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Introduction to Soil Structure Interaction

Analysis

Rational Design of Shallow Foundations

- Every engineering structure, whether it is a

building, bridge, highway pavement or railway

track, consists of a superstructure (above

ground) and a foundation

- The function of the foundation is to transmit the

load from the superstructure to the soil or rock

below the foundation.

Rational Design of Shallow Foundations

- A proper foundation design has to ensure that no

component of either the superstructure or the

foundation experiences distress of any kind in

the above process of load transmission - The conventional method of design of a footing is

to assume the footing as rigid and the

distribution of contact pressure at the surface

of contact between the base of a foundation and

the supporting soil as planar, that is, uniform

or uniformly varying depending upon whether the

foundation supports symmetric or eccentric

loading. - This assumption of planar contact pressure

distribution is far from reality and therefore,

to be realistic in design, the flexibility of the

footing and the soil type (which together give

rise to variable contact pressure distribution)

should be considered (Kurian, 1992).

Rational Design of Shallow Foundations

- The design of foundation system consists of two

phases. These are referred to as - Geotechnical (GT) design and
- Structural design.
- The aim of GT design essentially is to arrive at

the plan dimensions of the foundation, satisfying

the soil design parameters, viz bearing capacity

and settlement. - The structural design is taken up only after its

GT design is completed, which determines the

footing thickness and also the quantum and

location of reinforcement. - However the design has to be carried out as per

local codes of practice.

Shallow Foundations

- Foundation structures are customarily divided

into shallow or deep on the basis of their depth

in relation to their width, the typical divide

being the unit value for the ratio (Df/B), that

is, Df/Blt1 for shallow foundations and Df/B gt 1

for deep foundations. - The real difference between shallow and deep

foundations is based on the structural response

as well as the depth to which the foundation is

taken. - Bending (flexure) is the predominant structural

action in the case of shallow foundations. - The behaviour of deep foundations could result in

axial and lateral loads besides bending moments

and torsional moments. - The deep foundationsoil interaction needs a

detailed analysis.

Types of Shallow Foundations

Types of Shallow Foundations

Types of Shallow Foundations

Is the Assumption Realistic ?

- In the conventional design of footings, the soil

pressure is assumed to be uniform or linearly

varying depending upon whether the foundation

supports symmetric or eccentric loading.

Actual Contact Pressure Distribution

- In general, foundations are not perfectly

flexible and are embedded at a certain depth

below the ground surface. - If the foundation is subjected to a uniformly

distributed load, the contact pressure will be

uniform and the foundation will experience a

sagging profile.

Actual Contact Pressure Distribution

- If we consider a perfectly rigid foundation

resting on the ground surface subjected to a

uniformly distributed load, the contact pressure

and foundation settlement profile will be as

shown in Figure the foundation will undergo a

uniform settlement and the contact pressure will

be redistributed.

Actual Contact Pressure Distribution

- Additionally, there is a lack of lateral

confinement on the edge of the foundation at the

ground surface. - The sand at the edge of a flexible foundation is

pushed outward, and the deflection curve of the

foundation takes a concave downward shape. The

edges of the foundation will undergo a larger

settlement than the center.

Actual Contact Pressure Distribution

- A rigid foundation resting on a sand layer will

settle uniformly. - The contact pressure on the foundation will

increase from zero at the edge to a maximum at

the center, as shown in Figure.

Max BM will be underestimated and Unsafe

- Hence the assumption of uniform pressure

distribution results in a slightly unsafe design

for rigid footings on clays as the maximum

bending moment at the center is underestimated.

Max BM overestimated conservative design

- It will give a conservative design for rigid

footings on sandy soils as the maximum bending

moment is overestimated.

Realistic distribution of contact pressure needs

to be considered

- Hence the necessity for developing effective and

safe design for foundations based on realistic

distribution of soil pressure, obtained by a

rational interaction analysis, known as flexible

or elastic designs, arises from the above

drawbacks. - While the footing can be modeled as a beam

(one-dimensional) or a plate or a shell

(twodimensional) and classical bending theories

can be used for representing their response, the

soil reaction has to be incorporated in the

integrated analysis of soilstructure interaction

equation by modeling the soil appropriately using

different models

Soil Structure Interaction Analysis

- The problem of foundationstructure interaction

is generally solved by incorporating the reaction

from the foundation, into the response mechanism

of the structure, by idealizing the foundation by

a suitable mathematical model. - Even if the foundation medium happens to be

complex in some problems, in a majority of cases,

the response of the structure at the contact

surface is of prime interest and hence, it would

be of immense help in the analysis, if the

foundation can be represented by a simple

mathematical model, without foregoing the desired

accuracy. - To accomplish this objective, many foundation

models have been proposed and a comprehensive

review pertaining to these has been given by many

authors.

