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International Conference on Case Histories in (2013) - Seventh International Conference on

Geotechnical Engineering Case Histories in Geotechnical Engineering

03 May 2013, 10:30 am - 10:55 am

Shallow Foundations for Seismic Loads: Design Considerations

Vijay K. Puri
SIU Carbondale, IL

Shamsher Prakash
Missouri University of Science and Technology, prakash@mst.edu

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Puri, Vijay K. and Prakash, Shamsher, "Shallow Foundations for Seismic Loads: Design Considerations"
(2013). International Conference on Case Histories in Geotechnical Engineering. 6.
https://scholarsmine.mst.edu/icchge/7icchge/session14/6

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 SHALLOW FOUNDATIONS FOR SEISMIC LOADS: DESIGN CONSIDERATIONS
Vijay K. Puri Shamsher Prakash
Professor, Civil Engineering Professor Emeritus
SIU Carbondale, IL MST, Rolla ,MO
puri@engr.siu.edu prakash@mst.edu

ABSTRACT

The seismic design of foundations for structures depends on dynamic bearing capacity, dynamic settlements and liquefaction
susceptibility of soil. The dynamic bearing capacity problem has been attracting the attention of researchers during the last about fifty
years. Till today (2013), there is no accepted dynamic bearing capacity theory. Most analysis for design of shallow foundations under
seismic loads are based on the assumption that the failure zones in soil occur along a static failure surface. This is the pseudo-static
approach. An attempt has been made in this paper to summarize the currently available information on design of shallow foundations
under seismic loading. The case of a foundation resting on an upper non-liquefying layer overlying a layer susceptible to liquefaction
is also included. The methods for determining the foundation settlements are also discussed.

INTRODUCTION

Shallow foundations may experience a reduction in bearing liquefiable. Settlements of as much as 0.5-0.7m have been
capacity and increase in settlement and tilt due to seismic observed in loose sands in Hachinohe during the 1968
loading as has been observed during several earthquakes. The Tokachioki earthquake of magnitude 7.9. Settlements of 0.5 -
foundation must be safe both for the static as well for the 1.0 m were observed at Port and Roko Island in Kobe due to
dynamic loads imposed by the earthquakes. The earthquake the Hygoken Nanbu (M=6.9) earthquake. Foundation failures
associated ground shaking can affect the shallow foundation in may occur due to reduction in bearing capacity, excessive
a variety of ways: settlement and tilt, both in liquefying and non-liquefying soils.
(1) Cyclic degradation of soil strength may lead to
bearing capacity failure during the earthquake. CONSIDERATIONS IN FOUNDATION DESIGN
(2) Large horizontal inertial force due to earthquake may
cause the foundation to fail in sliding or overturning. Foundation design depends on the several factors like site
(3) Soil liquefaction beneath and around the foundation location and conditions, soil parameters and nature of applied
may lead to large settlement and tilting of the loads on the foundation . The foundation must be safe which
foundation. can be ensured by meeting the design criteria. Foundation
(4) Softening or failure of the ground due to must be safe for the static condition as well as for the seismic
redistribution of pore water pressure after an condition. The information on seismic design of shallow
earthquake which may adversely affect the stability foundations is presented below for four different cases:
of the foundation post-earthquake.
(1) Shallow Foundations on Soils Not Prone to
Bearing capacity failures of shallow foundations have been Liquefaction.
observed in Mexico City during Michoacan earthquake of (2) Settlement of Shallow Foundations on Soils Not
1985 (Mendoza and Avunit (1988), Zeevart (1991)) and in Prone to Liquefaction.
city of Adapazari due to 1999 Kocaeli earthquake (Karaca (3) Shallow Foundation on Soil Prone to Liquefaction.
(2001), Bakir et.al. (2002) and Yilmaz et. al (2004)).Typical (4) Settlement of Shallow Foundations on Soil Prone to
examples of bearing capacity failure in Adapazari are shown Liquefaction.
in Fig. 1. The surface soils at the site of foundation damage
belong to CL/ ML group which are generally considered non-

Paper No. OSP6 1

The pseudo-static approach is commonly followed for design Terzaghi’s Analysis
of foundation under seismic conditions. Therefore a brief
review of commonly used bearing capacity theories is given The static approach based on Terzaghi’s general shear failure
first. is shown in Fig.2. For a continuous or strip foundation, the
ultimate bearing capacity is obtained as:

qu = c Nc + q Nq + 0.5 γ B Nγ (1)

c = Cohesion of soil
γ = unit weight of soil
q = Surcharge Pressure = γ D
B=width of the foundation
D= depthe of the foundation.

(a)

Fig. 2 Failure mechanism suggested by Terzaghi (1943)

Nc, Nq, Nγ = Bearing capacity factors (depend only on the soil

friction angle ø) . These bearing capacity factors can be
obtained from Table 1.

