DEPARTMENT OF STRUCTURAL ENGINEERING MALAVIYA NATIONAL INSTITUTE
OF TECHNOLOGY, JAIPUR December 2011 A Seminar on SUPERVISED BY
DR.S.K. TIWARI Associate Professor SUBMITTED BY ANKIT SURI
(2010PST125) Slide 2 SOIL STRUCTURE INTERACTION Soil is a very
complex material for the modeling. It is very difficult to model
the soil-structure interaction problem. In RCC buildings slab on
grade is a very common construction system e.g. mat footing Very
heavy slab loads occur in these structures. Slide 3 For safe and
economical design, compute plate displacement and stresses
accurately. Difficult to obtain samples for testing producing
results in accordance with ground behavior. Necessary to make
simplifying assumptions. Slide 4 SCOPE OF STUDY To develop a
workable approach for analysis of plates on elastic foundations.
Structural Engineers go for simplified assumptions of rigid
foundation STAAD Pro is used to incorporate the elasticity of soil
that will provide approximate solutions as close to the exact
solutions. Slide 5 TYPES OF FOUNDATION MODELS The plate-foundation
system is idealized as a thin elastic plate resting on a linearly
elastic foundation. Various foundation models were given by the
investigators which are discussed ahead. Slide 6 WINKLER MODEL
Winkler first studied beam on elastic springs Model based on the
pure bending beam theory. p = Kw Here, w = vertical translations of
the soil p = contact pressure K = modulus of subgrade reaction
Slide 7 Plates based on Winkler model involve fourth order
differential equation: D 4 w+ Kw = q Here D is the plate flexural
rigidity, q is the pressure on the plate and is the Laplace
operator. The deformations outside the loaded area were neglected
and taken as zero. Slide 8 DEFORMATION OF A UNIFORMLY LOADED PLATE
ON TYPICAL WINKLER MODEL Source : Kerr A. D., "Elastic and
visco-elastic foundation models." Journal of Applied Mechanics,
ASCE, 31, 1964. p. 491-498 Slide 9 Winkler foundation model has two
major limitations: No interaction between springs is considered.
The spring constant may depend on a number of parameters, such as
stiffness of beam, geometry of beam, soil profile, and behavior.
Slide 10 FILONENKO BORODICH MODEL Top ends of springs connected to
a elastic membrane stretched to constant tension T. It was done to
achieve some degree of interaction between the spring elements,
Modulus of subgrade reaction is given by p = Kw T 2 w Slide 11
FILONENKO-BORODICH FOUNDATION MODEL Source : Kerr A. D., "Elastic
and visco-elastic foundation models." Journal of Applied Mechanics,
ASCE, 31, 1964. p. 491-498 Slide 12 HETENYI MODEL Embedded a plate
in the three-dimensional case in the material of the Winkler
foundation to accomplish interaction among springs. Assumed that
the plate deforms in bending only. p = Kw + D 2 2 w Here, p = load
w = vertical translation D = flexural rigidity of plate. Slide 13
PASTERNAK FOUNDATION MODEL Pasternak assumed shear interactions
between spring elements. Connecting the ends of springs to a beam
or plate consisting of incompressible vertical elements, which can
deform only by transverse shear. p = Kw - G 2 w Slide 14 TIMOSHENKO
MODEL This model is based on Timoshenko beam theory Plane sections
still remain plane after bending but are no longer normal to the
longitudinal axis. This model considers both the bending and shear
deformations. Slide 15 MODULUS OF SUBGRADE REACTION Pressure
sustained per unit deformation of subgrade at specified deformation
or pressure level. Calculated from plate load test from the plot of
q versus K = q/ Here, q = mean bearing pressure K = modulus of
subgrade reaction = mean settlement Slide 16 LOAD DEFORMATION CURVE
FROM PLATE BEARING TEST Source : Bowles J E., Foundation Analysis
and Design, McGraw-Hill, Inc., 1982 Slide 17 DETERMINATION OF
MODULUS OF SUBGRADE REACTION TERZAGHI His work showed that value of
k depends upon dimensions of area acted upon by subgrade reaction.
