ANALYSIS OF MULTISTOREY BUILDINGS INCORPORATING SUPPPORT SETTLEMENT

INTRODUCTION:

The domain of earthquake engineering has been paid comprehensive attention internationally in recent decades. SSI phenomena concern the wave propagation in a coupled system: structures built on or in the soil surface. Its origins trace back to the late19th century, which evolved and matured gradually in the ensuing decades and during the first half of the 20th century, and progressed rapidly in the second half stimulated mainly by the needs of the nuclear power plant and offshore industries, by the debut of powerful computers and simulation tools such as finite elements, and by the needs for improvements in seismic safety.

Investigations of SSI have shown that the dynamic response of a structure supported on flexible soil may differ significantly from the response of the same structure when supported on a rigid base. One of the important reasons for this difference is that part of the vibrational energy of the flexibly mounted structure is dissipated by radiation of stress waves in the supporting medium and by hysteretic action in the medium itself. When there is more than one structure in the medium, because of interference of the structural responses through the soil, the SSI problem evolves to a cross-interaction problem between multiple structures.

As in the metropolises, such as Kobein, Japan, structures, such as buildings, stations, and tunnels, are built closely to each other over the soft soil deposit. Under such circumstances, the dynamic interaction among structures must occur through the radiation energy emitted from a vibrating structure to other structures. Hence, the dynamical characteristics as well as the earthquake response characteristics of a structure are unable to be independent of those of the adjacent structures.

Structure–soil–structure interaction (SSSI), just put forward in recent decades, means the dynamic interaction problem among the multi structures system through soil-ground. It is an inter disciplinary field of endeavor, which lies at the intersection of soil and structural mechanics, soil and structural dynamics, earthquake engineering, geophysics and geo-mechanics, materials science, computational and numerical methods, and diverse other technical disciplines. With the successful outcome about SSI, various kinds of theoretical methods and experimental installations are used to promote the study of SSI.

SOIL STRUCTURE INTERACTION:

Soil-structure interaction (SSI) analysis is a special field of earthquake engineering. It is worth starting with definition. Common sense tells us that every seismic structural response is caused by soil-structure interaction forces impacting structure (by the definition of seismic excitation). However, engineering community used to talk about soil-structure interaction only when these interaction forces are able to change the basement motion as compared to the free-field ground motion (i.e. motion recorded on the free surface of the soil without structure). So, historically the conventional definition of SSI is different from simple occurrence of the interaction forces: these forces occur for every structure, but not always they are able to change the soil motion.

This simple fact leads to important consequences. If a structure can be analyzed as based on rigid foundation with free-field motion at it, then they use to say that “no SSI effects occur” (though structure is in fact moved by the interaction forces, and the same forces impact the foundation). Looking at the variety of the real world situations, we can conclude that only part of them satisfies the conventional definition of SSI.

The ability of the interaction forces to change the soil motion depends, of course, on two factors: value of the force and flexibility of the soil foundation. The value of the interaction force may be often estimated via the base mat acceleration and inertia of the structure. For given soil site and given free-field seismic excitation the heavier is the structure, the more likely SSI effects occur. Usually most of civil structures resting on hard or medium soils do not show the signs of considerable SSI effects.

BRIEF HISTORY: (Alexander Tyapin, “Soil-Structure Interaction”, 2012.)

As SSI field combines structures’ and soil modeling, the level of such modeling is generally lower than in the classical soil mechanics and in the structural mechanics standing alone.

