Computers & Strvetwcs Vol. 40, No. 5, pa. 12354247, 1991 cw5-7949j91 s3.00 +o.oo Ptintcd in Great Britain. papmon~p*

SOIL-STRUCTURE INTERACTION OF SPACE FRAME-RAFT-SOIL SYSTEM-A PARAMETRIC STUDY

J. NOORZAJZI, M. N. VILADKAR and P. N. GODBDLR

Department of Civil Engineering, University of Roorkee, Roorkee 247 667, India

A~-This study deals with physical modelling of space framcraft and soil system by using isoparametric beam bending element to represent beams and columns of the frame, plate bending element for representing raft as well as slabs of the structure. The soil mass has been idealized by coupled finite-infinite btick elements. Furthermore, a detailed parametric study of the e&t of variation in raft and slab thicknesses on the interactive behaviour of space frame-raft-soil system has been carried out.

1. INTRODUCTION

The intluence of interaction between a space frame, raft, and soil mass on the redistribution of bend- ing moments, shear forces, contact pressures and differential settlements have been reported by several authors. Hain and Lee [l] and King and Chandrasekaran [2,3] have proposed the use of sub- structure techniques in conjunction with finite el- ement formulation to model space frame-raft-soil systems. Brown[4] examined the effect of the se- quence of construction on the interactive behaviour of space frame-raft-soil system.

2. PROBLEM DEFINITION

The review of earlier work suggests that although attempts have been made to analyse the problem of space frame-raft-soil interaction, very little information is available regarding the effect of slab thickness on the behaviour of the entire space frame-raft-soil mass system. Moreover, the effect of variation of raft thickness on the three compatible components has not been reported.

Therefore, the present work concerns with the interactive analysis of a four-storey, five-bay by three- bay space frame-raft-soil system [2,3]. The isometric view of the quarter of the space frame-raft is shown in Fig. la. Figures lc and d show the front and side elevations of the frame along with the geometry of the superstructure.

Figure 2 shows the finite-infinite element dis- cretixation of the superstructure including slab, raft and soil medium using quarter symmetry. This figure shows the detailed discretization of the top floor and the slabs of other floors follow the same trend of discretization.

Since, the present idealization includes the slab as part of superstructure, it is possible to represent the loading in the most natural way, i.e. the beams carry only dead load (5 kg/cm) and slabs are subjected to live load as well as their own weight (0.08 kg/c&) as demonstrated in the Fig. la. The variation of

Young’s modulus of elasticity of soil with depth has also been taken into consideration.

Furthermore, the present study brings out the importance of the stiffness of superstructure and raft on the interactive nature of frame-raft+oil mass. This has been achieved by carrying out the following parametric study:

(a) effect of variation of raft thickness. The various raft thicknesses considered were 40, 50, 60, 80, 100 and 120cm,

(b) effect of variation of slab thickness. The various slab thicknesses considered were 10.0, 12.5, 15.0, 17.5 and 20.0 cm.

3. MATHEMATICAL MODELLING (FOBMULA‘IION)

The interactive analysis of a space frame-raft-i1 system was carried out by representing beams and columns of the superstructure by means of isopara- metric beam bending element. Plate bending element was used to model the slabs of the superstructure and the raft supporting the frame. The soil medium was discretixed using the coupled Gnite-infinite elements. Figure 3 shows the various elements along with their degrees of freedom per node which have been em- ployed in the mathematical modelling of space frameraft and soil mass system.

The details of the formulation of these elements have already been presented elsewhere [5,6]. As the discretization consists of a variety of elements with varying degrees of freedom per element, a specially developed frontal solver with multi-elements and variable degrees of freedom features[7], has been used for the purpose of assembly and solution of the resulting equation system.

4. RESULTS AND DIBCUBBION

4.1. Eflect of variation of raft thickness

4.1.1. Settlements. Figure 4, shows the plot of total settlement at the centre and comer of the raft and also the differential settlement with respect to various

1235

1236 J. NOORZAEI et al.

I

: I

(c f LONGITUOINAL ELEVATION (SECTION-BE)

500 _,Soo -500 4 t t

.o:

SCALE 1

I’

C7 2

CS 3

C3

C: 5

(d) SIDE ELEVATION f~)lSOMETRIC VIEW OF THE QUARTER SPACE FRAME (SECTION - DD 1

AN0 RAFT SHOWING APPLIED LOAD

SE-a

lb) PLAN OF RAFT FOUNOATION

+ COLUMN POSITION (ALL DlMENSiONS IN cm)

Fig. I. Layout of space frame.