He incorporated shape and size effects in his equations Slide 18
For footings on clay: k = k1 x B f For footings on sand : k = k1 *
For rectangular footing on sand of dimensions b x mb: k = k1*
Where, k = desired value of modulus of subgrade reaction k1 = value
of k from a plate load test B f = footing width Slide 19 VALUES OF
K FOR SLAB ON WINKLER FOUNDATION Boit found that he could obtain a
good correlation with the Winkler model for the maximum moment case
by setting the value of k as follows: Where, Es = modulus of
elasticity of soil v s = Poissons ratio of the soil B = modulus of
elasticity of the beam I = moment of inertia of the beam Slide 20
Vesic showed that K depends upon the stiffness of the soil, as well
as the stiffness of the structure. Vesics work extended Boits
solution by providing the distribution of deflection, moment, shear
and pressure along the beam. He found the continuum solution
correlated with the Winkler model by setting Slide 21 Bowles (1982)
suggested an indirect method of approximate estimation of the value
of modulus of subgrade reaction. According to him it may be assumed
that net ultimate bearing capacity of a footing occurs at a
settlement of 25 mm. q nu = cN C S C + 1 D f NqSqr w + 0.5 2 BN S r
w k = = 40 q nu Slide 22 Values of modulus of subgrade reaction
(suggested by Bowles 1982) Type of SoilK (KN/m2/m) Loose sand4800 -
16000 Medium dense sand9600 - 80000 Dense sand64000 - 128000 Clayey
medium dense sand32000 - 80000 Silty medium dense sand24000 - 48000
Clayey soil : q u < 200 Kpa12000 - 24000 20048000 Slide 23
PROBLEM DEFINITION AND STRUCTURAL MODELLING STRUCTURAL MODEL
Three-dimensional structure is modeled for the analysis utilizing
the STAAD Pro software. The plan dimensions of the building are
34.92 m x 16.85 m. The Structure has 10 (G+9) stories with height
of 3.66 m each. Slide 24 The raft is modeled with the structure.
The total area of the raft is divided into finite number of plates.
The soil under the raft slab is represented by a set of springs for
which the spring constants k, adjusted to reflect the corresponding
soil type. Slide 25 PLAN OF THE STRUCTURE Slide 26 3 D VIEW OF
STRUCTURE Slide 27 MEMBER AND RAFT SIZES BEAM SIZE - 300mm X 450mm
COLUMN SIZE 450mm X 600mm RAFT SLAB is divided into finite number
of plates Approximately 1.0m x 1.0m plates are used. Thickness is
taken as 600mm. Slide 28 SUPPORTING SOIL MODELLING IN STAAD STAAD
has a facility for automatic generation of spring supports
specified under the SUPPORT command. The modulus of subgrade
reaction constant k for each soil type is taken as 10,000 kN/m 3,
45,000 kN/m 3, and 95,000 kN/m 3, representing soft, medium, and
stiff soil, respectively Slide 29 DESIGN LOADS DEAD LOAD (IS: 875
PART 1-1987) Self weight of floor slabs = 0.15 x 25 = 3.75 kN/m 2
Weight of floor finish (4 inches thick) = 0.1 x 20 = 2 KN/m 2
Weight of flooring (1 inch thick) = 0.025 x 26.70 (marble) = 0.6675
KN/m 2 Incidental load due to partition wall = 1.0 KN/m 2 (as per
clause 3.1.2 of IS 875 Part II) Slide 30 Dead load of wall (230 mm
thick) = 19 x 0.23 x 3.66 = 16 kN/m Dead load of plaster on wall =
2 x 0.012 x 20 x 3.66 = 1.76 kN/m Dead load of parapet wall =
19x0.23 x 1.0 + 2 x 0.012 x 20 x 1.0 = 4.85 kN/m Slide 31 IMPOSED
LOAD (IS: 875 - 1987 PART II) The magnitude of minimum imposed load
