CVLE451

Lecture 4
 Settlement
Compressibility of Soils

• A stress increase caused by the construction of foundations or other

loads compresses soil layers. The compression is caused by

• (a) deformation of soil particles,

• (b) relocations of soil particles, and
• (c) expulsion of water or air from the void spaces.
 Types of Settlement
In general, the soil settlement caused by loads may be divided into three broad categories:

1. Elastic settlement (or immediate settlement), which is caused by the elastic deformation of dry
soil and of moist and saturated soils without any change in the moisture content. Elastic settlement
calculations generally are based on equations derived from the theory of elasticity.

2. Primary consolidation settlement, which is the result of a volume change in saturated cohesive
soils because of expulsion of the water that occupies the void spaces.

3. Secondary consolidation settlement, which is observed in saturated cohesive soils and organic
soil and is the result of the plastic adjustment of soil fabrics. It is an additional form of compression
that occurs at constant effective stress.

The total settlement of a foundation can then be given as ST= Sc+Ss+Se

Sc primary consolidation settlement

Ss secondary consolidation settlement
Se elastic settlement
 Consolidation Settlement
• When a saturated soil layer is subjected to a stress increase, the pore water pressure is
increased suddenly.
• In sandy soils that are highly permeable, the drainage caused by the increase in the pore water
pressure is completed immediately.
• Pore water drainage is accompanied by a reduction in the volume of the soil mass, which results
in settlement.
• Because of rapid drainage of the pore water in sandy soils, elastic settlement occurs
simultaneously.
• When a saturated compressible clay layer is subjected to a stress increase, elastic
settlement occurs immediately.
• Because the hydraulic conductivity of clay is significantly smaller than that of sand, the excess
pore water pressure (u) generated by loading gradually dissipates over a long period.
• Thus, the associated volume change (that is, the consolidation) in the clay may continue long
after the elastic settlement. The settlement caused by consolidation in clay may be several times
greater than the elastic settlement
Calculation of Settlement from One-Dimensional
Primary Consolidation
• For NC clays

• For OC clays when 0 +c

• For OC clays when 0 +>c

 Problems on Consolidation Settlement
Problem 1

Skempton (1944)

LL=Liquid limit
Problem 2
Problem 3
Problem 4

Determine the consolidation settlement of the clay layer under the

given loading condition using the consolidation parameters obtained
in part (a).

e0=1.35
Problem 4

Top clay
• clay
Problem 5
Shape and depth factors for use in either the Hansen (1970) or Vesic
(1975) bearing-capacity equations

Table of inclination, ground, and base factors for the Vesic (1975)
equations
BEARING CAPACITY OF SHALLOW FOUNDATIONS
Terzaghi and Vesic Methods

Date April 20, 2020

Identification Example 6.4

Input Results
Units of Measurement Terzaghi Vesic
SI SI or E Bearing Capacity
q ult = 15,038 kPa 14,954 kPa
Foundation Information qa= 5,013 kPa 4,985 kPa
Shape SQ SQ, CI, CO, or RE
B= 4 m Allowable Column Load
L= 5 m P= 80,203 kN 79,755 kN
D= 2 m

Soil Information
c= 2000 kPa
phi = 0 deg
gamma = 109 kN/m^3
Dw = 4 m

Factor of Safety
F= 3

Copyright 2000 by Donald P. Coduto

SETTLEMENT ANALYSIS OF SHALLOW FOUNDATIONS
Schmertmann Method

Date April 20, 2020

Identification Example 7.6

Input Results
Units SI E or SI
Shape SQ SQ, CI, CO, or RE q= 44 kPa
B= 5 m delta = 7.24 mm
L= 5 m
D= 1 m
P= 500 kN
Dw = 20 m
gamma = 18 kN/m^3
t= 50 yr