For several decades (up to 1960-s) only soil flexibility was considered without soil inertia springs modeled soil. At that time mostly the machinery basements were analyzed for the dynamic interaction with soil foundation (the largest of them probably being turbines). In fact, it was a quasi-static approach – the well-known static solution for rigid stamps, beams and plates on elastic foundation was applied at every time step. The model was so simple, that nobody even used the special term “SSI” at that time. The key question of such a simple approach appeared to be damping. The material damping measured in the laboratories with soil samples proved to be considerably less than the damping measured in the dynamic field tests with rigid stamps resting on the soil surface. The nature of this effect was discovered in 1930-40s, (Schechter in the USSR) and proved to be in inertial properties of the soil. Inertia plus flexibility always mean wave propagation. It turned out that in the field test’s actual energy dissipation in the soil was composed of two parts: conventional “material” damping (the same as in laboratory tests) and so-called “wave damping”. In the latter case the moving stamp caused certain waves in the soil, and those waves took away energy from the stamp, contributing to the overall “damping” in the soil-structure system. This energy was not transferred from mechanical form into heat (like in material damping case), but was taken to the infinity in the original mechanical form. In reality waves did not go to the infinity, gradually dissipating due to the material damping in the soil, but huge volumes of the soil were involved in this wave propagation. Even without any material damping in the soil this “wave damping” contributed a lot to the response of the stamp. In practice it turned out that the level of wave damping was usually greater than the level of material damping.

FINITE ELEMENT METHOD:

The principle of Finite Element Method is simple and it helps to solve complicated problems effectively. In this method, the solution of a complicated problem is replaced by a simpler solution. The main drawback noticed in this method is that the solution obtained is an approximate one rather than an exact solution. The reason is that the problems which are solved by this method often involve mathematical constraints which prevent the calculation of an exact solution.

CurrentlyFinite Element Method is accepted as the most powerful general technique for the numerical solution of a variety of engineering problem. Application of Finite element method ranges from the stress analysis of solids to the solution of acoustical phenomena, neutron physics and fluid dynamic problem. It can be argued that Finite Element Method is established as a general numerical method for the solution of partial differential equation subjected to known boundary initial condition.

The finite element method is a general method of structural analysis. It is approximated by the analysis of an assemblage of finite elements. They are interconnected at a finite number of nodal points and represent the solution domain of the problem. The method is specially extended form of matrix analysis.

STEPS INVOLVED IN FEM:

1. The unknown field variables are expressed in terms of approximate functions known as interpolating function or shape functions with each element. (The shape function is defined in terms of field variables of nodal points)

2. The principle of minimum potential energy is used to derive the equation of equilibrium for each element, by duly considering the loading and constraints.

3. Thus element stiffness matrix of each individual element is formed.

4. Calculation of governing equations of equilibrium of each element written that indeed describes the behavior of the system as a whole.

5. Finally these equations are used to obtain the unknown displacement field.

Introduction to FEM Software:

Since there is lot of hand calculation using Finite element method number of computer application has been developed along with advancement of technology.

Some of the FEM packages are ANSYS, STAAD Pro Vi8, SAP, NISA, ALGOR, LS DYNA and NASTRAN.

One cannot always trust this software, so basic theoretical background is must for anyone who intends to use this software.

Introduction to STAAD ProVi8 Software:

It is a multipurpose finite element program which is used for several classes of engineering analysis.

The steps followed in STAAD Analysis are:

· Define geometry

· Specify elements

· Define material properties

· Create nodes and number each of them\

· Apply boundary conditions

· Attribute load cases and assign particular loads to individual entities

· Check for further specification

· Run analysis

· Select what all results one wants

· Extract results such as displacements, stresses, deformation, mode shapes, stress distribution, etc.\

· Use graphical interpretation to have more clear view of the results.

Types of structural analysis:

1. Static Analysis:

To determine displacements, stresses, etc. under static loading conditions.

2. Modal Analysis:

To calculate the natural frequencies and mode shapes of a structure.

3. Harmonic Analysis:

Used to determine the response of a structure to harmonically time varying loads.

4. Transient Dynamic Analysis:

5. Spectrum Analysis:

6. Buckling Analysis:

Model of ground for the investigation, a finite soil mass around the building is modeled by placing soil in a rigid box. The structure is kept over this soil with sufficient embedment depth. The Size of the box used for the ground modeling is 1.5 x 0.96 x 0.9 m in which 600mm of its depth is filled with soil which represents the 15 x 9.6 x 6 m soil on ground. The soil used for modeling of ground is sand. The properties of soil used in model and prototype are identical.

