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INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING

Volume 2, No 1, 2011

© Copyright 2010 All rights reserved Integrated Publishing services

Research article ISSN 0976 – 4399

Received on June 2011 published on September 2011 1

Influence of structural and soil parameters on Mat deflection Imam, Md. Hasan.

Lecturer, Department of Civil Engineering, Southern University, Bangladesh.

[email protected]

ABSTRACT

The present study was carried out to investigate the deflection characteristics of mat

foundation for structural and soil parameters. The gap in knowledge about mat deflection

characteristics brings some uncertainty in analysis of mat foundation and may result in its

uneconomical design or unsafe design. For economy in design of mat with service core

requires comprehensive understanding of the influence of it on mat. This work involved

an extensive investigation of structural parameters effect on deflection of mat foundation

using Finite Element Program SAFE V8. A comparative study has been made among

some critical positions of the mat foundation using finite element methods in order to

perceive the influence of different parameters that assist to understand the practical safety

limit of the design characteristics. As only rigid frame structure with gravity and lateral

load cases are considered here for the present work, further scope of the study maybe

based on other types of structural system and mathematical modeling of mat response.

Key words: Deflection, Mat, Finite Element, Structural Parameters, Soil parameter

1. Introduction

1.1 Overview

Mat foundation is a simple structure. Once everything is set by engineers and architects

for a particular project, it has a relatively small number of parameters to be dealt with,

such as elastic properties of mat materials, modulus of sub grade reaction of supporting

soil and mat thickness. But difficulty with the formulation of the characteristics of mat

arises from its loading patterns, geometric properties and supported superstructure

parameters. So the enthusiasm of present work goes to investigate the mat response

against the structure parameters such as mat thickness, column spacing, column size,

width of overhanging portion, span-width (L/B) ratio of panel and type of soil.

1.2 Objectives of the work

The objectives of this thesis work are

1. To select the effective parameters for mat foundation that affects the mat

response.

2. To study the influence of different structure parameters such as mat thickness,

column spacing and size, overhanging portion of mat and span –width ratio of

panel etc. on mat deflection.

Influence of structural and soil parameters on Mat deflection

Imam, Md. Hasan.

International Journal of Civil and Structural Engineering

Volume 2 Issue 1 2011 2

1.3 Scope of the Work

An understanding of the actual behavior of mat foundation is essential to ensure

economy and safety in design. Present study focuses on influences of structural

parameters of framed structure building and that of mat foundation. This study

recommends mat deflection characteristics. It reveals the changes in mat deflection

behavior due to variation of different parameters.

2. Modeling and Structural Idealization

2.1 Overview

Finite element method is the most powerful and versatile of all the available numerical

analysis techniques. In this method the structure to be analyzed is modeled as an

assemblage of a finite number of elements and the displacements of the

connecting points. The applied loads are transferred into equivalent nodal points

and for each element; the relationship between the nodal points and nodal

displacements is established. Through displacement method assembling of the

element load-displacement relations for the whole structure can be found upon which

nodal displacements and stress- strain at the nodes are found concurrently.

The ultimate objective of this study is to analyze mat foundation by Finite Element

Method. Mat foundation is a three dimensional thick plate structure. When superstructure

loads are being transferred, mat transverse bending moment and flexural shear are the

most important internal forces produced in response to the loads. Super structural loads

usually axial column forces and column base transferred moments. Thick plate option

has been taken into considerations readily available in most recent and pioneer mat

foundation analysis and design by Finite Element Method named SAFE. Non linear

analysis is well adjusted along with discrete elastic springs under mat foundation found

very favorable in this software. For parametric study a number of idealized fifteen storey

buildings with mat foundation has been modeled and analyzed both for vertical and

lateral loads with renowned three dimensional structural analysis software ETABS.

Three dimensional analysis model support reactions i.e. axial forces and base moments

have been transferred to finite element mat foundation analysis software SAFE.. In

present study mat with different mat thickness, column spacing, column size, width of

overhanging portion, L/B ratio of panel and type of soil have been taken into account for

sensitivity analysis and comparison considering sub grade reaction is already known

by soil test results and conventional method.

For present study of mat response a typical fifteen storey frame building is modeled as a

reference building-mat system. This reference model has four bays in both directions. In

this model column center to center spacing and column cross sectional properties were

taken uniform. For profound study other building-mat systems with different structural

and bearing soil parameters were modeled which have same number of bays. The

variations of parameters of these models are given below in Table 1.


Imam, Md. Hasan.



Table 1: Variations of parameters of the models

Parameters

Reference

value

Ranges of variations

Mat thickness 5ft 4ft, 4.5ft, 5ft, 5.5ft, 6ft

Column spacing 20ft 16ft, 18ft, 20ft, 22ft, 24ft

Column Size 20”x20” 16”x16”, 18”x18”, 20”x20”, 22”x22”, 24”x24”

Over hanging portion 3ft 2ft, 2.5ft, 3ft, 3.5ft, 4ft

L/B ratio of the panel 1.0 0.8, 0.9, 1.0, 1.1, 1.2

Modulus of sub grade

reaction

150 psi/in For sandy soil :

18 psi/in, 35 psi/in, 60 psi/in, 150 psi/in, 236

psi/in, 295 psi/in, 472 psi/in.