which has to be considered for the structural safety is provided in
IS: 875 -1987 (part II). Here imposed load of intensity 3kN/m 2 and
4kN/m 2 have been taken as per the code and same is applied in all
floors. On the roof it is taken as 1.5kN/m 2. Slide 32 SEISMIC LOAD
(IS: 1893 - 2002) The total design lateral force or design seismic
base shear V b is computed in accordance with the IS 1893 (Part I)
-2002 V b = A h x w Where Slide 33 Calculation of base shear is
carried out for structure located in seismic zone IV. Z = 0.24 I =
1.0 considering the structure is of general category. R = 3 for
OMRF Slide 34 PRIMARY LOAD COMBINATIONS ELX ELZ DL LL Where, ELX =
Earth-quake Load in X-direction ELZ = Earth-quake Load in
Z-direction DL = Dead Load LL = Live Load Slide 35 LOAD
COMBINATIONS 1. 1.5 (DL + IL) 2. 1.2(DL + IL + ELX) 3. 1.2 (DL + IL
- ELX) 4. 1.2 (DL + IL + ELZ) 5. 1.2 (DL + IL - ELZ) 6. 1.5 (DL +
ELX) 7. 1.5 (D L - ELX) 8. 1.5 (DL + ELZ) 9. 1.5 (DL - ELZ) 10. 0.9
DL + 1.5 ELX 11. 0.9 DL - 1.5 ELX 12. 0.9 DL + 1.5 ELZ 13. 0.9 DL -
1.5 ELZ Slide 36 RESULTS AND CONCLUSIONS It has been observed that
the stiff stratum at the base does not change the design forces
significantly. The bending moments at the base of the columns under
gravity loadings show a greater increase for soft soils as compared
to the medium and soft soil. As the stiffness of the soil strata
increased, structure behavior became closer to that observed for
rigid supports. Slide 37 BENDING MOMENT FOR EXTERIOR COLUMNS FOR
1.5(DL+LL) TABLE 7.2 Floor Level MZ (K=10000 KN/m 2 /m ) MZ (K=
45000 KN/m 2 /m ) MZ (K= 95000 KN/m 2 /m )MZ Bottom node Top node
Bottom node Top node Bottom node Top node Bottom node Top node
90.23-4.28871.753.8858.227.1-5.7814.76
0-23.3222.61-17.7820.44-17.3821.05-17.623.95
1-23.9225.44-24.0824.61-25.0125.34-27.5927.83
2-27.0328.09-26.7327.57-27.4928.27-29.4930.27
3-30.130.87-29.4430.19-30.0630.8-31.8632.52
4-32.4933.19-31.6632.35-32.1932.87-33.7434.36
5-34.535.07-33.5534.11-34.0134.56-35.3735.87
6-36.2736.56-35.1935.52-35.5935.92-36.7937.09
7-38.0238.25-36.7637.06-37.0937.4-38.1538.46
8-38.6744.27-37.3241.57-37.6241.54-38.5742
9-27.235.55-29.1136.51-30.1537.59-32.239.96 Slide 38 BENDING MOMENT
FOR INTERIOR COLUMNS FOR 1.5(DL+LL) TABLE 7.4 Floor Level MZ
(K=10000 KN/m 2 /m ) MZ (K= 45000 KN/m 2 /m ) MZ (K= 95000 KN/m 2
/m ) MZ Bottom node Top node Bottom node Top node Bottom node Top
node Bottom node Top node
-71.3434.43-33.9318.76-20.2112.95-1.631.91
0-15.5720.89-7.8211.38-6.18.85-2.884.27
1-22.8523.55-13.4414.24-10.6311.57-5.386.65
2-24.6924.53-15.4515.36-12.7912.74-7.787.84
3-24.5124.76-15.4715.76-12.9213.22-8.188.53
4-24.6824.43-15.7815.57-13.313.12-8.728.57
5-23.9923.64-15.2214.92-12.8112.52-8.348.08
6-23.1722.83-14.5214.23-12.1611.88-7.777.53
7-22.5222.3-13.9513.74-11.6211.41-7.297.08
8-22.1422.26-13.7614.16-11.5111.99-7.297.96
9-22.3328.4-13.0616.72-10.4813.48-5.687.42 Slide 39 ABRUPT CHANGE
IN BENDING MOMENTS AT THE BASE FOR FOUNDATIONS ON SOFTER SOILS
Generally this portion of the structure is not given consideration
in most of the practical designs which are based on the assumption
of rigid support system. Slide 40 DEFLECTION PROFILE FOR CASE OF
FIXED SUPPORT FIG 6.12 (a) (EQX) Slide 41 DEFLECTION PROFILE FOR
CASE OF ELASTIC SUPPORT FIG 6.12 (b) (EQX) Slide 42 For seismic
forces, magnitude of bending moments in the columns and beams of
