Foundation Engineering
Engineering Department
Building Technology (Civil) Engineering
Instructor: Luay I. Qrenawi, PhD Candidate
Second Semester 2018 – 2019
1

7.1 Introduction
7.2 Elastic Settlement of Shallow Foundation on Saturated Clay (ms = 0.5)
7.3 Settlement Based on the Theory of Elasticity
7.4 Improved Equation for Elastic Settlement
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor
7.6 Settlement of Foundation on Sand Based on Standard Penetration Resistance
(Meyerhof’s Method)
7.14 Tolerable Settlement of Buildings
Settlement of Shallow Foundations

Settlement of Shallow Foundations
• Settlement of a shallow foundation can be divided into two major categories:
(a) elastic, or immediate, settlement
(b) consolidation settlement.
• Immediate, or elastic, settlement of a foundation takes place during or
immediately after the construction of the structure.
• Consolidation settlement occurs over time.
• Pore water is extruded from the void spaces of saturated clayey soils
submerged in water.
• The total settlement of a foundation is the sum of the elastic settlement and the
consolidation settlement.
7.1 Introduction

Settlement of Shallow Foundations
• Consolidation settlement comprises two phases: primary and secondary.
• The fundamentals of primary consolidation settlement were explained in detail
in Soil Mechanics Course.
• Secondary consolidation settlement occurs after the completion of primary
consolidation caused by slippage and reorientation of soil particles under a
sustained load.
• Primary consolidation settlement is more significant than secondary settlement
in inorganic clays and silty soils.
• However, in organic soils, secondary consolidation settlement is more
significant.
• This chapter presents various theories presently available for estimating of
elastic and consolidation settlement of shallow foundations.
7.1 Introduction

Settlement of Shallow Foundations
7.2 Elastic Settlement of Shallow Foundation on Saturated Clay (ms = 0.5)
• Janbu et al. (1956) proposed an equation to evaluate the average settlement
of flexible foundations on saturated clay soils (Poisson’s ratio, ms = 0.5).
• Referring to Figure 7.1, this relationship can be expressed as:
where
A1 = f (H/B, L/B)
A2 = f (Df/B)
L = length of the foundation
B = width of the foundation
Df = depth of the foundation
H = depth of the bottom of the foundation to a rigid layer
qo = net load per unit area of the foundation
…… (7.1)

Settlement of Shallow Foundations
7.2 Elastic Settlement of Shallow Foundation on Saturated Clay (ms = 0.5)
Fig. 7.1 Values of A1 and A2 for elastic
settlement calculation—Eq. (7.1)

Settlement of Shallow Foundations
7.2 Elastic Settlement of Shallow Foundation on Saturated Clay (ms = 0.5)
• Christian and Carrier (1978) modified the values of A1 and A2 to some extent
and is presented in Figure 7.1.
• The modulus of elasticity (Es) for saturated clays can be given as:
Es = bcu
Where: cu = undrained shear strength.
• The parameter b is a function of the plasticity index and overconsolidation
ratio (OCR).
• Table 7.1 provides a general range for b, and proper judgment should be used
in selecting the magnitude of b.
…… (7.2)

Settlement of Shallow Foundations
7.2 Elastic Settlement of Shallow Foundation on Saturated Clay (ms = 0.5)

Settlement of Shallow Foundations
7.2 Elastic Settlement of Shallow Foundation on Saturated Clay (ms = 0.5)

Settlement of Shallow Foundations
Consider the shallow foundation subjected to pressure of Ds.
Let Poisson’s ratio and the modulus of elasticity of the soil supporting it be ms and Es,
respectively.
If the foundation is perfectly flexible, the settlement is expressed as:
Where:
qo = net applied pressure on the foundation
ms = Poisson’s ratio of soil
Es = average modulus of elasticity of the soil
(It is measured from z = 0 to about z = 5B)
B’ = B/2 for center of foundation
B’ = B for corner of foundation
Is = shape factor
7.3 Settlement Based on the Theory of Elasticity
…… (7.4)

Settlement of Shallow Foundations
7.3 Settlement Based on the Theory of Elasticity
…… (7.5)
…… (7.6)
…… (7.7)
…… (7.8)
…… (7.9)
…… (7.10)
…… (7.11)