The ultimate bearing capacity for various foundation shapes

can be obtained as follows:
(b)
For square footing:
Fig.1 Examples of Bearing Capacity Failures of Shallow qu = 1.3 c Nc + qD Nq + 0.4 γ B Nγ (2)
Foundations in Adapazari (Yilmaz et. al. 2004).
For circular footing:
STATIC CASE qu = 1.3 c Nc + qD Nq + 0.3 γ B Nγ (3)

The static loads covers loads like self-weight of the structure, For rectangular footing:
soil loads, surcharge loads and live loads. The calculations
then involve estimation of the safe bearing capacity of the qu = c Nc (1+0.3 B/L) + qD Nq + 0.4 γ B γ (4)
footing and the amount of settlement. The conventional design
procedure involves selection of allowable bearing capacity as Where B= width or diameter of the footing and L=length of
the smaller of the following two values; the safe bearing the footing.
capacity, based on ultimate capacity and the allowable bearing
pressure and based on tolerable settlement. Terzaghi (1943), Meyerhoff’s Analysis
Meyerhof (1951), Hansen (1970), Vesic (1973), Kumar
(2003), Dewaikar and Mohapatro (2003) and many others The Terzaghi’s (1943) equation for ultimate bearing capacity
have done research in this area and either proposed new was modified by Meyerhoff (1963) to give a more general
design equations or proposed correction factors for the solution. The value of qu is obtained as (Meyerhoff ,1963):
prevalent equations.
qu = c Ncsc dc ic +q Nq sqs dq iq + 0.5 γ B Nγ sγ dγ iγ (5)

Paper No. OSP6 2

 sc, sq, sγ =Shape Factors The shape, depth and inclination factors can be calculated
dc, dq, dγ = Depth Factors using equations given in Table 3.
ic, iq, iγ = Load Inclination Factors.
SEISMIC CASE
The values of bearing capacity factors for use in Eq. 5 may be
obtained from Eqns. 6 through 8. Shallow Foundation on Soils Not Prone to Liquefaction

Table 1. Terzaghi’s Bearing Capacity Factors (General Shear The design of foundations in earthquake prone areas requires
Failure) different design approach involving earthquake forces along
with the usual dead and live loads considered in the static
analysis. The design approach involving limit equilibrium
ø Nc Nq Nø
method or equivalent static method with consideration of
0 5.7 1 0 pseudo-static seismic forces along with other static forces has
5 7.3 1.6 0.5 been used as a primary method for the design of shallow
10 9.6 2.7 1.2 foundations in seismic areas. Reduction in bearing capacity of
15 12.9 4.4 2.5 the underlying soil and increase in settlement and tilt are the
main causes of failure of a shallow foundation when subjected
20 17.7 7.4 5
to seismic loading (Sarma and Iossifelis (1990), Richards et.
25 25.1 12.7 9.7 al. (1993) and Budhu and Al-Karni (1993), Kumar and Kumar
30 37.2 22.5 19.7 (2003) Choudhury and Rao (2005)). So, the main interest lies
34 52.6 36.5 35.0 in first determining the soil parameters and then soil-structure
35 57.8 41.4 42.4 interaction and seismic behavior to determine the nature of
40 95.7 81.3 100.4 failure and finally, estimate the seismic bearing capacity of the
footing as accurately as possible. A good design approach
45 172.3 173.3 297.5 would require consideration of all possible factors such as soil
parameters, seismic vulnerability, nature of applied loads and
Nq = eπtanφ tan2 (45⁰ + Ø /2) (6) seismic soil-foundation interaction for an effective estimation
Nc = (Nq -1) cot Ø (7) of the seismic bearing capacity.
Nγ = (Nq – 1) tan (1.4 Ø) (8)

Table 2. Meyerhof’s Shape, Depth and Inclination factors

Shape Factors Depth Factors Inclination Factors

Sc= 1 + 0.2 Kp dc = 1+ 0.2 √Kp ic = iq = (1 - )2
°

(i) for ∅ = 0° (i) For ∅ = 0° iy = (1 - ) 2

∅

Sq = Sγ = 1.0 dq = dy =1.0
(ii) For ∅ 10° (ii) For ∅ 10° α angle of resultant measured
from vertical axis
Sq = Sγ = 1 + 0.1 Kp dq = dy = 1 + 0.1 √Kp
∅
Kp = tan2 45°

Pseudo-static Approach. This analysis technique uses limit loads and moments, then it may be designed as eccentrically
equilibrium methods in which the inertial forces generated on loaded foundation. The eccentricity ‘e’ is defined as;
the structure due to shaking of the ground are simply
accounted for by an equivalent unidirectional horizontal and (9)
vertical forces, is termed as the Pseudo-static Approach. The
equivalent forces are taken as the mass of the body multiplied
In which, V = vertical load and,
by coefficients of acceleration for both horizontal and vertical
M = Moment.
directions. These coefficients are termed as seismic
acceleration coefficients, Kh and Kv, for horizontal and vertical
The effective width 2
direction respectively. The horizontal force may also produce
a moment. The foundation may thus, be treated as being
The ultimate bearing capacity may be obtained using Eqs. 1-5
subjected to combined action of vertical and, horizontal loads
and moments. If the foundation is subjected only to vertical by replacing B with

