Indian Geotechnical Conference (IGC-2010)igs/ldh/files/igc 2015 pune/THEME 3 DESIGN OF... · Dhar_ Pritam1, Civil Engineering, ... hydropower dam sites. g) Structural Damages: a)

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INDIAN GEOTECHNICAL CONFERENCE

17th

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DECEMBER 2015, Pune, Maharashtra, India

Venue: College of Engineering (Estd. 1854), Pune, India

BEHAVIOR OF SHALLOW FOUNDATION UNDER DYNAMIC LOAD

PRITAM DHAR1, DR. BIKASH CHANDRA CHATTAPADHY

2,

ABSTRACT

Most in many cases final portion of path of the earthquake waves passes through soils and properties of

these soils greatly influencece the nature of shaking at the ground surface. As soil conditions vary widely

over short distance both horizontally and vertically. Modifications of the resulting shakings will be large

even over a small area. The resulting ground shaking at any site is prime cause of all hazards due to

earthquake at the site. To study the effect of an devastating earthquakes great lessons can be obtained

from examining the resulting hazards occurred due to various earthquake. Excellent reports on hazards

occurring due to several earthquakes which visited India over last five decades are available. A recently a

devastating earthquake visited Nepal in April 2015 causing human death over eight thousand and huge

loss of property in that country and also some losses in adjoining zones in India and China. From review

of damages from such earthquake causes for failure of structures and damages can be grouped in four

divisions namely

(i) Structural deficiencies and use of improper construction and materials.

(ii) Ground movement,

(iii) Liquefaction in supporting medium ,

(iv) Loss of strength of resting material under dynamic condition loading is decreased in

supporting power to the constructed structures.

Out of the four major major factor listed above the last one is considered in detail in this paper

During earthquakes the foundations are subjected to dynamic forces which are generally assumed

to be horizontal, while during nuclear blasts the forces are taken to be acting vertically. Due to occurrence

of an earthquake at a location there is possibility of liquefaction in soil at some depth below ground level,

causing tilting, sinking or destruction of the structure. But when liquefaction does not occur, there is

possibility of decrease of bearing power of the foundation to unknown degree causing distress of the

foundation. In such cases the loss of bearing, need to be investigated and taken into consideration to safe

guard the safety of the foundation under possible earthquake at the location. The earthquake forces along

with the static forces over the foundation constitute the force system on the foundation. There are simple

approaches to analysis the condition, which are basically pseudo static. For considering the earthquake

effects India has been divided into four zones for estimating causable seismic forces shown in figure

below.

1Dhar_ Pritam1, Civil Engineering, SDET Brainware Group of Institutions, Barasat, India, [email protected]

2Chattpadhyay_ Bikash.Chandra2, Civil Engineering, Ex Head of Bengal Engineering and Scince University, Kolkata, India,

[email protected]

mailto:[email protected]

mailto:[email protected]

Pritam Dhar, Dr.Bikash Chandra Chattapadhyay

Fig. Seismic zones of India

Generally under earthquake loading condition allowable bearing capacity is reduced to certain extent (I.S

1893), or a pseudo static approach is made to reduce the bearing capacity under static condition to a

reduced value considering the eccentricity introduced over the foundation under a pseudo static horizontal

loading during earthquake condition. Some rigorous analysis have been proposed for pseudo dynamic or

dynamic analysis for bearing capacity of footing for transient vertical loadings Wallace (1961) and

Triandafilidis (1965) and for horizontal transient loading Chummar(1965) presented rigorous analysis.

However applicability of those analyses are not tested to justify their use in practice. To verify the

acceptability of such cases there is necessity to analysis with the proper case study of failure case under

dynamic load. Such procedure could help to validation those theories. In this paper a review has been

made in the present scenario.

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BEHAVIOR OF SHALLOW FOUNDATION UNDER DYNAMIC LOAD

Pritam Dhar, Assistant Professor, CE Department, SDET Brainware Group of Institutions,. [email protected].