Settlement of Shallow Foundations
Values of F1 and F2 are given in Tables 7.2 and 7.3, while If values are given in
Table 7.4.
When Df = 0, the value of If = 1 in all cases.
7.3 Settlement Based on the Theory of Elasticity

Settlement of
Shallow Foundations
7.3 Settlement Based on
the Theory of Elasticity

Settlement of
Shallow Foundations
7.3 Settlement Based on
the Theory of Elasticity

Settlement of
Shallow Foundations
7.3 Settlement Based on
the Theory of Elasticity

Settlement of
Shallow Foundations
7.3 Settlement Based on
the Theory of Elasticity

Settlement of Shallow Foundations
• The elastic settlement of a rigid foundation can be estimated as:
• Due to the nonhomogeneous nature of soil deposits, the magnitude of Es may
vary with depth.
• For that reason, using a weighted average value of Es is considered.
Where:
Es(i) = soil modulus of elasticity within a depth Dz
z’ = H or 5B, whichever is smaller
Representative values of the modulus of elasticity and Poisson’s ratio for different
types of soils are given in the following tables.
7.3 Settlement Based on the Theory of Elasticity
…… (7.12)
…… (7.13)

Settlement of Shallow Foundations
Source: Principles of Geotechnical Engineering, Braja M. Das. CH. 11.
7.3 Settlement Based on the Theory of Elasticity

Settlement of Shallow Foundations
7.3 Settlement Based on the Theory of Elasticity

Settlement of Shallow Foundations
7.3 Settlement Based on the Theory of Elasticity

Settlement of Shallow Foundations
7.3 Settlement Based on the Theory of Elasticity

Settlement of Shallow Foundations
7.3 Settlement Based on the Theory of Elasticity

Settlement of Shallow Foundations
7.3 Settlement Based on the Theory of Elasticity

Settlement of Shallow Foundations
7.3 Settlement Based on the Theory of Elasticity

Settlement of Shallow Foundations
7.3 Settlement Based on the Theory of Elasticity

Settlement of Shallow Foundations
7.4 Improved Equation for Elastic Settlement
• Mayne and Poulos presented an improved formula for calculating the elastic
settlement of foundations.
• The formula takes into account the rigidity of the foundation, the depth of
embedment of the foundation, the increase in the modulus of elasticity of the
soil with depth, and the location of rigid layers at a limited depth.
• To use Mayne and Poulos’s equation, one needs to determine the equivalent
diameter Be of a rectangular foundation, or
where
B = width of foundation
L = length of foundation
For circular foundations: Be = B (B = diameter of foundation).
…… (7.14)
…… (7.15)

Settlement of Shallow Foundations
7.4 Improved Equation for Elastic Settlement
• Fig. 7.5 shows a foundation with an equivalent diameter Be located at a depth
Df below the ground surface.
• Let the thickness of the foundation be t and the modulus of elasticity of the
foundation material be Ef .
• A rigid layer is located at a depth H below the bottom of the foundation.

Settlement of Shallow Foundations
7.4 Improved Equation for Elastic Settlement
• The modulus of elasticity of the compressible soil layer can be given as:
Es = Eo + kz
• Now, the elastic settlement below the center of the foundation is:
Where
IG = influence factor for the variation of Es with depth = f(b, H/Be)
IF = foundation rigidity correction factor
IE = foundation embedment correction factor
…… (7.16)
…… (7.17)

Settlement of Shallow Foundations
7.4 Improved Equation for Elastic Settlement
Fig. 7.7 and 7.8 show the variation of IF and IE.
• Fig. 7.6 shows the variation of IG with b and
H/Be .
• The foundation rigidity correction and
foundation embedment factors are:
…… (7.18)
…… (7.19)

Settlement of Shallow Foundations
7.4 Improved Equation for Elastic Settlement

Settlement of Shallow Foundations
7.4 Improved Equation for Elastic Settlement

Settlement of Shallow Foundations
7.4 Improved Equation for Elastic Settlement

Settlement of Shallow Foundations
7.4 Improved Equation for Elastic Settlement

Settlement of Shallow Foundations
7.4 Improved Equation for Elastic Settlement

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor
• The settlement of granular soils can also be evaluated by the use of a
semiempirical strain influence factor proposed by Schmertmann et al. (1978).
• According to this method (Figure 7.9), the settlement is:
Where:
Iz = strain influence factor
C1 = correction factor for the depth of foundation embedment = 1 – 0.5 [q/(q – q)]
C2 = a correction factor to account for creep in soil = 1 + log (time in years / 0.1)
q = stress at the level of the foundation
q = gDf = effective stress at the base of the foundation
Es = modulus of elasticity of soil
–
–
…… (7.20)