Paper No. OSP6 3

When the foundation is subjected to a combination of vertical new approach, which also used the limit equilibrium method
loads, horizontal loads and moments, it may be designed as to find the seismic bearing capacity factors including the
foundation subjected to inclined eccentric load. seismic forces on both soil and structure and considered planar
and log-spiral failure surfaces below the foundation.. They
The angle inclination with the vertical ‘α’ is given by: also calculated seismic bearing capacity factors for cohesion,
surcharge and unit weight of soil for various soil friction
(10) angles and seismic acceleration coefficients. Unlike previous
researches, Choudhury and Rao (2005) considered the seismic
acceleration in both horizontal and vertical directions and also
In which, H = horizontal load.
determined the critical failure surface.
Some of these significant developments in estimation seismic
In this case Eq. 5 should be used to calculate the value of the
bearing capacity determination are discussed below.
ultimate bearing capacity. It may be noted that in this
approach, the bearing capacity is estimated using the static
Estimation of Seismic bearing capacity
bearing capacity factors and any effects of the earthquake
loads on the supporting soil are not considered. This implies
Richards, Elms and Budhu (1990, 1993)
that the failure surface below the foundation for the
earthquake load is assumed to be the same as for the static
Richards, Elms and Budhu’s (1990) developed the concept of
case. The estimated bearing capacity should, therefore, be
‘Dynamic Fluidization of Soils’ which implies an increase in
considered as approximate only. Attention has been given in
the shear flow in soil with an increase in ground acceleration.
recent years to better define the failure surface below the
They observed that, although dynamic fluidization looks
foundation for the seismic case and estimate the bearing
similar to liquefaction, it is an altogether different
capacity factors and still following the pseudo-static approach.
phenomenon. Their work shows that in dynamic fluidization
This is discussed below:
the shear flow takes place at finite levels of effective stress,
whereas liquefaction is accompanied by the reduction in the
Developments in Determination of Seismic Bearing Capacity
effective stress to zero due to increase in pore pressure. The
difference is also shown in the displacements, which are
Sarma and Iossifelis (1990), Richards et. al. (1993) and
unbounded in case of liquefaction and finite and incremental
Budhu and Al-Karni (1993) made changes in Meyerhof’s
in case of fluidization. Richards, Elms and Budhu (1993) used
(1963) model and used a different approach based on limit
the concept of dynamic fluidization of soil to formulate
equilibrium method with consideration of the upper bound
equations for the seismic bearing capacity of foundation. They
solutions only. These solutions were dependent on the
modified Prandl’s bearing capacity analysis using planar
predetermined failure mechanism. Pecker and Salencion‘s,
failure surfaces.
(1991) considered the soil inertial force to be independent to
correctly account for its influence. They (Pecker and
Budhu and Al_Karni (1993)
Salencion ; 1991) considered this inertial force to estimate the
reduction in the bearing capacity of the foundation and on top
Logarithmic failure surfaces shown in Fig. 3 were assumed by
of that they also considered the same seismic horizontal
Budhu and Al-karni (1993) to determine the seismic bearing
coefficient Kh for both soil and structure . This led to
capacity of soils. They suggested modifications to the
somewhat erroneous conclusions. This approach was later
commonly used (Terzagh’s ) equations for static bearing
modified by Dormieux and Pecker (1995), who determined
capacity to obtain the dynamic bearing capacity as follows:
load inclination and eccentricity on the foundation to be the
main cause for the reduction of bearing capacity rather than
qud = c Nc sc dc ec +q Nq sq dq eq + 0.5 γ B Nγ sγ dγ eγ (11)
soil inertial force. Moreover, unlike previous researches which
used limit equilibrium method (Dormieux and pecker (1995),
Where,
Soubra (1997, 1999)) used upper bound limit analysis for the
estimation of the seismic bearing capacity factors. Later a
Nc , Nq, Nγ are the static bearing capacity factors.
new approach was introduced by Kumar and Rao (2002, 2003)
sc, sq, sγ are static shape factors.
to determine seismic bearing capacity of footing using method
dc, dq, dγ are static depth factors
of characteristics. Their analyses also didn’t consider the
ec , eq and eγ are the seismic factors estimated using following
effect of the vertical component of the ground acceleration.
equations
Up to this time, the effect of ground shaking was only
(12)
considered in the horizontal direction, in other word, only
horizontal acceleration due to earthquake was taken into

ec  exp  4.3k hl  D 
account. Among others, Sarma and Iossifelis (1990), Richards   5.3k h1.2  (13)
et. al. (1993) and Budhu and Al-Karni (1993), Kumar and eq  (1  k v ) exp   
Kumar (2003) assumed focus of the log spiral surface to be at   1  k v 
the edge of the footing. Choudhury and Rao (2005) proposed a 2   9k 1.2  (14)
e  (1  k v ) exp   h 
3   1  k v 

Paper No. OSP6 4

 Fig. 3. Failure Surfaces used by Budhu and al-karni (1993)
for Static and Seismic Case

Where, Fig. 5. Effect of kh on NqE/Nq for Ø = 30° (Budhu and Al-

Karni;1993)
Kh and Kv are the horizontal and vertical acceleration
coefficients respectively.

H= depth of the failure zone from the ground surface and

H 0.5B  
D exp tan    D f (15)
C     2 
cos  
 4 2 

Df = depth of the footing and

φ = angle of internal friction
c=cohesion of soil

Budhu and Al-Karni’s (1993) also compared the effects of Kh Fig. 6. Effect of kh and kv on NqE/Nq for ϕ =30̊ ; (Budhu and Al-
and Kv on NcE/Nc , NqE/Nq and NᵧE /Nᵧ for various angles of Karni ; 1993)
friction and also with results of other researchers. The
comparisons are shown in Figs. 4 through 8.

