This paper presents numerical analysis of soil-structure-interaction (SSI) of tall reinforced concrete chimneys with piled raft foundation subjected to El Centro ground motion (1940) using finite element method. Seismic analysis in time domain was performed on the basis of direct method of SSI on the three-dimensional SSI system. The chimney, foundation, and soil were assumed to be linearly elastic in the analysis. The stress resultants and settlement of raft of piled raft foundation were evaluated under different soil properties and different geometrical features of raft and chimney. Soil properties were selected based on the shear wave velocity corresponding to sand in the loose to dense range. Chimneys with different elevations of 100 m, 200 m, and 400 m were taken with a ratio of height to base diameter of chimney of 17. Raft of different thickness was considered to evaluate the effect of stiffness of foundation. Results were analysed to assess the significance of characteristic of the ground motion. It is found that the response in the raft depends on the different parameters of chimney, foundation, and soil. It is also found that the higher modes of SSI system are significant in determining the response in the raft.
Most of the analysis of piled raft foundation neglects the effect of geometrical and material features of the superstructure. Generally the loads and moments from the superstructure to foundation are only considered for the analysis of foundation. The shape and size of the superstructure such as chimney have their own significance to determine the responses in foundation. Chimneys are tall and slender structures with tapering geometry. Analysis of such kind of chimney-foundation system that rests on soil which is of unfavorable geotechnical conditions will be too complex especially when it is subjected to earthquake ground motions. The present study deals with the seismic analysis of chimney with piled raft foundation considering the flexibility of soil in time domain.
Very few studies have been carried out in the area of dynamic analysis of soil-piled raft-structure interaction compared to that of soil-pile-structure interaction [
The two basic methods involved in the solution of soil-structure interaction (SSI) problems are referred to as the direct method and substructure method. Wolf [
Very few studies were conducted for the static and dynamic SSI analysis of chimney-foundation system. The distribution of bending moments and shear force along the height of chimneys due to earthquake ground motion considering the soil flexibility was studied by Arya and Paul [
The annular raft foundations are more reasonable and economical than the full circular raft for industrial chimneys. If the geotechnical conditions are not favorable for raft foundations, piled foundations can also be used. Skin-friction piles are more suitable to chimney foundations than end-bearing piles, since greater uplift capacity is generally available [
The basic assumptions of conventional method of analysis of annular raft foundation given in IS:11089-1984 [
(a) Cross-sectional elevation of chimney and annular raft foundation, (b) plan view of chimney and annular raft foundation, and (c) pressure distribution under the annular raft due to dead weight and bending moment.
For
The finite element analysis was carried out based on direct method of SSI for the tall RC chimney with piled raft foundation founded on soil with different geotechnical properties. The geometrical properties of chimney and the foundation were also varied to study the effect of SSI. The integrated chimney-piled raft-soil system was analysed for El Centro (1940) ground motion in time domain. The stress resultants of the raft of piled raft foundation obtained from SSI analysis were compared with that obtained from the conventional analysis considering rigidity at the base of the foundation. The settlement of raft is also studied due to the effect of SSI of chimney-piled raft system.
The tallest chimney in the world has more than 400 m height. Therefore, in this study, chimney elevations of 100 m, 200 m, and 400 m were considered. Practical range of slenderness ratio (ratio of height to base diameter) of chimneys varies from 7 to 17 [
Geometric parameters of chimney.
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100 | 6 | 3.6 | 0.2 | 0.2 |
200 | 12 | 7.2 | 0.35 | 0.2 |
400 | 24 | 14.4 | 0.7 | 0.3 |
The chimney is supported by piled raft foundation. The raft of piled raft foundation was considered as annular with uniform thickness. The overall diameter of raft for a concrete chimney is typically 50% greater than the diameter of the chimney shaft at ground level [
Geometric parameters of piled raft foundation.
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No. of piles | ||
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100 | 14 | 4 | 1.12 | 0.8 | 0.62 | 18 |
200 | 26 | 6 | 2.08 | 1.5 | 1.2 | 45 |
400 | 60 | 8 | 4.8 | 3.4 | 2.7 | 311 |
The soil is idealized by single homogeneous strata of 30 m depth beneath the foundation. To study the effect of SSI, the properties of the soil stratum were varied. For this, four types of dry cohesionless soil were selected and they are S1, S2, S3, and S4 which represent loose sand, medium sand, dense sand, and rock, respectively. The properties of the soil stratum were defined by its shear wave velocity, mass density, elastic modulus, and Poisson’s ratio as per [
Properties of the soil types.