Dr. Bikash Chandra Chattapadhyay, Ex H.O.D & Ex Head, CE Department, Bengal Engineering & Scince

University,Sibpur [email protected]

ABSTRACT: The earthquake forces along with the static forces over the foundation constitute the force system

on the foundation. There are simple approaches to analysis the condition, which are basically pseudo static.

Generally under earthquake loading condition allowable bearing capacity is reduced to certain extent (I.S 1893) or

a pseudo static approach is made to reduce the bearing capacity under static condition to a reduced value

considering the eccentricity introduced over the foundation under a pseudo static horizontal loading during

earthquake condition. Some rigorous analysis have been proposed for pseudo dynamic or dynamic analysis for

bearing capacity of footing for transient vertical loadings Wallace (1961) and Triandafilidis (1965) and for

horizontal transient loading Chummar(1965) presented rigorous analysis. However applicability of those analyses

are not made to justify their use in practice. To verify the acceptability of such cases there is necessity to analysis

with the proper case study of failure case under dynamic load. Such procedure could help to validation those

theories.

In this paper a review has been made in the present scenario.

INTRODUCTION

Due to earthquake natural hazards may occur

causing deaths, injuries, property damages, change

of topography and destruction of immense

magnitude. During earthquake, earthquake waves

radiate from the source and travel through earth’s

crust. As the waves reach the ground, they produce

shaking, lasting over few seconds to minutes. Even

sometimes seismic waves may come as successive

shocks occurring during several months as in

Crimean Earthquake in 1927. A typical example

was seen in 1966, when during Tashkant

Earthquake, waves appeared over a year almost

uninterrupted. The resultant shakings are

dependent on the size of the earthquake, location of

the site with respect to focus of the earthquake,

characteristics of materials along the path of travel

of the earthquake waves and local site conditions.

The resulting ground shaking produced at the site,

is the prime cause of all hazards caused at the site.

In many cases the final portion of the path of

earthquake waves from its origin, lies through soils

and characteristics of these soils greatly influence

the nature of shaking at the ground surface. As soil

conditions vary widely over short distance in space

, the effect of soils on modifying the resulting

shaking is also widely varying , even over a small

area. The soil deposits tend to act as a filter to

seismic waves by attenuating motion at certain

frequencies and amplifying them at others.

It will be of great interest to summarise effects of

last few devastating earthquake which had visited

India in recent few decades at different parts of the

country.

BRIEF REVIEW ON HAZARDS FROM

RECENT EARTHQUAKES

Indian Concrete journal has recently brought out a

very informative compilation of the different

aspects of recent earthquakes in the country

reported by distinguished earthquake specialists,

Brief review of such observations are made below.


Koyna Earthquake (1967): In 11th

December,

1967, a strong earthquake with the epicentre close

to Koyana Hydro-electrical project, shook the

western coast of India and the whole of

Maharashtra state. The effect of the earthquake on

the area were reported by Chandrasekhar, Srivastav

and Arya (2004) [1].

Bihar Earthquake (1988): A moderate earthquake

had rocked at Bihar-Nepal border region on August

21, 1988, causing damages in areas around northen

part of Bihar and south-eastern part of Nepal.

Thakkar (2004) verified critically these damages

due to this earthquake [2].

Uttarkashi Earthquake(1991): On October 20,

1991, an earthquake struck the Garhwal Himalayas

in northern India near Uttarkashi, causing wide

spread devastation and loss of life. Paul (2004)

reported the lessons learnt from this earthquake [3].

The observations of structural performance of

building during earthquakes provide volumes of

information’s about the merit and demerits of the

design and construction practice in a region since it

is based on the actual test on the prototype

structures.

Poor quality of workmanship, ignorance of

earthquake engineering practice, inadequacies of

road construction leading to instability of hill

slopes are identified as some of cause adding

severity of the damages.

Killari Earthquake (1993): Decan traps of

peninsular India was generally thought to be

seismically stable. But a devastating earthquake

struck south central India in September 30, 1993.

The epicentre was near village Killari in Latur

district in Maharasthra. Sinha and Murthy (2004)

reported engineering lessons from this earthquake

[4].