Fig. 7. Effect of kh on NγE/Nγ for Various Ø values ( Budhu

and Al-Karni ;1993)
Fig. 4. Effect of kh on NcE/Nc for Ø = 30° (Budhu and Al- Chaudhury and Rao (2005, 2006)
Karni, 1993)
A study of the seismic bearing capacity of shallow strip
footing was conducted by Chaudhury and Subba Rao
(2005,2006). The failure surfaces for the static and seismic
case are shown in Fig. 9. They used the limiting equilibrium
approach and the equivalent static method to represent the
seismic forces and obtained the seismic bearing capacity
factors.

Paper No. OSP6 5

 γ
α ϕ α ϕ
ϕ ϕ
Nγd =
α α

- (19)
α α

α –ϕ α ϕ
ϕ ϕ

Ncd = α α (20)
α ϕ α α α
α α ϕ α α

α ϕ α ϕ
ϕ ϕ
Nqd = (21)
α α

Fig. 8. Effect of kh and kv on Nγd/Nγ for various angles of γ

α ϕ α ϕ
friction by Budhu and Al-Karni’s (1993) Nγd =
ϕ ϕ

α α

- (22)
α α

Where, ϕ values considered in the analysis are to satisfy the

relationship given by

ϕ > tan-1

The variation of bearing capacity factors for various values

seismic coefficients given by Chaudhury and Rao (2005,
2006) are shown in figures 10, 11 and 12.

Fig. 9. Failure mechanism Assumed by Chaudhury and Rao

(2005, 2006)

Using equilibrium of all vertical forces Choudhury and Rao

(2005, 2006) formulated the final expression for the ultimate
seismic bearing capacity qud.

qud = c Ncd + q Nqd + 0.5 γ B Nγd (16)

Where, Ncd, Nqd and Nγd are seismic bearing capacity factors
which are quantified using equilibrium of all the forces in the
horizontal direction. The expressions are as follows:

α –ϕ – α ϕ
ϕ ϕ

Ncd = α α (17)
α ϕ α α α
α α ϕ α α

α ϕ α ϕ
ϕ ϕ
Nqd = (18) Fig. 10. Variation of Ncd with kh. by Chaudhury and Rao
α α
(2005, 2006)

Paper No. OSP6 6

 Hence, the comparison concludes that Chaudhury and Rao’s
work yields conservative seismic bearing capacities of a
shallow footing.

Fig. 13. Comparison of Ncd by Chaudhury and Rao (2005,

2006) with other studies in seismic case for ø = 30° and kv = 0

Fig. 11. Variation of Nqd with kh by Chaudhury and Rao (2005,

2006)

Fig. 14. Comparison of Nqd by Chaudhury and Rao (2005,

2006) with other studies in seismic case for ø = 30° and kv = 0

Fig. 12. Variation of Ncd with kh by Chaudhury and Rao (2005,

2006)

Chaudhury and Rao (2005, 2006) also made a comparison of

seismic bearing capacity factors obtained by them with those
reported by other researchers. Typical such comparisons with
other investigations are shown in Figs.13, 14 and15.

It is quite apparent from the comparisons shown in Figs. 13-15 Fig. 15. Comparison of Nγd by Chaudhury and Rao (2005,
that the values for the seismic bearing capacity factors 2006) with other studies in seismic case for ø =
suggested by Chaudhury and Rao (2005, 2006) are somewhat
smaller than those suggested by other previous researchers.

Paper No. OSP6 7

Code Provisions agR = the reference peak ground acceleration on type A ground
γI = the importance factor
The relevant guidelines given by Eurocode and International S = the soil factor can be obtained from Table 3 as defined in
Building Code regarding design of foundations in seismic EN 1998-1:2004, 3.2.2.2
areas are briefly enumerated here. Unlike Euro-code 8, IBC
2006 doesn’t provide us with the equations for the bearing Table 3. The Soil Factor (S) for different elastic response
capacities but rather provides prerequisites in selecting spectra
parameters for designing foundation under earthquake loads.
Soil Factor ( S )
Eurocode 8 - Part 5. Eurocode 7 mainly covers the Type 2
specifications for the static geotechnical designs. The Ground Type 1 elastic
elastic
Type response
dynamic design and analyses are covered in Eurocode 8 and response
the earthquake resistive design criteria for foundations, spectra
spectra
retaining structures and geotechnical aspects are covered in A 1.0 1.0
Part 5 of Eurocode 8. The code suggests the procedure to B 1.2 1.35
check the stability of the shallow strip foundation under C 1.15 1.5
seismic bearing capacity failure for different types of soils. D 1.35 1.8
E 1.4 1.6
The general expression for the check is given as

and constraints are to be satisfied.