Soil types | Shear wave velocity |
Poisson’s ratio |
Density |
Elastic modulus |
Angle of friction |
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S1 | 100 | 0.4 | 16 | 108,752 | 30 |
S2 | 300 | 0.35 | 18 | 445,872 | 35 |
S3 | 600 | 0.3 | 20 | 1,908,257 | 40 |
S4 | 1200 | 0.3 | 20 | 7,633,028 | 45 |
The finite element modeling and seismic analysis were carried out using the finite element software, ANSYS. In the finite element modeling, SHELL63 elements were used to model the chimney and the raft of piled raft foundation. SHELL63 element is defined by four nodes having six degrees of freedom in each node. The three-dimensional soil stratum and the pile were modeled with SOILD45 elements with eight nodes having three translational degrees of freedom at each node. The surface-surface contact elements were used to represent the interaction between pile and soil. The pile surface was established as “target” surface (TARGE170), and the soil surface contacting the pile as “contact” surface (CONTAC174); these two surfaces constitute the contact pair. The coefficient of friction was defined between contact and target surfaces and is shown in Table
The chimney shell was discretised with element of 2 m size along height and with divisions of 7.5° in the circumferential direction. Diameter and thickness of chimney were varied linearly along the entire height. The raft and soil strata were discretised with divisions of 7.5° in the circumferential direction. Three-dimensional finite element model of the integrated 200 m high chimney-piled raft-soil system was generated using the ANSYS software and is shown in Figure
Finite element model of 200 m high chimney-piled raft-soil system.
Finite element model of (a) piled raft foundation and (b) pile.
Plan view of raft of piled raft foundation of 200 m chimney.
Linear elastic material behaviour was assumed for chimney, piled raft, and soil. M30 grade concrete was selected for chimney and foundation. The modulus of elasticity for chimney was taken as 33.5 Gpa as per IS:4998 (Part1)-1992 [
Elastic continuum approach was adopted for modeling the soil. The material properties such as elastic modulus, Poisson’s ratio, and density for the three-dimensional soil stratum were taken from Table
The time history analysis of the integrated SSI system was carried out for ground motion corresponding to the longitudinal component of Imperial Valley earthquake at El Centro (1940) with a magnitude of 7.0 and peak ground acceleration of 0.319 g. The total duration of the ground motion taken is 30 seconds. Acceleration time history and associated fourier spectrum of this ground motion are shown in Figures
Time history plot of El Centro ground motion.
FFT plot of El Centro ground motion.
Damping is a function of frequency and Rayleigh damping is more appropriate for transient dynamic analysis. The Rayleigh damping is introduced through the coefficients
The responses in annular raft of piled raft foundation of chimney founded on flexible base obtained from finite element analysis were compared with that of rigid base obtained from conventional analysis. The variation of responses in annular raft due to the effect of flexibility of soil, effect of thickness of raft, and effect of frequency content in the ground motion is studied.
The three-dimensional seismic SSI analysis was conducted for RC chimneys with piled raft foundation. The effect of SSI was studied by considering four different soil types with respect to the geotechnical characteristic and three different ratios of outer diameter to thickness of raft. The significance of characteristics of the ground motion was also studied. The responses in terms of tangential and radial bending moment and settlement of raft of piled raft were evaluated from the finite element analysis. The absolute maximum response of tangential and radial bending moment and settlement of annular raft were considered from their response time histories. The tangential and radial bending moment in the raft of piled raft obtained from SSI analysis was compared with that obtained from the conventional analysis considering rigidity at the base of the raft foundation. The bending moments evaluated from conventional method are designated as
Four types of soils were selected, namely S1, S2, S3, and S4 which represent loose sand, medium sand, dense sand, and rock, respectively, in order to understand the effect of SSI on the tangential and radial bending moment in raft as well as the settlement of the raft of piled raft foundation.
Effect of stiffness of soil on the tangential moments in raft of piled raft foundation was evaluated. The tangential moment in raft of piled raft obtained from SSI analysis was compared with that obtained from conventional analysis as per IS:11089-1984. The representative graphs for tangential moments at various radial locations from inner to outer edge of the raft of 100 m, 200 m, and 400 m chimneys are shown in Figure
Tangential moment in raft (
It is found that the maximum tangential moment in raft is obtained at inner edge of the raft and it decreases towards the outer edge of the raft from conventional analysis of annular raft foundation. From the three-dimensional seismic analysis of integrated chimney-piled raft soil system, it is seen that the maximum tangential moment in raft is obtained at the chimney shell location (
It is well clear that the tangential moment increases with the decrease in stiffness of soil. This may be due to the fact that the raft of piled raft foundation behaves as a rigid plate when the structure interacts with loose sand. The time history plot of tangential moment in raft at chimney windshield location of 100 m chimney (
Time history plot of tangential moment in raft of 100 m chimney (
The maximum tangential moment obtained from conventional analysis and SSI analysis is given in Table
Percentage variation of maximum tangential moment.