LITERATURE REVIEW

Mubbera Eser Aydemir ( )

This paper addresses the behaviour of multi-storey structures considering soil structure interaction under earthquake excitation. For this purpose, sample 3, 6, 9 storey RC frames are designed based on Turkish Seismic Design Code and analyzed in time domain with incremental dynamic analysis. Strength reduction factors are investigated for generated sample plane frames for 64 different earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil. According to the analysis result, strength reduction factors of sample buildings considering soil structure interaction are found to be almost always smaller than design strength reduction factors given in current seismic design codes, which cause an unsafe design and non- conservative design forces.

Paolo Negro, Roberto Paolucci, StefaniaPedretti and EzioFaccioli (2000)

In this paper an experiment was carried out in which large-scale specimens of sand were constructed and tested under the cyclic loading imposed on a shallow foundation model. The tests were designed to provide validation data for the calibration of new and existing constitutive soil models, and to improve the assessment of the permanent deformations and bearing capacity of the soil-foundation systems. Two tests were performed, with relative densities 45% and 85%. The set-up consisted of a model of shallow foundation (1m x 1m in plan) resting on a large volume (4.6m x 4.6m, 3 m deep) of saturated sand of uniform properties, and well known geo-mechanical characteristics (Ticino sand). The specimens were subjected to the same loading sequence. After application of the vertical load and stabilization of the settlement, a series of small-amplitude force cycles of increasing level were applied, to identify the onset of non-linear behaviour. A realistic time-history of horizontal force and overturning moment, representative of the seismic actions transmitted by the super-structure to the foundation during an earthquake was then applied on top of the foundation. The paper provides a description of the experimental activity and of the global results. In particular, the different behaviour of the high and low-density specimens is discussed. The limitations of the set-up are critically analysed. Some relevant engineering results, especially the permanent deformations developed during the earthquake-like loading phase, are illustrated and emphasis is given to the need for improving the current predictions of earthquake-induced foundation settlements and rocking.

Alexander Tyapin (2012 )

Initially the definition of the soil-structure interaction (SSI) effects is discussed in this paper .The author states that this phenomenon is particularly peculiar asevery seismic structural response is caused by soil-structure interaction forces, but only in certain situations they talk about soil-structure interaction (SSI) effects. Then a brief history of this research field is given covering the last 70 years. Basic superposition of wave fields is discussed as a common basis for different approaches – direct and impedance ones, first of all. Then both approaches are described and applied to a simple 1D SSI problem enabling the exact solution.

Nowadays SSI models are linear. Nonlinearity of the soil and soil-structure contact is treated in a quasi-linear way. Special approach used in SHAKE code is discussed and illustrated. Some non-mandatory additional assumptions (rigidity of the base mat, horizontal layering of the soil, vertical propagation of seismic waves) often used in SSI, are discussed. Finally, two of the SSI effects are shown on a real world example of the NPP building. The first effect is soil flexibility; the second effect is embedment of the base mat. Recommendations to engineers are also included in the conclusions.

AnooshShamsabadi and Liping Yan (2008)

A global three-dimensional finite-element model was developed for the seismically instrumented Painter Street Overpass in this paper. This model included elements to simulate nonlinear foundation-soil interaction and structure foundation details. A direct approach was used in the model, which has the advantage of implementing either material or geometric nonlinearity for soil-foundation supports. In dynamic analyses, the model was excited using the record of the 1992 Cape Mendocino/Petrolia earthquake. The soil-structure interaction model parameters were based on actual engineering soil properties obtained from in-situ field and laboratory tests conducted during a geotechnical field investigation at the abutments. The results of the analyses show that the proposed model can represent fairly well the seismic response of the Painter Street Overpass and that the modelling of the pile foundations at the bent had much less of an impact on the overall bridge response as compared to the abutments.