For purely cohesion-less soil

(23)

Where, (26)
F̅ is given by

F̅ = dimensionless inertia force

NEd, VEd, MEd = the design action effects at the foundation
level (27)
γRd = model partial factor
qud = Ultimate bearing capacity of the foundation under a av = may be taken equal to 0.5 ag.S
vertical centered load Nγ = the bearing capacity factor, as a function of the shearing
a, b, c, d, e, f, m, k, k’, cT, cM, c’M, β, γ are numerical angle Ø
parameters depending on type of soils
The expressions and values for these entities are defined later
for different types of soils. and constraint is to be satisfied.

For purely cohesive soil The values for the numerical parameters and model partial
factor are given in Tables 4 and 5.

In most situations F̅ may be taken as being equal to 0 for

(24) cohesive soils and may be neglected for cohesion-less soils if
Where, ag.S < 0.1g (i.e. if ag.S < 0.98 m/s2)
c̅ = the un-drained shear strength of soil, cu, for cohesive soil,
or the cyclic un-drained shear strength, τu, for cohesion-less IBC (2006). IBC 2006 provides provisions for designing
soils foundations under seismic loading conditions closely in
relation to ASCE 7. Chapter 18 of IBC 2006 deals with Soils
γRd = the partial factor for material properties and Foundations. As per ASCE code the structures are
categorized into six Seismic Design Categories A, B, C, D, E
Now, F̅ is given by and F. These categories are based on the use, importance and
size of the structures. The IBC 2006 makes use of this
categorization and suggests necessary provisions for structures
and footing falling in the respective categories.
(25)
ρ = the unit mass of the soil
ag = γI agR = the design ground acceleration on type A ground

Paper No. OSP6 8

 Table 4. Values of Numerical Parameters Eurocode 8-5  The potential for liquefaction and loss in soil
strength shall be evaluated for site peak
Purely Purely ground acceleration magnitudes and source
cohesive soil cohesionless soil characteristics consistent with the design
a 70 0 92 earthquake ground motion. The peak ground
motion is as specified by ASCE 7.
b 29 1 25
c 14 0 92 Other provisions
d 81 1 25  Interconnected ties are to be provided for the
e 21 0 41 individual spread footings supported on the
soil defined as Site Class E or F. IBC2006
f 44 0 32
specifies standards for these ties to be
m 21 0 96 capable of bearing a force equal to the
k 22 1 00 product of the larger footing load times the
k' 00 0 39 seismic coefficient, divided by 10 unless it is
cT 00 1 14 demonstrated that equivalent restraint is
cM 00 1 01 provided by reinforced concrete beams
within slabs on grade or reinforced concrete
c'M 00 1 01 slab on grade.
β 57 2 90
γ 85 2 80 Settlement of Shallow Foundations on Soils Not Prone to
Liquefaction

Table 5. Values of the model partial factor γRd Eurocode 8-5 The settlement of the foundation due to applied loads is one of
the most important considerations in ensuring the safe
Medium- performance of the supported structure. A foundation
Loose Loose Non subjected to seismic load may undergo vertical settlement, tilt
dense to Sensitive
dry saturate sensitive and may also experience sliding. The settlement and tilt of the
dense clay
sand d sand clay foundation is commonly obtained by using same procedures as
sand
1.00 1.15 1.50 1.00 1.15 for a foundation subjected static vertical loads and moments.
The following methods can be conveniently used in this case.
For Seismic Design Category C
IBC 2006 suggests for conducting an investigation Prakash and Saran (1977) Method
and evaluation of the potential earthquake hazards
like slope instability, liquefaction and surface rupture A procedure to determine the settlement and tilt of foundations
due to faulting or lateral spreading for the structures subjected vertical load and moment was developed by Prakash
determined to be in the this category. and Saran (1977) which uses Eqs. (28) and (29)

For Seismic Design Category D, E or F 1.0 1.63 2.63 5.83 (28)

According to IBC 2006 the structures falling under 1.0 2.31 22.61 31.54 (29)
the Seismic Design Category D, E or F are subject to
additional soil investigation requirements on top of
that suggested by Seismic Design Category C. These
Where, So = settlement at the center of the foundation for
investigations can be listed as follows:
vertical load only
 A determination of lateral pressures on
basement and retaining walls due to
Se = settlement at the center of the eccentrically
earthquake motions.
loaded foundation (combined ction of vertical load and
 Assessment of potential consequences of moment)
any liquefaction and degradation of soil Sm = maximum settlement of the eccentrically loaded
strength along with estimation of differential foundation
settlement, lateral movement and reduction B= width of the foundation
in bearing capacity.
e= eccentricity given by e = ,
 This provision also addresses mitigation
measures. Measures range from soil Q = vertical load and M = moment.
stabilization to the selection of appropriate
type and depth of foundation The tilt of the foundation ‘t’ may then be obtained from the
following equation:

Paper No. OSP6 9

 2. There must be an adequate thickness of un-
sin (30) liquefiable soil layer to prevent damage due to sand
boils and surface fissuring. Otherwise, there could be
damage to the shallow foundations.
Se , Sm and ‘t’ can thus be obtained if So can be determined.
Prakash and Saran (1977) have suggested the use of plate load
If the above two conditions are not met, then the site-soil
test to determine So. The value of So can also, be obtained any
condition is highly susceptible to liquefaction and requires
other procedure commonly used for determination of elastic
special design considerations such as the use of deep
settlement of foundations.
foundations or ground modification.
If the above two requirements are met, then there are two
Richards et al, (1993) Method
different types of bearing capacity analysis that can be
performed.
Richards et al, (1993) suggested the use of the following
equation to estimate the seismic settlement of a strip footing.
Type I: Punching shear Analysis.
2 k 4 Type II: Reduction in Bearing Capacity due to Build up of
V h*
S E q ( m )  0 .1 7 4 ta n  A E (31) Pore water Pressure.
Ag A
where SEq = seismic settlement (in meters) , V = peak velocity LOAD
for the design earthquake (m/sec), A = acceleration coefficient
for the design earthquake, g = acceleration due to gravity (9.81
m/sec2). The value of tan αAE in Eq (31) depends on φ and
kh*. Figure 16 shows the variation of tan αAE with kh* for φ
values from 15° - 40°.
Unliquefiable soil
layer
f f

Liquefied soil layer

Fig. 17. Schematic Sketch Illustrating Punching Shear

These two analyses are discussed below:

Type I: Punching shear Analysis. Figure 17 shows the concept

of punching shear failure occurring in a non-liquefying upper
layer which is underlain by a liquefying layer. In this analysis,
the footing will punch vertically downwards into the liquefied
Fig. 16. Variation of tan αAE with kh* and φ (Richards et al soil. This situation will arise when the upper non-liquefying
1993) layer is thin. The factor of safety FS against bearing capacity
failure may be calculated as follows:
Whitman and Richart (1967) and Georgiadis and Butterfield
(1988) have suggested procedures for determining the FS= R/P (32)
settlement and tilt of the foundations subjected to static
vertical loads and moments. For Strip Footing
Where, R= shear resistance of soil per unit length of the
Shallow Foundations on Soil Prone to Liquefaction footing

The most common cause of seismic bearing capacity failure is R = 2T*τ (33a)
the liquefaction of the underlying soil. Localized failure due to
punching can also lead to seismic bearing capacity failure. τ = shear strength of unliquefiable soil layer
Liquefaction analysis can help determine the soil layers T= vertical distance from the bottom of footing to the
susceptible to liquefaction. This analysis involves the top of liquefiable oil layer, m
following two requirements:
P= Load per unit length of the footing. This load
1. The foundation must not bear directly on soil layers includes dead, live and seismic loads acting on footings as
that will liquefy during the design earthquake. Even well as weight of footing itself.
the lightly loaded foundations can sink in to the
liquefied soil.

Paper No. OSP6 10

For Spread footing: Since the liquefied soil layer has zero shear strength, c2=0 &
c2/c1 =0 for use in Fig. 18.
R= 2(B+L) T* τ (33b)
B STRENGTH PROFILE

There are two unknown parameters in the equations of factor C2 / C1

of safety for each of the two types of footing, i.e. vertical q

distance from the bottom of footing to the liquefied soil layer D
LAYER 1
and the shear strength of un-liquefied soil layer. C1
T
If the un-liquefiable upper soil layer consists of cohesive soil
(eg: clay) or clayey sand, using total stress analysis, the
following equations may be used to obtain τ. LAYER 2
C2

For clays: (a)

τ = su (34a)
RATIO C2 / C1

0 0.2 0.4 0.6 0.8 1.0

For clayey sands: 5.53
τ= c+ h tanØ (34b) 5

5
1.

0
Where, su = undrained shear strength of cohesive soil

1.
4

BEARING CAPACITY FACTOR, NC

c & Ø are undrained shear strength parameters
VALUE OF T/B

25
0.
5
= Normal stress on the failure surface.

0.
h

0
3

Since shear surfaces are vertical, the normal stresses acting on

shear surfaces will be the horizontal total stress. For cohesive 2
soil, h may be taken as σv/2.
1
If the unliquefied soil layer is cohesionless (sand), using
effective stress analysis,
0
τ = ’h tanØ’ (b)
= ko ’v tanØ’ (35)
Fig. 18. Bearing Capacity Factor Nc for two layer soil system
Where ’h = horizontal effective stress (Day, 2002)
Ø’ = effective angle of internal friction.
The value for ultimate load Qult can be determined by
v’= Effective vertical stress at (T/2 + footing depth from the multiplying the qult and the footing dimensions. FS= Qult / P
ground surface) Reduction in Bearing Capacity due to Build Up of Pore water
Pressure.
Type II Reduction in Bearing Capacity due to Build Up of
Pore Water Pressure. Terzaghi bearing capacity theory Granular Soil. There are many factors involved in the
discussed earlier may be conveniently used for this purpose. determination of bearing capacity of soils that may liquefy
For the situation of cohesive soil layer overlying sand which is during design earthquake. Distance from of bottom of footing
susceptible to liquefaction, a total stress analysis is used and to the top of the liquefied soil layer is an important
the equations used are: consideration. This parameter is difficult to determine for soil
that is below ground water table and has factor of safety
For strip footing, qult= cNc = Su Nc (36) against liquefaction that is slightly greater than one. The
For spread footing, qult=su Nc (1+0.3 B/L) (37) reason being earthquake might induce liquefaction or partial
liquefaction of the upper layer as well. In addition to vertical
Where su= undrained shear strength=cohesion c loads, footing might also be subjected to the static and
Nc = bearing capacity factor determined from Fig. 18 for the dynamic lateral loads during earthquake. They are usually
condition of un-liquefiable cohesive soil layer that is expected dealt with separately. There may be reduction in the shear
to liquefy during design earthquake. In Fig. 18, T represents strength of the upper dense layer of granular soil due to an
the vertical distance from the bottom of the footing to the top increase in the pore water pressure following liquefaction of
of the liquefied soil layer. the lower layer. Sands and gravels that are below the ground
water table may have a factor of safety against liquefaction
B= width of footing & L= Length of footing greater than 1.0 but less than 2.0. If the factor of safety against
liquefaction is greater than 2.0, the earthquake induced pore