Depth to Soil Layer

Top Bottom Es zf I epsilon strain delta
(m) (m) (kPa) (m) (%) (mm)
0.0 1.0
1.0 1.2 4902 0.1 0.119 0.0618 0.1236
1.2 1.4 4902 0.3 0.156 0.0812 0.1623
1.4 1.6 4902 0.5 0.193 0.1005 0.2010
1.6 1.8 4902 0.7 0.230 0.1199 0.2397
1.8 2.0 4902 0.9 0.267 0.1392 0.2784
2.0 2.2 7353 1.1 0.304 0.1057 0.2114
2.2 2.4 7353 1.3 0.341 0.1186 0.2372
2.4 2.6 7353 1.5 0.378 0.1315 0.2630
2.6 2.8 7353 1.7 0.415 0.1444 0.2888
2.8 3.0 7353 1.9 0.452 0.1573 0.3146
3.0 3.2 7353 2.1 0.490 0.1702 0.3404
SETTLEMENT ANALYSIS OF SHALLOW FOUNDATIONS
Classical Method

Date April 20, 2020

Identification Example 7.4

Input Results
Units SI E or SI
Shape CO SQ, CI, CO, or RE q= 66 kPa
B= 1.2 m delta = 48.90 mm
L= m
D= 0.5 m
P= 65 kN/m
Dw = 2.5 m
r= 0.85

Depth to Soil Layer

Top Bottom Cc/(1+e) Cr/(1+e) sigma m' gamma zf sigma c' sigma zo' delta sigma sigma zf' strain delta
(m) (m) (kPa) (kN/m^3) (m) (kPa) (kPa) (kPa) (kPa) (%) (mm)
0.0 0.5 18
0.5 0.6 0.13 0.04 300 18 0.05 310 10 57 67 2.82 2.820
0.6 0.7 0.13 0.04 300 18 0.15 312 12 57 68 2.61 2.606
0.7 0.8 0.13 0.04 300 18 0.25 314 14 56 69 2.41 2.409
 Problem on Design Chart (Past MT question)
A design chart is prepared for square footings
6000
to be designed for a project, showing bearing
capacity and settlement lines.
Design Chart 32 mm
(a) What should be the minimum footing size
5000
25 mm
for a column load of 1600 kN if tolerable
settlement is 25 mm?
B= 1.75 m
4000 19 mm
Column load, P, kN

(b) What would be the footing size for the

same column load, if the tolerable settlement
3000 was chosen to be 13 mm?
13 mm B=2. 75 m

2000
(c) What is the bearing capacity for a footing
of size 2.5 m x 2.5 m?
Pcolumn = 3800 kN
6.5 mm Therefore qall=3800/2.5x2.5= 608 kPa.
1000

(d) Is it economical to choose a footing of 3.5

m x 3.5 m to carry 2200 kN column load if the
0 tolerable settlement is 25 mm? If not what
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 size of footing would you recommend?
Footing width, B,m No. It is too large. 2.25 x 2. 25 m would be OK
 Problem on Design Chart (Past MT question)
6000
A design chart is prepared for a rectangular combined footing to 5500 50 mm
be designed for a specific project, showing bearing capacity and
settlement lines. The length ,L=5.0 m 5000 30 mm

(a) What should be the width, B of the footing to be able to carry 4500
two column loads of 1200 kN and 1800 kN and not to fail in bearing 4000 20 mm
capacity? P= 3000 kN, from the graph intersects the BC line at

∑Column loads, kN
B=2.25 m. 3500
3000
(b) If tolerable settlement is 30 mm, will this size be safe in
settlement? No. B has to be minimum 2.8 m. 2500
(c) What is the bearing capacity for a footing width, B of 2.5 m, if 2000
the tolerable settlement is 30 mm? qall = 2500 kN/2.5 x 5= 200 kPa 1500
(d) Is it economical to choose a footing width, B of 4.5 m to carry a 1000
total column load of 4500 kN, if the tolerable settlement is 30 mm?
500
B=4.0 is the min required. It can be bigger but not 4.5 m.
0
(e) If not, what size of footing would you recommend? 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
B=4-4.25 m Footing width, B (m)

(f) How much load a 4.5 m x 5 m footing can carry, provided

tolerable settlement is 30 mm? P= 5250 kN
Problem on Elastic Settlement 1/DAS
 Problem on PLT (Past MT question)

Results of a plate load test in sandy deposits are given in the figure. If the size of
the plate used is 0.3 x 0.3 m, q (kN/m2)
0 50 100 150 200 250 300 350 400 450
0
(a) Determine the ultimate bearing capacity of the soil-plate.
(b) What will be the settlement of the plate at this value?
(c) Determine the allowable bearing capacity of the soil-footing if he footing 10

size is 2 m x 2 m. (FS=2.5)
(d) Find the settlement of the footing at this allowable value. 20
(e) Would a footing of size 2 m x 2 m carry 1000 kN in this soil stratum?