B.R.Jayalekshmi, Lohith.K, R.Shivashankar, KattaVenkataramana(2008)

In this paper the Soil-Structure-Interaction (SSI) effects on the seismic response of structures founded on Shedi soil of Dakshina Kannada has been evaluated. Experimental investigations have been carried out on 1:10 scaled single bay three dimensional multistorey building models made of aluminium with its foundation resting on locally available Shedisoil (classifying as sandy silt) and sand in the saturated and dry conditions. The structure is subjected to dynamic loading and the response is measured at each level of the model which represents a floor . This response is compared with that of a fixed base model to isolate the effect of soil structure interaction. The variations in natural frequency with various parameters such as different types of soil, degree of saturation of soil, number of storeys and the stiffening effect of walls are evaluated. The experimental results are presented and the modifications in dynamic characteristics due to the incorporation of soil flexibility are studied. Free vibration analysis of the three dimensional finite element model of the soil foundation structure system is carried out in ANSYS and the results are compared with the experimentally obtained values.

PRESENT STUDY:

Practically when designer analyse the building he tends to consider base as fixed and run the further analysis and design the building assuming there is no interaction. But one can know that this leads to overestimation of the design that is not economically viable. So by involving soil properties, we can have a good prospect on the design capability and further make it economical. The involvement of Soil characteristics turns out to be crucial factor in design and analysis of Nuclear power Plant (NPP) and Refinery structure.

Observing the above mentioned factors we intent to focus our study on the involvement of soil characteristics in the analysis of the structure. In the present study, multistorey 3-dimensional three bay aluminium framed structure in 1:25 ratio with its foundation resting on different types of soil (sandy and shedi soil) is considered for experimental investigation. As our preliminary investigation, we have experimentally found out the soil properties i.e Particle size distribution, Specific gravity and drydensity. This structure is indeed drafted in STAAD Pro Vi8 and analysed for variation in bending moments, shear force and deflection under different loading condition.As our preliminary investigation, we have conducted few Soil test on Sand. Sieve analysis, Specific gravity and relative density test was done to find few characteristics of the sand. Further experiments like tri-axial test on drained and undrained sand is to be done. All these properties of sand are utilized during analysis of the structure using FEM software.

The model is considered as distorted model since the material used in prototype and model are not same and also their stress strain behaviour is not similar, hence the corresponding load factor is assumed as 15 which simulate the equal effect on both materials. The load factor is used for computing the load and stiffness on the model from prototype. Since the factor is used in stiffness and mass quantity there will be no error indicated on natural frequency of building frame model.

Computation of scaling factor is as Follows:

Geometry scale, S= 25

Load scale factor,SL = 15

Modulus of elasticity of prototype, Ep=25 X 106 KN/m2­

Modulus of elasticity of model, Em = 69 X 106 KN/m2

SE = Ep/Em

SE = 0.362

SE(Actual) = 0.362 X 15 = 5.43

When Geometric scale factor, S= 15

Stiffness scale factor, SK = SE(Actual) X S

                                         = 5.43 X 25 =135.75

Force scale factor, SL = SE(Actual) X S2

                                    = 3393.75

Table 1: Scale Factors of different parameters

Scale Factors of different parameters

3-bay Aluminimum model of the 3 storeyed building

Table 2: DIMENSIONS OF BUILDING FRAME MODEL AND PROTOTYPE:

DIMENSIONS OF BUILDING FRAME MODEL AND PROTOTYPE

MODEL DEVELOPMENT AND ANALYSIS IN STAAD Pro:

A model of the structure has been developed in STAAD Pro Vi8 and analysed in detail for fixed base and with sub grade soil.

The material assigned to the structure elements is isotropic aluminium with the following material properties:

1.Elastic Modulus= 68.9476 KN/mm2

2.Density = 2712.63 Kg/m3

3. Poisson’s Ratio=0.33

4.Damp=0.3

The above properties have been used for the development of all structure elements i.eplates , beams and columns.