For clayey soil:

44 psi/in, 88 psi/in, 150 psi/in, 177psi/in,

250psi/in, 350 psi/in.

The material properties of mat are taken as follows –

Poison’s ratio, = 0.25

Modulus of elasticity, E = 3600 ksi

Shear modulus, G = 1500 ksi

Concrete strength, f’c = 4 ksi

and steel yield strength, fy = 60 ksi.

2.2 Idealization of Mat

Mat is a three dimensional thick plate structure that acts integrally with the building

frame and supported by soil strata. Now-a-days, parking access for high rise

building is totally dependent on underground basement. Available methods do

not emphasis different structural parameters such as modulus of sub grade reaction, mat

thickness, column spacing, column size, over hanging portion, L/B ratio of the panel and

mat foundation interactions. Variation of theses parameter can influence the behavior

of mat significantly. For present study uniform mat thickness was varied from 4.0 feet

to 6.0 feet both for square and rectangular column grids model. Later column

spacing variation from 16 feet to 24 feet and column size variation from

16’’x16”to 24”x24” were critically reviewed. Finally over hanging portion variation from

2 feet to 4 feet and the panel span-width(L/B) ratio variation from 0.8 to 1.2 were also

decisively observed.

A soil structure interaction is an important process of predicting overall structural

response of any sub grade structure. Settlement profile and soil pressures for mat

foundations are dependent on relative stiffness of mat and it’s supporting soil strata. In

present study Winkler's model on foundation on elastic medium has been used for

representation of the soil behavior by discrete vertical nonlinear springs. Soil has

been idealized by modulus of sub grade reaction (ks).


Imam, Md. Hasan.



Bowles (1988) suggested the following equations for approximating k value from

allowable bearing capacity.

k = 12* Factor of Safety * q, (In kip per cubic feet unit).

Where,

q= Allowable bearing capacity in ksf.

F.S = 2.5 (BNBC, 1993)

In present study modulus of sub grade reaction (k) for sandy soil was varied from 18

psi/in to 472 psi/in and for clayey soil modulus of sub grade reaction (k) was varied

from 44 psi/in to 350 psi/in and were assigned in SAFE program as an input spring

data. ACI318-95 design code was reviewed by this program and concrete's Poison

ratio was taken as 0.25.

3. Analysis of Mat deflection characteristics

3.1 Overview

Structurally mat is a two way flexural member supporting superstructures and directly

supported by soil support. Naturally, design of mat is governed by moment, shear,

punching shear and deflection considerations. In order to be structurally safe, mat must

be strong enough to resist the moments, shear and punching coming from the supported

column loads. And deflection must be within allowable limits. So for the present study

the deflection characteristic is observed.

Figure 1: Plan view of 15-storied building mat showing locations for study of mat

response

This behavioral characteristic is studied in the selected critical locations of mat which are

shown in Figure. 1. In this figure points A, E and F are selected for deflection study. The

selected behavioral characteristic is investigated for variation of structure parameters and

soil type.


Imam, Md. Hasan.



3.2 Effect of Mat Thickness on mat deflection

Deflection of mat at mat center (location-A), at mat corner (location -E) and at interior

panel midpoint (location-F) against mat thickness using FEM is drawn in Figure 2. It is

seen that deflection decreases at mat center (location-A) and at mat corner (location -E)

but increases at interior panel midpoint (location-F) with increase of mat thickness. This

is because the stiffness increases with increase of mat thickness. In the figure the curves

are seen to be nonlinear.

Figure 2: Variation of deflection at location-A, at location-E and at location-F with the

variation of mat thickness.

3.3 Effect column spacing on deflection:


panel midpoint (location-F) against column spacing using FEM is drawn in Figure 3. It is

observed that deflection increases at mat center and decreases at interior panel midpoint

with increase of column spacing. And deflection varies in a wavy pattern with increase of

column spacing at mat corner. This is because the stiffness of mat changes with increase

of column spacing. These variations are seen to be nonlinear. These values are obtained

from the finite element analysis by SAFE.


Imam, Md. Hasan.




variation of column spacing

3.4 Effect of column size on deflection


panel midpoint (location-F) against column size using FEM is drawn in Figure 4.

Deflection varies at mat center, at mat corner and at interior panel midpoint in similar

nonlinear sinusoidal pattern with increase of column size.


variation of column size.


Imam, Md. Hasan.



This is because the stiffness of mat changes erratically with increase of column size.

These variations are seen to be nonlinear. Deflection values are obtained from the finite

element analysis by SAFE.

3.5 Effect of overhanging portion size on deflection


panel midpoint (location-F) against width of overhanging portion using FEM is drawn in

Figure 5. Deflection increases slightly at mat center and at interior panel midpoint in

similar linear pattern with increase of over hanging portion of mat. This is because the

earth pressure distribution below mat changes with changes of overhanging portion of

mat. Whereas at mat corner deflection decreases nonlinearly and more sharply with

increase of over hanging portion of mat. From these variations it is experientially

observed that when deflection within mat is not significantly influenced by overhanging

portion, it is sharply affected at mat corners. Deflection values are obtained from the

finite element analysis by SAFE program.


variation of overhanging portion of mat.