Bhuj Earthquake (2001): A devastating

earthquake visited the Kutch area in Gujrath on

26th

January 2001, causing more than 18000

human death and huge property loss. Salient

structures and geotechnical damages of this

earthquake had been reported by Murty et.al.

(2004) [5].

The earthquake caused excellent examples of large

scale liquefaction and embankment failure. The

Great Runn Kutch , The Arabian Sea and the Little

Runn of Kutch lock the affected area on three

sides. The enclosed area at near sea level sustained

extensive liquefaction. At least five earth dams

failed during earthquake. The earthen

embankments of the rail road and highway also

suffered widespread damage.

Nepal Earthquake (2015): Aydan and Ulusay

(2015) presented a quick report on the devastation

earthquake that has visited Nepal on 25th

april 2015

[6]. Some of the salient features of the damager are

detailed below.

a) Mass Movement: The epicentral area is

very mountainous and valleys are steep and

laid sedimentary rocks are heavily folded

and faulted resulting from the tectonic

movements and subjected to weathering

due to intense freezing thawing cycles as

well as water content variations. The mass

movements are quite similar to those

observed recently in the 2005 Kashmir and

2008 Wanehuan earthquakes.

b) Liquefaction induced ground failure:

Although detailed information on the

occurrence of liquefaction during this

earthquake has not been reported yet, some

picture from Kathmandu clearly confirmed

that liquefaction did occur in Kathmandu.

In addition, ground liquefaction did occur

in even Bihar region of India.

c) Roadway Damage: The roadway

embankments in Kathmandu city suffered

some damage in from of subsidence and

lateral spreading. Improper compaction,

lateral spreading of sidewalls and

subsidence of saturated soil beneath the

embankments would be the potential cause

as expected from various geotechnical

investigation in Kathmandu.

d) Damage to Bridges: There is no report yet

about the damage to bridges. Bridge in

Gorkha district is a single-span truss bridge.

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This bridge is also not damaged despite it

was located in the epicentral area.

e) Utility Poles: Some reinforced concrete

utility poles having rectangular cross

section were toppled down during

earthquake shaking. Some corossion of

reinforced bars was noticed in the poles

collapsed due to shaking.

f) Damages to dams: Nepal has been trying

to improve the energy storage by building

dams along major rivers. There is no report

of damage by the earthquake at other

hydropower dam sites.

g) Structural Damages:

a) Building Damage: The shallow depth

of the focus and the nature of

Kathmandu valley have contributed to

the high losses in the capital of Nepal.

However, it should be noted that the

quality of construction and materials of

building is very poor. Many recently

built reinforced concrete structures

failed in a pan-cake mode due to

improper column-beam connections.

Furthermore, many brick structures

collapsed or heavily damaged due to the

use of poor mortar material and tie

beams and slabs within the walls. The

wall of houses were built as dry

masonry and their resistance are mainly

due to frictional forces. In addition

plastic deformation of their foundation

on slopping ground shaking was a

another cause of collapse and heavy

damages. Although Nepal has been

trying to improve its safety and

infrastructure by updating building

codes for more than two decades the

efforts were not sufficient.

b) Damage to Monuments: Historical

monuments as well as religious

structures associated with Buddhism

suffered tremendous damage induced

by this earthquake. Most of the

structures are of masonry type using

brick and earth-mortar as a bonding

agents.

IMPORTANT LESSONS:

In general it could be surmised that at any location

major disasters due to earthquake depend on the

magnitude of the earthquake, site condition, focal

distance of the site and depth of the focus,

frequency of earthquake at the site and

concentration of population and property at the

region. From the review made on the damages

caused by several major earthquake which had

visited in recent few decades in different parts of

Indian sub continent , causal mode of damages and

failures due to earthquake may be associated with

(i) Structural deficiencies and use of

improper construction and materials

(ii) Ground movement

(iii) Liquefaction in supporting medium

(iv) Loss of strength of resting material

under dynamic condition loading is

decrease in supporting power to the

constructioned structures

Out of the above four major factors the last one is

considered in detail in this paper.