the structure increase with the increase in modulus of subgrade
reaction. The structure on soft soil deflects as a whole body (Fig
7.12.) The relative displacements between successive floors are
less for structure on soft soils. Slide 43 BENDING MOMENTS AT
SUPPORT OF BEAM CONNECTED TO EXTERIOR COLUMN FOR EQX TABLE 7.5
Floor Level MZ (K=10000 KN/m 2 /m ) MZ (K= 45000 KN/m 2 /m ) MZ (K=
95000 KN/m 2 /m ) MZ -66.13-82.68-88.7-98.66
0-145.49-160.56-165.81-176.13 1-152.31-165.77-170.47-179.92
2-146.86-159.63-164.04-172.85 3-137.6-149.74-153.89-162.12
4-124.37-136.00-139.94-147.7 5-106.25-117.47-121.25-128.64
6-82.38-93.29-96.95-104.07 7-52.20-62.87-66.44-73.34
8-14.78-25.38-28.94-35.87 95.16-2.30-4.86-9.89 Slide 44 BENDING
MOMENT FOR INTERIOR COLUMNS FOR EQX TABLE 7.1 Floor Level MZ
(K=10000 KN/m 2 /m ) MZ (K= 45000 KN/m 2 /m ) MZ (K= 95000 KN/m 2
/m ) MZ Bottom node Top node Bottom node Top node Bottom node Top
node Bottom node Top node 43.0358.7281.5850.8896.9947.59132.5943.88
0 124.62-61.32133.36-70.07136.09-73.02142.35-78.43 1
83.7-76.6190.08-83.3692.4-85.7297.32-90.48 2
75.24-76.982.02-83.3884.37-85.6389.07-90.1 3
69.48-74.6175.82-80.7678-82.8782.35-87.04 4
62.47-71.0468.52-76.9270.58-78.9174.65-82.83 5
52.8-65.4258.61-71.0860.58-72.9964.43-76.72 6
40.32-57.4945.93-62.9947.82-64.8351.5-68.4 7
24.42-46.3629.89-51.7431.72-53.5435.27-57.03 8
5.45-33.0910.79-38.3312.57-40.0416-43.31 9
-18.655.33-13.16-2.17-11.31-4.73-7.65-9.76 Slide 45 STOREY DRIFT
For soft soils very significant increase in displacements of the
structure can occur when subjected to lateral forces due to
earthquake. For EQX forces deflection at the top floor was 10 to
12% more for structure supported on soft soils than that observed
for the case of fixed supports. Slide 46 Storey drift along
exterior column for EQX Floor LevelFixed K=10000 KN/m 2 /m K= 45000
KN/m 2 /m K= 95000 KN/m 2 /m 011.51213.66712.40212.111
123.86827.32925.22924.752 236.39841.14838.21837.56
348.65754.68250.9350.09 460.33467.62763.05462.037
571.90379.64874.25673.059 680.54190.35784.14482.77
788.2399.32192.28390.726 893.7106.07498.20596.465
996.81110.536101.79299.861 Slide 47 Storey drift along interior
column for EQX Floor LevelFixed K=10000 KN/m 2 /m K= 45000 KN/m 2
/m K= 95000 KN/m 2 /m 011.47813.42612.28112.024
123.7626.90724.99724.569 236.27740.55937.88337.288
348.44753.94150.50949.752 460.11166.75962.57961.658
570.89278.67773.75472.672 680.3889.29783.63582.395
788.11698.15891.75990.363 893.6104.76697.62896.078
996.633108.958101.06799.352 Slide 48 MORE BM IN MEMBERS DUE TO
DIFFERENTIAL SETTLEMENT IN SOFT SOILS. The softer the soil, the
more the differential settlement. This differential settlement
resulted in an increase in bending moments of raft slab. Slide 49
BENDING MOMENT CONTOURS FOR RAFT UNDER SEISMIC LOADS EQX and 1.2
(DL+LL+EQX) loading conditions have been studied. The moments in
the raft have been affected by the change in the values of the
modulus of subgrade reaction K, which is responsible for
differential settlement of raft slab. Slide 50 BM variations in
raft slab for K = 10000 kN/m 2 /m in EQX loading case Slide 51 BM
variations in raft slab for K = 45000 kN/m 2 /m in EQX loading case
Slide 52 BM variations in raft slab for K = 95000 kN/m 2 /m in EQX
loading case Slide 53 BM variations in raft slab for K = 10000 kN/m