Soiitructum interaction 1237

Es% =1.&x lo5 kqtcm* s,tt = 0.3

J-NODE0 ISOPARAMETRIC SEAM eENOIN6 ELEMENT

8-NOOED ISOPARAMETRIC PLATE BENOING ELEMENT

16”NODE0 PARALINEAR ISOPARA- METRIC FIN tt ELEMENT

16- NODE0 ISOPARAMETRIC INFINITE ELEMENT

- 8- NODE0 lSOPARAMEtRIC LINEAR ELEMENT

=Sb- B-NOOEO I~~RAM~TRIC INFINttE ELEMENT

WITH OEPTH

ALI. BEAMS ARE OF (30x61) cm, INTERIOR COLUMNS OF GROUNO

- L AN0 FIRST FLOOR (&Ox&G) cm AN0 REST (36x36) cm

Fig. 2. Multielement discwtization of structure-raft-soil system.

1238 J. NOORZAE ez al,

(a) 3-NODED 1SOPARAMETRIC BEAM BENDING ELEMENT WITH 5 0.O.F /NODE

t b) &NC&D ISOPARAMET RIG ELEMENT WITH 5 0.0.F

Tt

PLATE BENDING / NODE

4 6 ---?

J Fs

k) O-NODE0 ISDPARAM~TR~C LINEAR FfNfTE ELEMENT

(c) 8- NODED ISOPARAMETRIC (9 1 I&- NODED ISOPAffA~~TRlC INFINITE ELEMENT INFINITE ELEMENT

fd) 164 NODED tSOPARAM~7RfC FARAL~NEAR FINITE ELEMENT

Fig. 3. Different element-configuration used in discretization

2.6 TOTAL SETTLEMENT AT THE CENYRE OF THE RAFY

_ TOTAL SEffLEMENf At YHE CORNER OF THE RAFT

_ f-- DIFFERENTIAL SE7TLEMENT

0.6 I f , I r , 1 L r

30 SO 70 90 II0

THICKNESS OF RAFT, cm

Fig. 4. Variation of total and differential settlements with various raR t~ckn~~.

raft thicknesses. It emphasizes that with increasing 4.1.2. Contact pressure. The variation of con- raA thickness, the total settlement at the centre of tact pressure distribution below the raft is illus- the raft reduces while that at the comer increases. trated in Fig. 5 which shows that as the thickness This causes a substantial reduction in differential of raft increases the contact pressure reduces, settiexnent. The values of raft thicknesses considered in the

J. COLUMN POSlTlON

Fig. 5. Variation of oontsct pressure distribution below the raft along section BB.

1240 J. NOORZAEI et al.

-2.5

-3.0

1. COLUMN POSITION

-3,s I I I I I I I I I I I 1

0 0.4 0.8 1.2 1.6 2.0 2.4

(X/B)

Fig. 6. Variation of moment M, in the raft along section BB.

analysis correspond to the values of relative stiff- 41.3. Bending moments. ness of raft to soil, 1.5 x 10m3, 2.95 x lo--‘, 5.1 x 4.1.3.1. Raft. Figures 6 and 7 show respectively the 10-3, 12.1 x 10-3, 23.6 x 10m3 and 40.8 x 10b3, variation of bending moments, M, and M, along respectively. section BB. As expected these moments increase with

2.8

(X/B)

Fig. 7. Variation of moment M, in the raft along section BB.

soil-stroct~ iRteraetian 1241

4L

3”

2-

l-

6-

ot 4 SEC~ON-~B , I I I 1 I I 1 I

20 40 60 80 100 120

THICKNESS OF RAFT, cm

Fig. 8. Variation of moment M, for end A at various storey levels.

the increase of raft thickness or increase of raft meut, contact pressure and stiffness. The positive values of bending moments results in significant changes _. _ .

foundation stiffness in the moments and

indicate hogging type and negative values indicate forces m superstructure. sagging moments. The plots of variation of bending moment, M,

along the section BB are sbown in Figs g-10 at 4.1.3.2. Frume. (a) Colwnnr. It has been an estab- various storey levels for different raft thicknesses. lished fact that any change in the diffe~tial settle- These plots ~~-~~t that in column A, there is an

1.6

i t

40 60 60 100

THICKNESS OF RAFT, cm

Fig. 9. Variation of moment M, for end B at various storey levels.

1242 J. NOORZAEI et al.

I .o

01 I I I END iB’ I 1 I I 1 30 50 70 90 110 130

THICKNESS OF RAFT cm

Fig. 10. Variation of moment, M, for end C at various storey levels.

increase in moment M, at ends A, and A, with (b) Beams. It is obvious from Figs 12 and 13 increasing raft thickness while at the other storey that the values of bending moment, M, for end, levels, the moment M, reduces marginally. The E increase with increasing raft thickness (up column, B gets relieved of the moment si~ifi~ntly to 8Ocm) whereas the end, F experiences the whereas the moment in column C increases up to a opposite trend. The end, D (Fig. 11) experiences thickness of the raft equal to 80 cm beyond which it no effect on M, values due to increasing raft practically remains constant. thickness.