Modeling Soil Structure Interaction

- It is generally observed that the modeling of the

superstructure and foundation are rather simpler

and straightforward than that of the soil medium

underneath. - However, soil is having very complex

characteristics, since it is heterogeneous,

anisotropic and nonlinear in forcedisplacement

characteristics. - The presence of fluctuation of water table

further adds to its complexity.

Modeling Soil Structure Interaction

- It is generally observed that the modeling of the

superstructure and foundation are rather simpler

and straightforward than that of the soil medium

underneath. - However, soil is having very complex

characteristics, since it is heterogeneous,

anisotropic and nonlinear in forcedisplacement

characteristics. - The presence of fluctuation of water table

further adds to its complexity.

Modeling Soil Media

- The search for a physically close and

mathematically simple model to represent the

soil-media in the soilstructure interaction

problem shows two basic classical approaches,

viz., Winklerian approach and Continuum approach. - At the foundation-supporting soil interface,

contact pressure distribution is the important

parameter. - The variation of pressure distribution depends on

the foundation behaviour (viz., rigid or

flexible two extreme situations) and nature of

soil deposit (clay or sand etc.).

- Since the philosophy of foundation design is to

spread the load of the structure on to the soil,

ideal foundation modeling is that wherein the

distribution of contact pressure is simulated in

a more realistic manner.

Modeling Soil Media

- From this viewpoint, both the fundamental

approaches have some characteristic limitations.

However, the mechanical behaviour of subsoil

appears to be utterly erratic and complex and it

seems to be impossible to establish any

mathematical law that would conform to actual

observation. - In this context, simplicity of models, many a

time, becomes a prime consideration and they

often yield reasonable results. - Attempts have been made to improve upon these

models by some suitable modifications to simulate

the behaviour of soil more closely from physical

standpoint. - In the recent years, a number of studies have

been conducted in the area of soilstructure

interaction modeling.

Modeling Soil Media

- From this viewpoint, both the fundamental

approaches have some characteristic limitations.

However, the mechanical behaviour of subsoil

appears to be utterly erratic and complex and it

seems to be impossible to establish any

mathematical law that would conform to actual

observation. - In this context, simplicity of models, many a

time, becomes a prime consideration and they

often yield reasonable results. - Attempts have been made to improve upon these

models by some suitable modifications to simulate

the behaviour of soil more closely from physical

standpoint. - In the recent years, a number of studies have

been conducted in the area of soilstructure

interaction modeling.

Winkler (1867)

The earliest use of these "springs" to represent

the interaction between soil and foundation was

done by Winkler in 1867 the model is thus

referred to as the Winkler method The

one-dimensional representation of this is a "beam

on elastic foundation," thus sometimes it is

called the "beam on elastic foundation"

method Mat foundations represent a

two-dimensional application of the Winkler method

Winkler Model

Winkler Model

- Winklers idealization represents the soil medium

as a system of identical but mutually

independent, closely spaced, discrete, linearly

elastic springs. - According to this idealization, deformation of

foundation due to applied load is confined to

loaded regions only. - Figure shows the physical representation of the

Winkler foundation. - The pressuredeflection relation at any point is

given by p kw, where k modulus of subgrade

reaction.

Winkler Model

- Winkler, assumed the foundation model to consist

of closely spaced independent linear springs. - If such a foundation is subjected to a partially

distributed surface loading, q, the springs will

not be affected beyond the loaded region.

Winkler Model

- For such a situation, an actual foundation is

observed to have the surface deformation as shown

in Figure. - Hence by comparing the behaviour of theoretical

model and actual foundation, it can be seen that

this model essentially suffers from a complete

lack of continuity in the supporting medium. - The load deflection equation for this case can be

written as p kw

Winkler Models

Limitations of Winkler Model

- According to this idealization, deformation of

foundation due to applied load is confined to

loaded regions only. - A number of studies in the area of soilstructure

interaction have been conducted on the basis of

Winkler hypothesis for its simplicity. - The fundamental problem with the use of this

model is to determine the stiffness of elastic

springs used to replace the soil below foundation.

Limitations of Winkler Model

- According to this idealization, deformation of

foundation due to applied load is confined to

loaded regions only. - A number of studies in the area of soilstructure

interaction have been conducted on the basis of

Winkler hypothesis for its simplicity. - The fundamental problem with the use of this

model is to determine the stiffness of elastic

springs used to replace the soil below foundation.