Due to earthquake at many cases it has been

observed, that isolated footing, raft foundation and

even pile foundations have failed , causing failure

of the structure. Even relatively low loaded

structures like pavement, rail road etc have been

seen to be totally dislocated due to earthquakes.

Such failure have generally been reasoned due to

liquefaction of soil under at some depth, due to

presence of water to saturated the void spaces in

soils in the layers and reducing effective stress to

zero under earthquake condition. However failure

have occurred where there is only partial saturation

or complete unsaturation, even in dense soils

(Rechards et.al. 1993). Such failure was observed

in Miyagihel-Oki earthquake of magnitude 7.8 in

1978 due to earthquake where soil was dry and

dense enough to avoid liquefaction. (Shafiee and

Jahanandish 2010) [7]. Such phenomenon is

refered as “Seismic Shear fluidization” and in such

case soil flows at finite levels of effective stress


and it can take place in dry soil in which no pore

water pressure is present(Rechards Etal 1990)[8].

During dynamic situation properties of soils get

modified and assume values largely different and

lesser the from those under static condition

(Barkan 1962). Thus during earthquake condition

load carrying capacity of soil is modified and may

get decreased to a significant amount. Thus seismic

bearing capacity of footing has become one of the

most interesting topics of research and also of

practical need at present days.

DYNAMIC BEARING CAPACITY UNDER

EARTHQUAKE CONDITION

During earthquake the engineering property of soil

, supporting the foundation, gets modified to

varying degree , depending on the site condition ,

magnitude of earthquake, ground water table

condition, types of soils etc. Under such condition

foundations are maybe subjected to dynamic form

which are generally assumed to be horizontal.

Suddenly approximate value of the seismic

coefficients, equivalent seismic forms are

evaluated. Bearing capacity of shallow foundation

can be estimated by three types of approaches,

those are

(a) Pseudo-static analysis

(b) Pseudo-Dynamic analysis

(c) Dynamic analysis

(a) Pseudo-static analysis : In this approach

the inertia forces generated by earthquake ,

On the footing is considered to acting on it

as static forces and modification in its load

carrying capacity is estimated. From the

viewpoint of possible earthquake effect,

India is divided into four zones (Fig.1), for

computing seismic forces , either seismic

coefficient methods or response spectrum

method is employed. The first method is

used for pseudo-static design of foundation

of buildings, bridges and similar structures.

The second method is generally used for

the analysing of earth dam [IS 1893-1979]

[9].

Fig.1: Seismic zones of India

In seismic coefficient method, the design

value of horizontal seismic coefficient (αh)

is obtained as:

αh = β . I . α0

Where,

α0 = Basic seismic coefficients

(Table : 1)

I = Coefficients depends on the

importance of structure. (Table 2)

β = Coefficients depends on the soil

structure system (Table 4)

Table 1 Values of basis seismic coefficients

Zone α0

II 0.02

III 0.04

IV 0.05

V 0.08

Table 2 Values of I

Type of structure Values of I

Dam 2.0

Important service and

community structures

1.5

All others 1.0

The vertical seismic coefficients , αV , shall be

considered in the case of structures in which

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stability in a criteria of design or for overall

stability of structures. It is generally taking as half

the value of horizontal seismic coefficient.

In response spectrum method, the response

acceleration coefficient is first determine from the

natural period and damping of the structure and the

design value of horizontal seismic coefficient αh is

computed from the expression below

αh = β I F0

Where,

F0 = Seismic zoning factor for average

accurating spectrum (Table 3)

= Avarage accuration coefficients as

read from Fig.2 for appropriate natural period and

damping of structures.

These forces along which static forces are

considered to be acting on the foundation as if in

static condition and solution for bearing capacity is

considered for the foundation subjected to resulting

load with becomes eccentric and inclined.

Fig 2. Response spectra for rock and soil sites for 5

% damping.