Analysis of structure:The structure has been analysed under two support conditions. These are:

1. Structure under fixed base .

2.Structure under sub-grade soil.

For both the above support conditions , the analysis is done for self load only.

1. STRUCTURE WITH FIXED BASE

Pre analyses print of structure:

The analysis was run successfully and the output file studied.

The summary of the node displacements and base reactions is as given below:

BENDING MOMENT DIAGRAM OF THE STRUCTURAL MEMBERS UNDER SELF-WEIGHT IN FIXED BASE CONDITION:

Diagram showing BMD of the structural members

2. STRUCTURE WITH SOIL SUPPORT

The sub-grade soil can be assumed as spring support with sub grade modulus.

Subgrade modulus for dry medium sand is found to be 1.5kg/cm3 from IS2950.

The summary of node displacements and reactions is as below:

EXPERIMENTS ON FINE AGGREGATE:

In order to determine the properties of sand that is used to examine the soil structure interaction, a series of tests are conducted and the properties of sand are established.

List of the experiments conducted for establishing the soil properties are listed below:

Experiment conducted

1. Specific gravity

2. Sieve analysis

3.Dry density of sand

1. SPECIFIC GRAVITY

Purpose:

This experiment is performed to determine the specific gravity of sand by using a pycnometer. The Specific Gravity is the ratio of the mass of unit volume of the soil at a stated temperature to the mass of same volume of gas-free distilled water at a stated temperature.

Standard reference:

ASTM D 854-00- Standard Test For Specific Gravity of Soil Solids by Water Pycnometer.

Significance:

The specific gravity of a soil is used in the phase relationship of air, water, and solids in a given volume of the soil.

Apparatus:

Pycnometer, electronic weighing machine, funnel, and spoon.

Procedure followed:

1. The weight of the empty and dry pycnometer is determined and recorded, Wp.

2. Pycnometer is filled one thirds with dry sand and the combined weight is determined and recorded, Wps

3. The pycnometer is filled completely with water and the exterior surface is cleaned with a neat cloth. It is seen that no air is entrapped in the sand. The weight of the pycnometer and its contents is noted, WB

4. The pycnometer is now filled only with distilled water and wiped dry. Weight is noted, WA

Formula used:

The following formula is used to calculate the specific gravity of sand:

Specific Gravity:             G= (W2-W1)/((W4-W1)-(W3-W2))

Where:

W1 = Empty weight of pycnometer

W2 = Wt. of empty pycnometer + sand

W3 = Wt. of empty pycnometer +sand + water

W4=Wt. of empty pycnometer + water

Tabular column:

Table 3: Specific Gravity of Soil sample

 Specific Gravity of Soil sample

Therefore, average Specific Gravity = 2.635

2. SIEVE ANALYSIS

Purpose:

This test is performed to determine the percentage of different grain sizescontained within a soil. The mechanical or sieve analysis is performed todetermine the distribution of the coarser, larger-sized particles, and the hydrometermethod is used to determine the distribution of the finer particles.

Standard Reference:

ASTM D 422- Standard Test Method for Particle-Size Analysis of solids.

Significance:

The distribution of different grain sizes affects the engineering properties of Soil.Grain size analysis provides the grain size distribution, and it is required in classifying the soil.

Equipment:

Balance, Set of sieves, Cleaning brush, Sieve shaker, Mixer (blender), 152H Hydrometer, Sedimentation cylinder, Control cylinder, Thermometer, Beaker, Timing device.

Procedure followed:

1. Weights of all the sieves are noted down. 1000 g of sand sample is taken.

2. The sieves are cleaned and arranged in ascending order of their sizes. Then the soil is poured carefully into the top sieve. The whole setup is shaken well.

