depth of (4.21)
δ , q ', B = as previously defined
The influence factors are shown in Figure 4.5.
Figure 4.5 Influence factors for use in Equation (4.21)
- 35 -
The greatest unknown in (4.21) is the soil modulus. There are numerous published
correlations that attempt to relate modulus to SPT N-values. Some examples are listed
below. E is given in kPa.
Granular Soil SPT
Sand E = 500(N+15)
E = 18,000 + 750N
Clayey Sand E = 320(N+15)
Silty Sand E = 300(N+6)
Gravelly Sand E = 1200(N+6)
The Pressuremeter modulus could also be used, if available, but there are separate
equations that have been developed for use with the pressuremeter values. (Burland,
1989) has suggested that values obtained by seismic survey methods may be
appropriate, provided the safety factor against bearing failure is at least 3.0. Be aware,
however, that seismic values are likely to be significantly higher than those obtained
from the pressuremeter or correlations with SPT or CPT.
Schmertmann’s Method Schmertmann’s Method involves the integration of strains beneath the footing to
obtain the settlement. The trick is to know what the strain profile beneath the footing
will be. Schmertmann developed an approximation to the strain profile based on
elastic theory and a few cases where the strain profile was actually measured, as shown
in Figure 4.5.
It should be noted that the curves in Figure 4.5 are either theoretical (a and c) or based
on laboratory-scale measurements (b and d). Some full-scale measurements seem to
suggest that the strains may taper off more quickly (see e.g., (Terzaghi, 1996)).
Remember in our discussion of the B&B method, their research suggested that the
zone of influence is only B 0.75 .
Based on the type of strain distribution shown in Figure 4.5, Schmertmann suggested
that the settlement of a footing on sand could be obtained from:
δ = ∫ ε z dz (4.22)
which could be approximated by:
- 36 -
δ =∫ dz (4.23)
Since the stain influence factor and soil modulus vary with depth and soil layering, it is
more convenient to express (4.23) as a summation:
δ = C1C2 q ' ∑ Δzi
i =1 Es
where, C1 , C2 = Correction factors discussed below
I z = Strain influence factor for layer i at depth z (4.24)
Δz i = Thickness of layer i
n = Number of soil layers with the zone of influence
Schmertmann’s recommended strain influence diagram is shown in Figure 4.7.
- 37 -
Figure 4.7 (a) Strain influence diagram for square and continuous footings, (b)
Explanation of terms for computing peak influence factor [From (Schmertmann,
Instructor’s note: Figure Note that both the value and location of the peak strain influence factor changes with
4.7 overcomplicates the footing shape. The location of the peak may be interpolated as a function of L/B.
strain influence diagram.
I suggest taking the peak The depth of influence also changes with footing shape and can also be interpolated as
value as a constant = 0.6. a function of L/B.
Also, increase the soil
modulus when L/B>1
(see below). The correction factor C1 is intended to account for reduced settlement due to
Alternatively, use the
axisymmetric diagram embedment. Schmertmann recommended the following correction.
for all cases and correct
for L/B with [4.9].
C1 = 1 − 0.5 ⎜ vo ⎟ ≥ 0.5
⎝ q' ⎠
where, σ vo = Effective vertical vertical stress
at base of foundation
Schmertmann also suggested a correction factor C2 to account for time-dependent
settlement that had been observed even for foundations on presumably cohesionless
soils. He recommended:
⎛ t ⎞
C2 = 1 + 0.2 log10 ⎜ ⎟
⎝ 0.1 ⎠ (4.26)
where, t = elapsed time since construction, yrs.
Note that (4.26) would suggest a 46% increase in settlement after 20 years.
- 38 -
(Holtz, 1991) questioned the validity of such time dependent (creep) settlement and
recommended setting C2 =1. In my opinion, the evidence for significant time-
dependent settlement in granular soils is weak, so I agree with Holtz. I know of no
case, were a structure founded on cohesionless soil was damaged by creep settlements.