Paper No. OSP6 11

water pressures will typically be small enough so that their conditions. Liquefaction is evaluated and empirical
effect can be neglected. For cohesionless soils, Terzaghi’s correlations developed for free field conditions are used. But,
ultimate bearing capacity can be expressed as: the presence of superstructure results in a significantly
different response than that under free-field conditions.
qult= (½) ɣ BNɣ (38)
Settlement of Foundations in Liquefying Soil
If the ground water table is at the bottom of the footing or
closer to the bottom of the footing, the effective unit weight ɣb Simplified Procedures for the Evaluation of Settlements of
used in place bulk unit weight ɣt in Eq. (37). In order to Structures During Earthquakes (Ishihara and Tokimatsu;
account for the increase in the excess pore water pressure 1988). A procedure to determine earthquake induced
during the design earthquake, the term (1- ru) can be inserted settlements of structures on saturated sand deposits due to pore
in Eq. (37) which becomes: water pressure generation was developed by Ishihara and
Tokimatsu (1988). To investigate the effectiveness of the
qult= (½) (1- ru )ɣb BNɣ (39) proposed method, the observed values of settlement of
structures were also compared with the values obtained from
The value for ru can be obtained from the plot in Fig. 19 which the proposed method.
is a plot of the pore water pressure ratio, i.e. ru=ue/ ’ versus
the factor of safety against liquefaction. To find ru, the factor The total settlement of the structure due to earthquake shaking
of safety against liquefaction (FSL) of soil located below the (Sst) is given as:
bottom of the footing must be determined. Equation (39)
established for the case with factor of safety against Sst = Sv + Se (40)
liquefaction greater than 1. If the value of (FSL) is less than 1,
the foundation design is not feasible unless counter-measures where, Sv = settlement due to volumetric strain caused by
against liquefaction failure are adopted. earthquake shaking
Se = immediate settlement due to change in soil
modulus
Knowing the value of the cyclic stress ratio developed in the
soil during earthquakes and normalized (N1)60 value, the
volumetric strain can be determined from Fig.20 below.

Fig.19. Residual Excess Pore water Pressure ru versus Factor

of Safety against Liquefaction. (Marcuson Hynes, 1990)

There is a need to be careful when dealing with foundation

design in soils that may liquefy during the design earthquake.
The site could experience liquefaction induced lateral
spreading and flow slides. If the soil is softened and gets
liquefied, ground deformations occur rapidly in response to
static or dynamic loading. The amount of deformation is a
function of loading conditions, amplitudes and frequencies of
seismic waves, the thickness and extent of the liquefiable
layer, the relative density and permeability of the liquefied Fig. 20: Cyclic Stress ratio, (N1)60 vs. Volumetric Strain
sediment and the permeability of surrounding sediment layers. (Tokimatsu and Seed: 1987)
Despite the severity of damages, there has been relatively little
progress towards the development of consistent methodology The relationship shown in Fig. 20 was proposed earlier by
for the design of foundation systems under these Tokimatsu and Seed (1987) which is based on the controlling
circumstances. Usually, the presence of superstructure is factors like maximum pore pressure generated before initial
neglected and calculations are performed for free-field liquefaction and the maximum shear strain after liquefaction.

Paper No. OSP6 12

The cyclic stress ratio developed in the soil during earthquakes can’t be accurately determined. Accordingly, they have
is given as: estimated an approximate relationship based on the field
observations as given in Eq. (43).
= 0.65 rm (41)
. Sst = Sv .rb (44)

where, = Equivalent Shear Stress Ratio induced by the Where, rb = scaling factor concerning the shear deformation
. which may be obtained from Fig. 22. Based on the studies of
earthquake shaking of M = 7.5 Niigata earthquake (1964) done by Yoshimi and Tokimatsu
1977, the importance of large width of the structure (compared
amax = maximum horizontal acceleration at the ground to the thickness of the liquefied layer) on reducing the
surface liquefaction induced settlement can be noted very clearly from
figure 21. It can be seen from Fig (22) that appreciable
σo =total overburden pressure at the depth considered. settlement occurred where the width ratio was less than 2
rd = Stress reduction factor that varies with depth. whereas the settlement was small and constant where the
rm = Scaling factor for a stress ratio concerning the width ratio exceeds 2 or 3. Ishihara and Tokimatsu (1988)
magnitude of earthquake . developed parameter ‘rb’ that is equal to the settlement ratio
normalized by the settlement ratio at width ratio equal to 3.
By integrating the volumetric strains for different depths, the They found the computed values generally consistent with the
settlement of the structure can be computed. For values of M observed values, and proposed that this simplified method of
other than 7.5, magnitude scaling factors may be used. computation can be used as a first approximation to predict
Ishihara and Tokimatsu (1988) suggested that the immediate earthquake induced settlement of structures.
settlement caused by the change in soil modulus can be
computed as:

Se = q .B .Ip (42)

Where, q = contact pressure of the structure

B = width of the structure
Ip = coefficient concerning the dimension of the
structure, thickness of soil layer and poisson’s ratio of soil.
E1 and E2 = Young’s Modulus of soil before and
during earthquake shaking respectively.