In pseudo-static analysis bearing capacity of

foundation adopting suitable value of horizontal

and vertical seismic coefficients at a site equivalent

seismic forces are evaluated .

Table 3 Values of Seismic Zoning factor , F0

Zone F0

II 0.10

III 0.20

IV 0.25

V 0.40

Effect of Eccentric inclined load:

If the resultant load on the foundation has an

eccentricity , e, only in one direction then the

dimension of the foundation in that direction is

allowed to be reduced bt 2e the modified

dimension shall be used in conventional generally

bearing capacity equation used the static cases. If

the load has double eccentricity eL and eB with

respect to centroied of the footing , the effective

dimension of the footing , L’ x B’ , in resisting the

load shall be determine has L’= L-2eL and B’ = B-

2eB Where L and B are original dimension.

In computing shape and depth factor for

eccentrically inclined loaded footings effective

length and bredth as calculated above shall be used

however eccentricity in any direction shall be

limited to 1/6 of the corresponding of the

foundation direction as per IS 6403 [10] the

inclination factor are given by ic= iq = [1-i/90]2

iy

= [1- i/fi]2

For more accurate determination of an

eccentrically or obliqulay loaded footing some

significant works are reported in last few decades

(Purakayastha & Char 1977 [11], Saran & Agarwal

1990) [12].


Table 4 Value of β for different soil foundation

support

Soil

β

Isolated footing

with

out tie

beam

Combi

ned isolated

footing

with

tie

beam

Ra

ft

Ra

ft

Pile

founda

tion

Well

found

ation

Roc

k or

hard

soil

1.0 1.0 1.0 1.0 1.0

Med

ium

Soil

1.2 1.0 1.0 1.0 1.2

Soft

Soil

1.5 1.2 1.0 1.2 1.5

Purakayastha and Char (1977) conducted

stability analysis of eccentrically loaded strip

foundations (α = 0) supported by granular soil

using method of slices proposed by Janbu (1957).

Based on their study it was proposed that, for a

given Df / B

( )

( ) =R = (

)

Where,

quv(e,α=0) = Avarage ultimate vertical load

per unit area of the foundation with load

eccentricity e and load inclination α = 0

quv(e =0,α = 0) = Avarage ultimate bearing

capacity with centric vertical load

R= reduction factor

C= Df /B only and independent soil

frictional angle φ. The variation of b and c with Df

/ B is given in table

Table 5 Variation of B and C with Df/B –Analysis

of purakayastha and char

Df/B b c

0 1.862 0.73

0.25 1.811 0.785

0.5 1.754 0.80

1.0 1.820 0.888

For Df/B between zero and 1 the average value of b

and c are about 1.81 and 0.8 respectively. So the

equation can be approximated as

( )

( ) = R = (

)

Saran and Agarwal (1991) reported an

equilibrium analysis to evaluate the ultimate

bearing capacity of strip footing subjected to

eccentrically inclined load. According to their for

foundation on granular soil

(

)

(

)

(

)

Where,

(

)

Avarage inclined load per unit

area with load eccentricity ration

and inclination

α.

(

) (

) Bearing capacity factors

expressed in terms of load eccentrically e and

inclined at an angle α to the vertical. Details of the

above factors are presented elsewhere.

Richard et.al. (1993) presented an analytical

solution for bearing capacity of strip footing of

width B, placed at a depth Df below existing

horizontal ground level (Df < B), with inertial

forces in soil and footing, using a Coulomb’s type

mechanism [13]. Using the simplification of

eliminating the fan shaped transition zone in

conventional Prandtl’s failure mechanism, and

there by averaging its effect concentrating the

shear strength on imaginary vertical wall through

one of the extremities of the footing (Fig. 3),

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bearing capacity factors for each component of

strength were derived and they presented the

ultimate bearing capacity in earthquake situation as

Where, NCE, NqE and NγE are bearing capacity

factors during earthquake, similar to those in Static

condition. But these factors are dependent on the

angle of shearing resistance of soil, φ, and also

magnitude of the developed values of acceleration

during earthquake.