2 /m in 1.2(DL+LL+EQX) loading case Slide 54 BM variations in raft
slab for K = 45000 kN/m 2 /m in 1.2(DL+LL+EQX) loading case Slide
55 BM variations in raft slab for K = 95000 in kN/m 2 /m
1.2(DL+LL+EQX) loading case Slide 56 As the value of modulus of
subgrade reaction decreases the differential settlements increase
leading to an increase in both the hogging and sagging bending
moments. The hogging moments produce tension at the top and can
cause the foundation to loose contact with soil. Hence due
consideration must be given to the elastic nature of soil in
design. Slide 57 RECOMMENDATIONS The soil structure interaction
must be considered in the design of structures. At the design
stage, specific effort must be made to find the realistic value of
modulus of subgrade reaction depending on the type of soil, so that
we can get the exact design forces for optimum design solution.
Slide 58 REFERENCES Bowles J E., Foundation Analysis and Design,
McGraw- Hill, Inc., 1982 Kerr A. D., "Elastic and visco-elastic
foundation models." Journal of Applied Mechanics, ASCE, 31, 1964.
p. 491-498. Daloglu A. T. and Vallabhan C. V. G., "Values of K for
slab on Winkler foundation" Journal of Geotechnical and
Geo-environmental Engineering, Vol. 126, No.5, 2000 p. 361-371. Fwa
T.F., Shi X.P. and Tan S.A., "Use of Pasternak foundation model in
concrete pavement analysis" Journal of Transportation Engineering,
Vol. 122, No.4, 1996 p. 323-328 Slide 59 Horvath J. S., "Modulus of
subgrade reaction: new perspective," Journal of Geotechnical
Engineering, Vol. 109, No. 12, 1983, p. 1591-1596. Liou G. S. and
Lai S.C., "Structural analysis model for mat foundations," Journal
of Structural Engineering, Vol. 122, No.9, 1996. p. 1114-1117.
Mishra R. C. and Chakrabarti S. K., "Rectangular plates resting on
tensionless elastic foundation: some new results", Journal of
Engineering Mechanics, Vol. 122, No 4, 1996. p. 385-387. Shi X.P.,
Tan SA and Fwa T.F., "Rectangular thick plate with free with free
edges on Pasternak foundation" Journal of Engineering Mechanics,
Vol. 120, No.5, 1971- 1988. Slide 60 STAAD Pro V8i, Structural
Analysis and Design Package, Research Engineers. Stavridis L. T.,
"Simplified analysis of layered soil- structure interaction,"
Journal of Structural Engineering, Vol. 128, No.2, 2002. p.
224-230. Wang C. M., Xiang Y. and Wang Q., 2001, "Axisymmetric
buckling of reddy circular plates on Pasternak foundation," Journal
of Engineering Mechanics, Vol. 127, No 3 Yin J-H., "Comparative
modeling study of reinforced beam on elastic foundation" Journal of
Geotechnical and Geo-environmental Engineering, ASCE, 126(3), 2000.
p 265-271. Slide 61 IS 875(Part 1): 1987: Indian Standard Code of
Practice for Design Loads (Other than earthquake loads) For
Buildings and Structures. (Dead Loads) IS 875(Part 2): 1987: Indian
Standard Code of Practice for Design Loads (Other than earthquake
loads) For Buildings and Structures. (Live Loads) IS 875(Part 5):
1987: Indian Standard Code of Practice for Design Loads (Other than
earthquake loads) For Buildings and Structures. (Special Loads and
Load Combinations) IS 1893 (Part 1): 2002: Indian Standard Code of
Practice for Criteria for Earthquake Resistance Design of
Structures. (General Provisions and Buildings) IS 456: 2000: Plain
and Reinforced Concrete Code of Practice Slide 62 THANK YOU