The reduction in the shear modulus of soil during earthquake

shaking can be computed based on the effective shear strain
(γeff) induced in the soil as given in Eq. (43) below:

γeff = 0.65. . σo .rd . (43)

where, Gmax= Shear modulus at low shear strain level

Geff = effective shear modulus at induced shear strain level
amax = maximum horizontal acceleration at the ground surface
σo =total overburden pressure at the depth considered
Fig. 21. Determination of induced Shear Strain (Tokimatsu
Using the computed value of γeff in Fig. 21, the value and Seed, 1987)
of corresponding effective shear strain (γeff) is obtained and
Geff can be computed. Ishihara and Yoshmine (1992). Ishihara and Yoshmine (1992)
have provided a chart to estimate the post-liquefaction
They have further emphasized that the change in effective volumetric strain of clean sand as function of factor of safety
stress due to pore pressure generation as well as the shear against liquefaction. This chart is shown in Fig. 23. This chart
strain level developed in the soil are highly influenced when can be easily used if any of the corrected SPT values, cone
there is liquefaction and therefore, do not recommend to use resistance at the site or the maximum cyclic shear strain
eq. (39) to compute the settlement of structure. In such induced by the earthquake are known.
condition, the settlement of the structure is affected due to the
shear deformation of the soil strata and thus young’s modulus

Paper No. OSP6 13

 For deposits consisting of various layers of saturated sand, the
settlement for each layer may be calculated and the total
settlement obtained as the sum of the settlements of each
layer.

Additional Comments on Foundation Performance on

Liquefied Soil

Gazetas et al (2004) studied tilting of buildings in it1999

Turkey earthquake. Detailed scrutiny of the “Adapazari
failures” showed that significant tilting and toppling were
observed only in relatively slender buildings (with aspect
ratio: H / B > 2), provided they were laterally free from other
buildings on one of their sides. Wider and/or contiguous
buildings suffered small if any rotation. For the prevailing soil
conditions and type of seismic shaking; most buildings with H
Fig. 22: Scaling factor vs. width ratio / B > 1.8 overturned, whereas building with H / B < 0.8
essentially only settled vertically, with no visible tilting.
The chart in Fig. 23 is convenient to use. The factor of safety Figure 24 shows a plot of H/B to tilt angle of building. Soil
against liquefaction failure is calculated and then the profiles based on three SPT and three CPT tests, performed in
volumetric strain is determined using value of relative density front of each building of interest, reveal the presence of a
of the deposit or its the corrected standard penetration number of alternating sandy-silt and silty-sand layers, from the
resistance or cone penetration resistance. The settlement of the surface down to a depth of at least 15 m with values of point
deposit may then be calculated as: resistance qc ≈ (0.4 – 5.0) MPa . Seismo–cone measurements
revealed wave velocities Vs less than 60 m/s for depths down
∈ (45) to 15 m, indicative of extremely soft soil layers. Ground
In which, S= settlement acceleration was not recorded in Tigcilar. Using in 1-D wave
H= thickness of the deposit propagation analysis, the EW component of the Sakarya
and ∈ = volumetric strain. accelerogram (recorded on soft rock outcrop, in the hilly
outskirts of the city) leads to acceleration values between 0.20
g -0.30 g, with several significant cycles of motion, with
2.0
dominant period in excess of 2 seconds. Even such relatively
small levels of acceleration would have liquefied at least the
1.8
upper-most loose sandy silt layers of a total thickness 1–2 m,
and would have produced excess pore-water pressures in the
1.6
lower layers Gazetas et al (2004).
1.4

1.2
3%
FS L
1.0 3.5 %

4%
0.8 Dr= 40 Dr= 30
Dr= 50 (N1)60 =6 (N1)60 =3
Dr= 60 (N1)60 =10 qc1=45 qc1=33
0.6 (N1)60 =14 qc1=60
6% qc1=80
Dr= 70
8% [(N1 )60 =20, qc1=110]
0.4 Dr=80
max= 10 % [(N1 )60 =25, qc1=147]
Dr= 90%
0.2 2
[(N1 )60 =30, qc1 =200kg/cm ]

Fig.24. The angle of permanent tilting as a unique function of

0 10 20 30 40 50 the slenderness ratio H/B (Gazetas et. al., 2004)
Post Liquefaction Volumetric Strain, v(%)

Fig. 23. Chart for Post Liquefaction Volumetric Strain (After

Ishihara and Yoshimine, 1992)

Paper No. OSP6 14

OVERVIEW ON SEISMIC DESIGN OF SHALLOW REFERENCES
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Paper No. OSP6 16