The active – passive Coulomb’s Wedge

mechanism, adopted by them, allowed adoption of

sliding block approach to calculate seismic

displacement of the footing. Though the

mechanism is not exact, it helps to estimate the

seismic bearing capacity factors. Authors

suggested that the values of seismic bearing

capacity factors and computed settlements are both

conservative.

The model directly allows the formulation of the

seismic bearing capacity factors to compare with

their counterparts in static conditions and at the

same time the model is capable of depicting the

pattern of the change in the surfaces with change of

the values of acceleration to explain the shear flow

and settlement occurring during earthquake.

Fig 3. Simplified static slip field (After Rechards

et.al. 1993)

Sarma and Iossifelis (1990) analysed the similar

problem by using a techniques for slope stability

based on a method of inclined slices [14].

Shafiee and Jahanandish (2010) presented a

finite element method was used to estimate the

seismic bearing capacity of strip footing for wide

ranges of value of angle of shearing resistance, and

seismic coefficients [15]. Using the pseudo-static

approach, seismic forces are considered as the

horizontal loads applied to the foundation,

surcharge at the underlying soil. Plain straw

elastic-plastic Mohr- Coulomb model encoded in

PLAXIS was used. Solution for the bearing

capacity factors are presented for different values

of horizontal acceleration and angle of shearing

resistance. With the increase in the value of earth

quake acceleration all the bearing capacity factors

decreases for any value of the angle of shearing

resistance further the analysis conclusively

indicated that soil inertia plays a negligible

compared to structural seismic loads

PSEUDO – DYNAMIC APPROACH

Pseudo-dynamic approach for finding seismic

bearing capacity of strip footing on uniform

cohesion less soil has been recently presented by

Ghosh and Choudhury (2011) [16], Considering

effect of both shear and primary waves, soil

amplification, duration and period of lateral

shaking. Similar failure wedges as proposed by

Richards et.al. (1993) are considered with linear

variations for horizontal and vertical seismic

acceleration with input acceleration at the base of

the failure wedges to the higher value at the level

of footings. Active and passive earth pressure

behind the imaginery vertical wall between the

active and passive wedge proposed by Richards

et.al. (1993) and pseudo dynamic approach had

earlier been presented by Chowdhury & Nimbalkar

(2006, 2008) [17].

DYNAMIC ANALYSIS

The bearing capacity of foundations under dynamic

condition started drawing attention of investigators

in geotechnical engineering from early 1960. The


attempted analyses have been developed on certain

simplifying assumptions. In general three different

approaches are made. In one of them it has been

assumed that during failure under dynamic

condition similar failure surface develops as under

static condition. The equation of motion is then

developed from the equilibrium conditions. In the

second method wave propagation theory is utilized.

The equation of wave motion resulting from

dynamic loads gives the surface displacement. In

the third approach the footing response is

considered as the presence of single degree of

freedom mass-spring-dash pot model.

Wallace [1961], Triandafilidis [1961,1965] and

Chummar [1965] have analysed the problem by the

first method. Selig [1959] and Carroll [1963] have

analysed the problem by second method. Fisher

[1962] and Landate [1954] have analysed the same

by third method.

Wallace [1961] analysed the dynamic bearing

capacity of long footing considering the failure

surface described by Terzaghi [1943] for static

loading for long footing with rough base. The

foundation medium was taken as C- φ soil [18].

The assumptions are

[i] The soils behaves like rigid –plastic

material.

[ii] The soil mass with in failure surface

acts as rigid body.

[iii] The critical spiral surface under static

condition will be also critical under dynamic

condition

[iv] The footings fails by punching in the

soil without any rotation

[v] Dynamic load on the footing is

triangular pulse.

[vi] Footing is weightless and imparts

uniform pressure on the soil.