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor
• The recommended variation of the strain influence factor Iz for square or
circular foundations and for rectangular foundations with L/B ≥ 10 is shown in
Figure 7.9.
• The Iz diagrams for 1 < L/B < 10 can be interpolated.
• The maximum value of Iz = Iz(m) occurs at z = z1 and then reduces to 0 at z = z2.
• The maximum value of Iz can be calculated as
Where:
q’z(1) = effective stress at a depth of z1 before construction of the foundation
…… (7.21)

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor
• The following relations are suggested by Salgado (2008) for interpolation of Iz:
At z = 0:
Variation of z1/B for Iz(m):
Variation of z2/B:
• Schmertmann et al. (1978) suggested that:
Es = 2.5qc (for square foundation)
Es = 3.5qc (for L/B ≥ 10)
Where:
qc = cone penetration resistance.
• It appears reasonable to write (Terzaghi et al., 1996)
…… (7.22)
…… (7.23)
…… (7.24)
…… (7.25)
…… (7.26)
…… (7.27)

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor
The procedure for calculating elastic settlement using is given below:
Step 1: Plot the foundation and the variation of Iz with depth to scale (Fig. 7.10a).
Step 2: Using the correlation from standard penetration resistance (N60) or cone
penetration resistance (qc), plot the actual variation of Es with depth (Fig. 7.10b).
Step 3: Approximate the actual variation of Es into a number of layers of soil
having a constant Es, such as Es(1), Es(2), . . . , Es(i), . . . Es(n) (Fig. 7.10b).
Step 4: Divide the soil layer from z = 0 to z = z2 into a number of layers by drawing
horizontal lines. Number of layers will depend on the break in continuity in the Iz
and Es diagrams.
Step 5: Prepare a table (such as Table 7.5) to obtain
Step 6: Calculate C1 and C2.
Step 7: Calculate Se from Eq. (7.20).

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor
• Terzaghi, Peck, and Mesri (1996) proposed a slightly different form of the
strain influence factor diagram, as shown in Fig. 7.12.
• According to this method:
At z = 0, Iz = 0.2 (for all L/B values)
At z = z1 = 0.5B, Iz = 0.6 (for all L/B values)
At z = z2 = 2B, Iz = 0 (for L/B = 1)
At z = z2 = 4B, Iz = 0 (for L/B ≥ 10)
For L/B between 1 and 10 (or > 10),
• The elastic settlement can be given as:
qc in MN/m2
…… (7.28)
…… (7.29)

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor
qc in MN/m2
Es = 3.5 qc (for circular and square foundations)
Es(rectangular) = [1 + 0.4 (L/B)] × Es(squre) (for L/B ≥ 10)
Cd = Depth factor obtained from Table 7.6
…… (7.30)
…… (7.31)

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.5 Settlement of Sandy Soil: Use of Strain Influence Factor

Settlement of Shallow Foundations
7.6 Settlement of Foundation on Sand Based on Standard
Penetration Resistance (Meyerhof’s Method)
• Meyerhof proposed a correlation for the net bearing pressure for foundations
with the standard penetration resistance, N60.
• The net pressure has been defined as: qnet = q – gDf
Where: q = stress at the level of the foundation.
• According to Meyerhof’s theory, for 25 mm of estimated maximum settlement:
1. For B ≤ 4 ft, qnet (kip/ft2) = N60 ÷ 4
2. For B > 4 ft, qnet (kip/ft2) = (N60 ÷ 6) × [(B + 1) / B]2
• Bowels proposed a modified form of bearing equations as follows:
1. For B ≤ 4 ft, qnet (kip/ft2) = (N60 ÷ 2.5) × Fd × Se
2. For B > 4 ft, qnet (kip/ft2) = (N60 ÷ 4) × [(B + 1) / B]2 × Fd × Se
Where:
Fd = depth factor = 1 + 0.33(Df/B)
B = foundation width, in feet
Se = settlement, in inches
–
–