Limitations of Winkler Model

- A number of studies in the area of soilstructure

interaction have been conducted on the basis of

Winkler hypothesis for its simplicity. The

fundamental problem with the use of this model is

to determine the stiffness of elastic springs

used to replace the soil below foundation. - The problem becomes two-fold since the numerical

value of the coefficient of subgrade reaction not

only depends on the nature of the subgrade, but

also on the dimensions of the loaded area as

well.

Limitations of Winkler Model

- Since the subgrade stiffness is the only

parameter in the Winkler model to idealize the

physical behaviour of the subgrade, care must be

taken to determine it numerically to use in a

practical problem. - Modulus of subgrade reaction or the coefficient

of subgrade reaction k is the ratio between the

pressure p at any given point of the surface of

contact and the settlement y produced by the load

at that point

Limitations of Winkler Model

- The value of subgrade modulus may be obtained in

the following alternative approaches

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- However, the basic limitations of Winkler

hypothesis lies in the fact that this model

cannot account for the dispersion of the load

over a gradually increasing influence area with

increase in depth. - Moreover, it considers linear stressstrain

behaviour of soil. - The most serious demerit of Winkler model is the

one pertaining to the independence of the

springs. So the effect of the externally applied

load gets localized to the subgrade only to the

point of its application. - This implies no cohesive bond exists among the

particles comprising soil medium. - Hence, several attempts have been made to develop

modified models to overcome these bottlenecks.

Two Parameter Elastic Models

- The deficiency of the Winkler's Model in

describing the continuous behavior of real soil

masses and the mathematical complexities of the

elastic continuum has lead to the development of

many other simple soil behaviour models. - These models posses some of the characteristics

features of continuous elastic solids. The term

"Two Parameter signifies that the model is

defined by two independent elastic constant.

Two Parameter Elastic Models

- The development of these models has been

approached along following different lines. - The First type stems from the discontinuous

Winkler's model and eliminates its discontinuous

behavior by providing mechanical interaction

between the individual spring elements by either

elastic membranes, elastic beams or elastic

layers capable of purely shearing deformations

(i.e. Filonenko-Borodich, Hetenyi, Pasternak and

kerr). - The Second approach proceeds from the elastic

continuum model and introduces constraints or

simplifying assumptions with respect to the

distribution of displacements and stresses

(Reissner, Vlazov and Leontiev).

Two Parameter Elastic Models

Filanenko Borodich Model

This model requires continuity between the

individual spring elements in the Winkler's model

by connecting them to a thin elastic membranes

under a constant tension T.

Filanenko Borodich Model

This model requires continuity between the

individual spring elements in the Winkler's model

by connecting them to a thin elastic membranes

under a constant tension T.

Concentrated Load

Filanenko Borodich Model

This model requires continuity between the

individual spring elements in the Winkler's model

by connecting them to a thin elastic membranes

under a constant tension T.

Rigid Load

Filanenko Borodich Model

This model requires continuity between the

individual spring elements in the Winkler's model

by connecting them to a thin elastic membranes

under a constant tension T.

Uniform Flexible Load

Filanenko Borodich Model

The response of the model can be expressed

mathematically as follows

Hence, the interaction of the spring elements is

characterized by the intensity of the tension T

in the membrane.

Hetenyis Model

This model suggested in the literature can be

regarded as a fair compromise between two extreme

approaches (viz., Winkler foundation and

isotropic continuum). In this model, the

interaction among the discrete springs is

accomplished by incorporating an elastic beam or

an elastic plate, which undergoes flexural

deformation only

Hetenyis Model

Pasternak Model

- In this model, existence of shear interaction

among the spring elements is assumed which is

accomplished by connecting the ends of the

springs to a beam or plate that only undergoes

transverse shear deformation. - The loaddeflection relationship is obtained by

considering the vertical equilibrium of a shear

layer.

Pasternak Model

The pressuredeflection relationship is given by

Pasternak Model

The continuity in this model is characterized by

the consideration of the shear layer. A

comparison of this model with that of

FilonenkoBorodich implies their physical

equivalency (T has been replaced by G).

Kerr Model

A shear layer is introduced in the Winkler

foundation and the spring constants above and

below this layer is assumed to be different as

per this formulation. The following figure shows

the physical representation of this mechanical

model. The governing differential Fig. 4. Hetenyi

foundation 30. equation for this model may be

expressed as follows.

Kerr Model

The governing differential equation for this

model may be expressed as follows.

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