Schmertmann suggested estimating the soil modulus for use in his method from CPT
data. Although not exactly equal to Schmertmann’s recommendations, the Canadian
Foundation Engineering Manual [ (Canadian Geotechnical Society, 1985)] suggests the
Es = kqc
where, k = 1.5 for silts and sand
= 2 for compact sand
= 3 for dense sand
= 4 for sand and gravel
qc = CPT tip resistance
Mesri (Terzaghi, et al, 1996) recommends k = 3.5 for square or circular foundations,
based on observation of 81 foundations and 92 plate load tests. A correction factor of
[1 + 0.4 log10 ] is applied to the modulus when L/B>1.
[As an exercise, compare Es obtained from (4.27) with those using the correlations on
page 31 and Figure 2.7.]
Pressuremeter Method According to the “Pressuremeter Manual” (Baguelin, 1978), settlement of shallow
foundations on homogeneous soil can be estimated from the semi-empirical formula:
2q ' Bo ⎡ B ⎤ α q ' B
δ= ⎢ λd ⎥ + λc
9 EM ⎣ Bo ⎦ 9E M
EM = Pressuremeter modulus
q ' = Net average bearing pressure (4.28)
Bo = Reference width = 2 ft, 60 cm, etc.
α = Rheological factor, which depends on soil type and *
λd , λc = Shape factors
- 39 -
Equation (4.28) is intended for foundations for which D / B ≥ 1.0 and B > Bo . If
embedment is less than the footing width, the settlements are increased by the factor
[1.2 − 0.2( D / B)] ≤ 1.2 .
Note that (4.28) contains two contributions to the total settlement. The first term
(containing λd ) is related to shear, or distortional deformations and the second
(containing λc ) is related to volumetric compression.
The recommended rheological and shape factors are given in Figure 4.7.
When the pressuremeter modulus varies with depth, the modulus values to use in the
two terms of [4.13a] are:
Ec = E0−0.5 B
1 1⎡ 1 1 1 1 1 ⎤ (4.29)
= ⎢ + + + + ⎥
Ed 4 ⎣ E0−0.5 B 0.85 E0.5 B − B EB − 2.5 B 2.5 E2.5 B − 4 B 2.5 E4 B −8 B ⎦
These two equations illustrate the fact that volumetric compression occurs mainly in
the range 0 to B/2; whereas, distortional compression (theoretically) extends to a depth
As a practical matter, there is rarely enough pressuremeter data to accurately evaluate
(4.29). Where there are gaps in the data, estimates may be made of intermediate values.
If an incompressible stratum is present above any of the ranges in(4.29), those terms
should be set equal to zero.
The meaning of the rheological factor is somewhat unclear. In one sense, it appears to
be a “size effect” in that it appears in combination with B. The values listed for various
soil types in Figure 4.8 seem to be consistent with that role; i.e., the values are greatest
for peat and clay and least for sand and gravel. This trend suggests that “size effects”
are greatest for “elastic” behaving soils and least for soils whose behavior is dominated
by individual grains. This explanation is also consistent with the use of the term
“rheological” which could be loosely interpreted as “behavior of the material under
The pressuremeter settlement equation can be used with both granular soils and
overconsolidated cohesive soils. As a practical matter, this will include most soils for
which shallow foundations are feasible. However, for normally consolidated soils
beneath large loaded areas, like tanks and mat foundations, consolidation theory should
be used to estimate settlement.
- 40 -
Figure 4.8 Rheological and shape factors for use in equation (4.28)
Settlement of foundations on cohesive soils is approached in one of four ways:
• Indirectly limiting settlement by applying a safety factor of at least three to the
• Analysis by pressuremeter method
• Analysis using elastic theory, as previously discussed for granular soils. This
method presupposes overconsolidated conditions
• Analysis by consolidation theory
The bearing capacity approach and pressuremeter methods were discussed in earlier
sections. The bearing capacity method is most often employed in routine foundation
design. It can be demonstrated that, for typical building foundations, settlement will be
limited to one inch or less if the foundation bearing pressure is limited to the
unconfined compressive strength. This method should not be used if the subsurface
conditions are such that significant consolidation may occur. The pressuremeter
method is applied as described in the preceding section.
- 41 -