Settlement of Shallow Foundations
• Bowels proposed a modified form of bearing equations as follows:
1. For B ≤ 4 ft, qnet (kip/ft2) = (N60 ÷ 2.5) × Fd × Se
Se = (qnet × 2.5) ÷ (N60 × Fd)
2. For B > 4 ft, qnet (kip/ft2) = (N60 ÷ 4) × [(B + 1) / B]2 × Fd × Se
Se = [(qnet × 4) ÷ (N60 × Fd)] × [(B + 1) / B]2
• In SI Units, the previous equations will be:
1. For B ≤ 1.22 m, qnet (kN/m2) = (N60 ÷ 0.05) × Fd × (Se/25)
Se = 1.25 qnet ÷ (N60 × Fd)
2. For B > 1.22 m, qnet (kN/m2) = (N60 ÷ 0.08) × [(B + 0.3) / B]2 × Fd × (Se/25)
Se = [(2 qnet) ÷ (N60 × Fd)] × [(B + 0.3) / B]2
Where: B = foundation width, in m
Se = settlement, in mm
N60 = the standard penetration resistance between the bottom
of the foundation and 2B below the bottom
7.6 Settlement of Foundation on Sand Based on Standard
Penetration Resistance (Meyerhof’s Method)

Settlement of Shallow Foundations
7.6 Settlement of Foundation on Sand Based on Standard
Penetration Resistance (Meyerhof’s Method)

Settlement of Shallow Foundations
7.14 Tolerable Settlement of Buildings
• In most instances of construction, the subsoil is not
homogeneous and the load carried by various shallow
foundations of a given structure can vary widely.
• As a result, it is reasonable to expect varying degrees of
settlement in different parts of a given building.
• The differential settlement of the parts of a building can
lead to damage of the superstructure.
• Hence, it is important to define certain parameters that
quantify differential settlement and to develop limiting
values for those parameters in order that the resulting
structures be safe.
• Fig. 7.27 shows a structure in which various foundations,
at A, B, C, D, and E, have gone through some settlement.

Settlement of Shallow Foundations
7.14 Tolerable Settlement of Buildings
• The settlement at A is AA’, at B is BB’, etc.
• Based on this figure, the definitions of the various parameters are as follows:
ST = total settlement of a given point
DST = difference in total settlement between any two points
D = relative deflection (i.e., movement from a straight line joining two
reference points)
a = gradient between two successive points
b = angular distortion = DST(ij)÷ lij
w = tilt
D ÷ L = deflection ratio
Note: lij = distance between points i and j

Settlement of Shallow Foundations
7.14 Tolerable Settlement of Buildings
• Various researchers and building codes have recommended allowable values
for the preceding parameters.
• A summary of several of these recommendations is presented next.
• Skempton and McDonald (1956) proposed the following limiting values for
maximum settlement and maximum angular distortion for building purposes:
Maximum settlement, ST(max)
• In sand 32 mm
• In clay 45 mm
Maximum differential settlement, DST(max)
• Isolated foundations in sand 51 mm
• Isolated foundations in clay 76 mm
• Raft in sand 51–76 mm
• Raft in clay 76–127 mm
Maximum angular distortion, bmax 1/300

Settlement of Shallow Foundations
7.14 Tolerable Settlement of Buildings
• On the basis of experience, Polshin and Tokar (1957) suggested the following
allowable deflection ratios for buildings as a function of L/H, the ratio of the
length to the height of a building:
D/L = 0.0003 for L/H ≤ 2
D/L = 0.001 for L/H = 8
• The 1955 Soviet Code of Practice allowable values are given in Table 7.10.

Settlement of Shallow Foundations
7.14 Tolerable Settlement of Buildings
• Bjerrum (1963) recommended the following limiting angular distortion, bmax for
various structures, as shown in Table 7.11.

Settlement of Shallow Foundations
7.14 Tolerable Settlement of Buildings
• The European Committee for Standardization has also provided limiting values
for serviceability and the maximum accepted foundation movements. (See
Table 7.12.)

Homework
7.4, 7.6, 7.10, 7.11, 7.12
Settlement of Shallow Foundations