Sp (mm)
(f) What will be the settlement of the footing under his load?
30
(g) Find the footing size for a tolerable settlement of 25 mm.

40

50

60

Figure 1. Plate load test result in sand.

 Problem on BC and Settlement (Past MT question)

(a) Correct the field N values to N60 using the

following field data: standard sampler,
safety hammer (USA), borehole diameter=
60 mm, rod length= 1.0 m. (5 points)
(b) Determine the allowable bearing capacity
of the foundation-uniform sand, using
Terzaghi’s approach. Is the chosen
foundation size safe to carry the given
column load? (10 points)
(c) Determine the elastic settlement of the
footing-sand system under the given load
using the strain-influence factor method
within a time period of 10 years
(Determine the soil stiffness, Es using the
average CPT results) (10 points)
(d) Determine the over-consolidation ratio
(OCR) of the clay using the appropriate
empirical approach. (2 points)
(e) Estimate the consolidation settlement of
the clay layer and determine the total
settlement to be expected under the given
load and foundation size. Is it an
acceptable limit if the tolerable settlement
is 25 mm? (13 points)
 Problem on Settlement and BC (Past MT question)

• For a given heterogenous soil profile 1

810 kN
2
810 kN
• Determine the allowable bearing capacity
(qall) of both footings 1 and 2, and state if 162 kNm 162 kNm
they can safely carry the applied loads.
You may use the general bearing capacity
formula from B.M. Das. (FS=3) (Hint: for
sandy soil use N60 in the determination of 1.0 m

 and Es). 0 0.1 0.2 Iz 0.3 0.4 0.5

0
• Determine the allowable bearing 3 m x 3m 3 m x 3m

capacity, qall from the SPT result. Use Clay

Sand
1

(N60)1. cu= 20 kPa

sat= 21.81 kN/m3
N60 =15 2
= 18 kN/m3
= 0⁰
• What will be the settlement of each 12 m Cc= 0. 15 6m
3

footing? State which one is more critical e0= 0.85 4

provided the tolerable limit is 25 mm. 5
(Assume time for settlement of sand is 10 6
years.)
•
 Problem on BC (Past MT question)

1000 kN

A certain column is to be supported on a 1.0 m deep rectangular

footing, subjected to a vertical downward load of 1000 kN, a 250 kN-m along
B dimension
horizontal load of 500 kN and a moment of 250 kN-m in the
direction of B . Soil properties: = 18 kN/m3, c= 15 kPa, = 25.
The groundwater table is at a depth of 1.5 m below the ground
1.0 m
surface. 3.0 m x 4.0 m
H= 500 kN

0.5 m
(a) Compute the allowable bearing capacity of the footing-soil = 18 kN/m3
system given, using the General Bearing Capacity Equation. sat= 21.81 kN/m3
c= 15 kPa
Use a factor of safety of 3.
= 25
(b) Is this size safe in bearing capacity?

(c) What will be the bearing capacity if the water table rises to
the ground level?

(d) Assume a ground inclination of 10◦ and determine the

allowable bearing capacity using Vesic’s equation.

(e) Could General BC Equation be used when ground inclination

exists?
 Problem on in situ test data analysis, BC and Settlement (Past MT question)

• A one-story building is to be supported by spread

footings on a soil profile as shown below.
Standard penetration test (SPT) has been
conducted at 1.5 m depth intervals in the sand
layer.
(a) Determine the average (N1)60 and correlate to
 (angle of internal friction angle) of sand
using Hatanaka and Uchida (1996) approach.
(b) Determine Young’s Modulus, Es using Kulhawy
and Mayne (1990) approach.
(c) Determine the allowable bearing capacity
using the average N60 of the sand layer. Is the
chosen foundation size safe to carry the given
column load.
(d) Determine the elastic settlement expected to
occur within a time span of 10 years.
•