Introduction to Soil Structure Interaction Analysis

Every engineering structure, whether it is a building, bridge, highway pavement or railway track, consists of a superstructure (above ground) and a foundationThe 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 transmissionThe 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.Rational Design of 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/B 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. Shallow Foundations

Types of Shallow Foundations

Types of Shallow Foundations

Types of Shallow Foundations

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.Is the Assumption Realistic ?

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.Actual Contact Pressure Distribution

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 will be underestimated and Unsafe

It will give a conservative design for rigid footings on sandy soils as the maximum bending moment is overestimated.Max BM overestimated & conservative design

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 modelsRealistic distribution of contact pressure needs to be considered

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.Soil Structure Interaction Analysis

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 Structure Interaction

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.).Modeling Soil MediaSince 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 MediaFrom 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 MediaFrom 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.

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" methodMat foundations represent a two-dimensional application of the Winkler methodWinkler (1867)

Winkler Model

Winkler ModelWinklers 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 ModelWinkler, 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 ModelFor 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 ModelAccording 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 ModelAccording 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 ModelA 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 ModelSince 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 ModelThe value of subgrade modulus may be obtained in the following alternative approaches:

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.

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

Two Parameter Elastic Models

Filanenko Borodich ModelThis 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 ModelThis 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 ModelThis 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 ModelThis 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 ModelThe 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 ModelThis 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 ModelIn 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 ModelThe pressuredeflection relationship is given by

Pasternak ModelThe 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 ModelA 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 ModelThe governing differential equation for this model may be expressed as follows.