3.6 Effect of span-width (L/B) Ratio of Panel on mat deflection


panel midpoint (location-F) against span-width (L/B) ratio of panel using FEM is drawn

in Figure 6. The deflection at mat center, at mat corner and at interior panel midpoint

increase up to an L/B ratio and after being maximized, deflection decreases with L/B

ratio. Deflection is maximized at unit L/B ratio at mat center and at interior panel

midpoint but at mat corner deflection is maximized at 1.1 L/B ratio.


Imam, Md. Hasan.




variation of L/B ratio of the panel.

3.7 Effect of soil subgrade reaction on deflection


panel midpoint (location-F) against modulus of sub grade reaction of soil using FEM is

drawn in Figure 7. Deflection decreases at mat center, at mat corner and at interior panel

midpoint with increase of soil sub grade reaction.


variation of subgrade reaction in soil.


Imam, Md. Hasan.



According to the definition the deflection is inversely proportional to the soil sub grade

reaction modulus (kS = ). This is because the stiffness of mat increases with increase of

soil sub grade reaction. In the figure the curves are nonlinear with negative and

decreasing slope. So the analysis values conform to the theoretical characteristics. These

values are obtained from the finite element analysis by SAFE.

4. Conclusions

A meticulous analytical and comparative study on effect of different structure parameters

and soil type on mat response is conducted in this work. In the light of the preceding

discussions the following conclusions may be drawn:

1. Deflection decreases at mat center and at mat corner with increasing mat

thickness. Deflection at interior panel mid point is, however seen to increase

with mat thickness. The variation is nonlinear in all cases.

2. Deflection at mat center increases and at interior panel center decreases with

column spacing. The variation of deflection at mat corner is sinusoidal with

column spacing.

3. Increase of column size shows a wavy effect on deflection.

4. Mat deflection within mat is not significantly influenced by overhanging

portion; it is sharply affected at mat corners.

5. Mat deflection shows a wavy (sinusoidal) character with changing of span-

width ratio of panel.

6. Mat deflection decreases nonlinearly with increasing modulus of sub-grade

reaction at all critical position.

5. References

1. ACI Committee 336(1966), “suggested design procedure for combined

Footings and Mats” (ACI 336.2R-66), Reaffirmed 1980, American concrete

Institute, Detroit, pp-13.

2. BNBC, 1993, “Combination of Loads for Strength Design Method”. part-6 :

pp. 67

3. Bowles, J.E (1974), Analytical and Computer Method in Foundation

Engineering, Mc Graw Hill Book Co., New York, NY10020.pp.128-145 and

207-253.

4. Bowles, J.E (1977), Foundation Analysis and Design, 5th Edition, Mc Graw

Hill Book Co., New York, NY10020.pp.501-506 and 537-588.

5. Coduto, Donald P. (2001), Foundation design: principles and practices,

Prentice Hall Pvt. Ltd. pp. 363-369.


Imam, Md. Hasan.



6. Curtin, William George; Seward,N. J.; Shaw,Gerry and Parkinson,Gary

(2006), Structural foundation designers' manual, Blackwell Publishing Asia

pty Ltd.

7. Design and Performance of Mat foundations - State of the Art Review, SP-

152, American Concrete Institute, Detroit, 1995.

8. Gupta, S. Chandra (2007), Raft Foundation Design And Analysis With A

Practical Approach, New Age International.

9. Imam,Syed Zubair (2003), Effect of Shear Wall on Behavior of Mat

Foundation.

10. Jumikis, A.R., Soil Mechanics and Foundation Engineering. ASCE, 1956.

11. Morshed, A.S.M. Monzurul (1996.), A Design Rationale for Mat Foundation

Based on Finite Element Analysis.

12. Nilson, A. H., D.Darwin, Dolan, C.W., (1943), Design of Concrete Structures-

13th Edition, Mc Graw Hill Book Co., New York, NY10020 pp 427-442.

13. Peck , R.B., Hanson , W.E., and Thornburn, T.H. (1974), Foundation

Engineering 2nd Edition , John Wiley & Sons , New York, pp.514.

14. Rahman, Syed Mizanur (2001), An Improved Design Approach for Mat

Foundation with Variable thickness.

15. Som , N. N. and Das , S. C. (2003), Theory and Practice of Foundation

Design, Prentice Hall Pvt. Ltd. New Delhi.

16. Technical reference, SAFE v8 Tutorial manual.

17. Teng, Wayne Chi-Yu (1962), Foundation Design, Prince-Hall Inc ,

Englewood Cliffs, pp. 151-154, 174-183, 189-191 and 466.

18. Timoshenko and Woinowsky – Krieger (1959), Theory of Plates and Shells.

19. Tomlinson, Michael John; Boorman, R. (2001), Foundation design and

construction, Prentice Hall Pvt. Ltd.

20. Varghese, P.C. (2005), Foundation Engineering, PHI Learning Pvt. Ltd.