4.9

4.8

l --

* * 01

4.3 -

z 0 0

04 f% F4

03 E3 F3

02 E2 F2

THlCl%EIESS OF RAFT, cm

Fig. 11. Variation of moment M, for end F at various storey levels.

ie.81 t i I I L t

Em” = 1 END F+

I ,-rND D I

20 40 SO 80 100 120

THiCnNESS OF RAFT, cm

Fig. 12. Variation of moment M, for end E at various stormy kvcls.

4.2. Ej’ect of variation of slab thickness

4.2.1. Bending moments in frame.

respectively. The outermost column, A is practically unaffected due to increase in slab thickness. The

4.2.1.1. Colrunn,p. Figures 14-16 illustrate the va& column B remains unaEected in the lowermost stony but the upper storeys show sign&ant increase (up to

ation of moment, M, at ail the storcy levels with 3%35%) in moment. Column C also shows same different slab thickness as for cohmms A, B and C, trend as column B.

E

P I

“9

4.0 - DI El Fl *

i 3.s e 1 I I t 1 I f I I L .

20 40 60 60 100 120

THICKNESS OF RAFT I =m Fig. 13. Variation of moment M, for cud F at various stony ievcis.

J. NOORZAEI ef al.

h h A A n 0 c ”

d

+ I T , *

As

At

A3

A2

Al

I t * t I ,

10 12 14 16 18 20

TnlCHNESS OF SLAB, cm

Fig. 14. Variation of momeat MS for column A at various storey levels.

4.2,1.2. &wns. The moment, Iw, for ends D, E 5. CONCLUSKkNS

and F are plotted in Fig 17-19, respectively. ft is 1. The mathemati~1 rn~~ll~n~ in the present obvious from these plots that beams are relieved, by study which takes into account the slab as part about 40-50%, of moments as the stiffness of slab of superstructure is the most natural way of increases. ~pre~ntation of the space frame raft-soil system.

2.8

2.4

2.0

1.6

1.2

0.6

8 , 1 I I s t I 1 1 a.4 I 8 8

8 to 12 14 16 te 20

THiCKNESS OF SLAB, cm

Fig. If. Variation of moment Aa, for column B at various atorcy fevels.

Soikructure interaction 1245

0.65-

E

,” 0.55-

.

“0

I

r” 0.45-

0.35 -

. l Ct 0.25. I 1 I t I 1 I I I t I I I

8 10 12 14 16 18 20

THICKNESS OF SLAB, cm

Fig. 16. Variation of moment M, for c&mm C at various stow levels.

2. The increase in the stiffness of raft overwhelm- 3. Increase in slab thickness causes insignifl- ingly leads to reduction in differential settlement, cant changes in the settlement, contact pressure, contact pressure, increase of moments in raft and and moments of raft. But it produces sign&ant further redistribution of moments in the superstruc- modification of the moments in superstructure ture members. members.

4-2 -

3.0-

2.6 -

THICKNESS OF SLAB , cm

Fig. 17. Variation of moment M, for end D at various storcy levels.

1246 J. NOQRZAEJ et al.

t t 1 1 1 I 1 1 1 1 I t I

8 10 12 14 16 18 20

THICKNESS OF SLAB ,cm

Fig. 18. Variation of moment M, for end E at various storey levels.

5.5 -

4.5 -

3.5 ”

s 10 12 14 16 16 7.0 22

THICKNESS OF SLAB , cm

Fig. 19. Variation of moment M, for end F at various storey levels.

REFERF#NCES

1. S. J. Hain and 1. K. Ltc, Rational analysis of raft foun- dation. J. Gecwch. Div., AXE 100, 843-860 (1974).

2. 0. J. W. King, An in~~on to superstruc- ture/raft/soil intrraction. Proc. Znt. Sym,p hn SoU Strut- ture Interaction, Vol. I, pp. 453466. Roorkee, India (1977).

3. G. J. W. King and V. S. Chandrasekaran, Interactive analysis of rafted multistoreyed space frame resting on the inhomogeneous clay stratum. Ibe. Irzt. Conf. on F.E.M. in Engng, pp. 493-509, University of New South Wales, Australia 0974).

4. I’. T. Brown, Load sequence and s~t~o~~- tion-interaction. J. Struct. I%., ASCE 11% 48148 (1988).

Soil-structure interaction 1241

5. P. N. Godbole, M. N. Viladkar and J. Noorzaei, variable degrees of freedom features. Compur. Struct. Space frame-raft-soil interaction including effect of (in press). slab stiffness. Comput. Stmct. (to be published). 7. M. N. Viladkar, P. N. Godbole and J. Noorzaei, Some

6. P. N. Godbole, M. N. Viladkar and J. Noonaei, new three dimensional infinite elements. Comput. Stmct. A modified frontal solver with multi-element and 34 455-467 (1!9!30).