The equation of motion was derived as

+ k∆ =

–

x t

Where,

∆ = Vertical displacement of the footing

k =

NR = Coefficient representing dynamic

shear resistance due to gravity restoring forces

N1 = Coefficient representing inertial shear

resistance

B = Width of footing

q = Peak value of dynamic pulse

[triangular]

qu = Static load on unit width of footing

td = maximum duration of pulse

For , t, from zero to td loading function = qB[1-

]

And for t greater than td loading function =0

The solution of the above equation yields the

footing displacement versus time relation. The

form of solution with boundary conditions being

satisfied, is

For t between zero to td

(

) (

)( )

( )

For t greater than td

[(

)

( )]

[

( )]

Where

Maximum displacement from above equations is

the permanent footing displacement, the value for

which can be obtained from above equations and is

available in graphical form [ Wallace (1961)]

Triandafilids [1965] presented a solution for

dynamic response of a continuous footing on a

saturated cohesive soil under vertical transient load

with several similar assumptions [19]. He assumed

that due to vertical dynamic load footing fails by

rotation about the base corner. The failure surface

is semi-circular with radius equal to width of

footing. For a transient vertical loading qd = qoe-βt

.

Wher overload factor λ = q0/qu (qu = Static bearing

capacity ) he developed the following equation by

balancing the moments of driving and resulting

forces,

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[

]

The natural frequency and time period of the

system are

Wn = √

& T =

The above equation is solved for maximum angular

deflection θ and charts have been developed for

various values of overload ratio λ for different

decay factor to give the dynamic load factor K,

where K is given by = (W/ 0.68g.qu) . θmax .

Chummar [1965] presented a solution for

dynamic response of a strip footing supported by

C-φ soil and subjected to horizontal transient load

[20]. However the above solutions are based on

several simplistic assumptions and validity of such

solutions are not yet verified for general

acceptance.

Lansdale [1954] had worked on the problem

considering the footing response to a transient load

as the response of single degree of freedom mass

spring dash-pot-model system [21]. He has

considered the mass which linearly increase as a

function of footing displacement. The initial mass

is that of the soil contained in a hemisphere with a

diameter 1.5 times the footing with the final mass

is that of the soil contained in static failure surface,

comparable to that assumed by Terzaghi’s long

footing. Fisher [1962] also worked in similar

manner for square footing placed on purely

cohesive or purely frictional soil. The responding

soil mass is considered to be of primordial shape,

the volume depending on the width of the footing.

He developed equation to give the settlement of the

footing under dynamic load and modified that to

correlate with experimental results.

CONCLUSIONS

From the view point of mitigation of seismic

hazards to safeguard possible damages caused due

to distress of foundation for earthquake effects,

need for estimate of safe bearing capacity of

foundation under earthquake loading are assuming

increasing importance both for researchers and

practising engineers. A brief review of the damages

caused due to earthquake in recent decades in India

has been made to indicate type of disasters caused.

Apart from the major failures due to lack of proper

earthquake resistant design of structure, use of

materials of adequate quality, ground movement

and liquefaction of soil at the location, it seems

partial loss of bearing capacity of footings has also

contributed to great extend for differential

movement at the base of constructed structures,

located over foundation medium having little or no

water content. It is to be noted that to estimate

allowable bearing capacity for design conventional

factor of safety used ranges from 2 to 3 over

ultimate bearing capacity. Hence decrease in

ultimate bearing capacity by even 100% during

seismic condition may not cause shear failure in

the supporting soils but generated deformation

particularly differential settlement, may be

excessive to cause great concern.

Different methods available in literature have been

discussed in the paper. Though numerical methods

are now extensively used in solving various

geotechnical problem but seismic bearing capacity

problem has hardly been attempted. Recently a

result of a numerical study based on pseudo-static

method of Richards et.al. has been presented (

Shafiee and Jahanandish [2010]). The study

indicates that effect of the pseudo-static force

applying to the soil mass, called soil inertia, has

very little effect on the result of seismic bearing

capacity. However there are little reported results

of experimental studies on the topic which would

be used to check the validity of methods discussed

in presented study. Thus comprehensive testing

programme is necessary to verify the validity of

assumptions made in different approaches and

identify the reasonable methodology for estimate

of dynamic bearing capacity of soil.


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