3. The amount of soil retained in each sieve is weighed and noted in the tabular column.

4. A graph is plotted between percentage fineness and particle size.

TABLE AND RELATED CALCULATIONS:

Grain size distribution for sand:

Grain Size Distribution of Sand

Particle size distribution curve:

Graph of Particle size distribution

Coefficient of uniformity(Cu) = D60/D10 = 0.52/0.31 (from graph)

                                          Cu=1.68

Coefficient of gradation(Cc) = D30 ^2/ (D10 X D60) = 0.42/(0.52*0.31) (from graph)

                                       Cc=1.00

                              % Fines= 0.15

Percentage of sand in soil= 99 (from graph)

Therefore, soil is sandy.

Cu is in between 1 and 3, Cc is less than 4 and %fines is below 5.

Hence the soil can be classified as Poorly Graded Sand.

3. DRY DENSITY OF SAND

Calculation of max and min dry density of sand:

Height of mould = 17 cm

Diameter of mould = 15 cm

Weight of mould= 2.408 kg

Weight of mould + wt of sample = 7.28

Wt. of sample = 7.28 kg

Volume of mould   = 3.004 * E-3

Minimum dry density = 15.675 KN/m^3

Decrease in height of 3.5 cm leads to increase in dry density

Recalculated volume = = 2.386 * E-3

Maximum dry density = 19.735 KN/m^3

Maximum void ratio (e max)= 0.58

Minimum void ratio (e min) = 0.26

Conclusion:

Experimental testing

In our study so far, the model is made ready for testing. The sand which is used as subgrade is classified as poorly graded sand (SP). The Specific Gravity (G) of the sand is determined to be 2.635. The maximum and minimum dry densities of the sand sample are determined to be 19.735 and 15.675.

Static load is applied on the aluminum frame and the settlements of supports will be measured. This steps will be repeted for different loads as well as for different types of soil, in our case sand and shedi soil. The obtained results will studied and the patterns will be analysed.

STAAD model testing

The model formed in STAAD is measured for settlement of supports on application of dead load. Two cases are taken, one for fixed base and the other for flexible base (soil having a sub grade modulus). These results are compared to realize the effect of settlement on shear force and bending moment of the members. The results of experimental tests and STAAD model tests are checked for consistency.

In future, the STAAD model will be examined for variatonsin the Bending Moment and Shear characteristics due to sinking of a row of supports as a whole and due to application of vertical as well as lateral loads. Modal analysis will also be performed in an attempt to understand the natural frequency response of the structure.

REFERENCES:

1. B R Jayalekshmi and others, “Experimental Investigation on Dynamic Characteristics of Structures Founded on a Dispersive Soil,” International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6, 1 (2008), 1–6.

2. Muberra Eser Aydemir, “SOIL STRUCTURE INTERACTION EFFECTS ON MULTISTOREY R / C STRUCTURES,” 2, 298–303.

3. Anoosh Shamsabadi and D Ph, “Dynamic Soil-Abutment-Foundation-Structure Interaction of an Instrumented Skewed Bridge”, 2008, 1–6.

4. Suleyman Kocak, “A Simple Soil ± Structure Interaction Model,” 24 (2000), 607–635.\

5. Paolo Negro and others, “LARGE SCALE SOIL-STRUCTURE INTERACTION EXPERIMENTS ON SAND UNDER CYCLIC LOADING”, 1–8.

6. Jean H. Prevost, “Nonlinear Dynamic Response Analysis of Soil and Soil-Structure Interacting Systems,” Soil Dynaics and geotechnical Earthquake Engineering, 1993.

7. Gary L Henderson, “Design and Construction of Driven Pile Foundations — Lessons Learned on the Central Artery / Tunnel Project”, 2006.

8. Jonathan P Stewart, “Interaction Principles.”

9. Alexander Tyapin, “Soil-Structure Interaction”, 2012.\

10. O F Indian, “CODE OF PRACTICE FOR DESIGN AND CONSTRUCTION OF RAFT,” 2950 (1998).