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Maximum tangential moment as per IS11089 (kNm) | Soil type | Percentage variation of maximum tangential moment (%) | ||
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100 | 1281.54 | S1 | −52.22 | −71.29 | −83.56 |
S2 | −66.61 | −82.61 | −90.73 | ||
S3 | −80.17 | −90.32 | −94.63 | ||
S4 | −88.5 | −93.45 | −95.62 | ||
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200 | 1611.1 | S1 | −22.88 | −47.74 | −64.5 |
S2 | −43.3 | −67.17 | −79.3 | ||
S3 | −65.94 | −82.57 | −89.58 | ||
S4 | −83.09 | −91.97 | −95.47 | ||
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400 | 6905.15 | S1 | −8.78 | −32.12 | −47.74 |
S2 | −33.8 | −53.97 | −65.15 | ||
S3 | −53.28 | −68.94 | −76.5 | ||
S4 | −69.97 | −80.37 | −85.42 |
The radial moment response in annular raft of piled raft foundation is studied due to that the effect of flexibility of soil is studied. The radial moment in raft is also evaluated from conventional analysis. The representative graphs for radial moments at various radial locations from inner to outer edge of the raft of 100 m, 200 m, and 400 m chimneys are shown in Figure
Radial moment in raft (
The time history plot of radial moment in raft at chimney windshield location of 100 m chimney (
Time history plot of tangential moment in raft of 100 m chimney (
Table
Percentage variation of maximum radial moment.
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Maximum radial moment as per IS11089 (kNm) | Soil type | Percentage variation of maximum radial moment (%) | ||
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100 | 401.096 | S1 | 65.51 | 11.34 | −25.81 |
S2 | 23.27 | −22.45 | −48.21 | ||
S3 | −19.26 | −49.84 | −65.69 | ||
S4 | −48.71 | −68.15 | −79.55 | ||
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200 | 737.951 | S1 | 244.32 | 162.38 | 105.02 |
S2 | 182.84 | 106.1 | 64.55 | ||
S3 | 109.69 | 51.34 | 21.58 | ||
S4 | 44.01 | 0.61 | −22.66 | ||
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400 | 5424.34 | S1 | −0.12 | −28.8 | −53.59 |
S2 | −20.74 | −48.04 | −62.07 | ||
S3 | −45.54 | −64.38 | −72.78 | ||
S4 | −64.62 | −76.07 | −81.66 |
The representative diagrams of the settlement of raft (
Settlement in raft (
The absolute maximum settlement of raft (
Maximum settlement of raft.
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Soil type | Maximum settlement (mm) | ||
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100 | S1 | 2.47 | 2.73 | 3.16 |
S2 | 0.99 | 1.3 | 1.5 | |
S3 | 0.45 | 0.54 | 0.63 | |
S4 | 0.17 | 0.19 | 0.21 | |
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200 | S1 | 3.44 | 3.8 | 4.3 |
S2 | 1.34 | 1.77 | 2.03 | |
S3 | 0.64 | 0.79 | 0.89 | |
S4 | 0.26 | 0.31 | 0.35 | |
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400 | S1 | 2.55 | 3.61 | 4.47 |
S2 | 1.21 | 1.76 | 2.12 | |
S3 | 0.64 | 0.84 | 0.97 | |
S4 | 0.28 | 0.35 | 0.39 |
The effect of thickness of the raft was investigated by considering three different ratios of diameter to thickness (
A decrease in the variation of bending moment in raft of flexible base from that of rigid base, with respect to increase in the
In the case of variation of radial moment, the maximum variation is seen for 200 m chimney resting on soil type S1. Here the reduction is 81.94% and 139.3% respectively for rafts with
The settlement of raft increases with increase in the
The effect of characteristics of the ground motion on bending moment response in raft is assessed. The fundamental natural frequency ranges from 0.365 Hz to 0.424 Hz for 100 m high chimney-piled raft-soil system. It ranges from 0.213 Hz to 0.25 Hz and from 0.126 Hz to 0.143 Hz, respectively, for SSI system of 200 m chimney and 400 m chimney. From the FFT plot of the El Centro ground motion (Figure
From the SSI analysis, the maximum settlements of raft of 100 m, 200 m, and 400 m chimneys are 3.16 mm, 4.3 mm and 4.47 mm, respectively. These maximum settlements are obtained for thinner rafts of
The effect of SSI is studied for tall reinforced concrete chimneys with piled raft foundation subjected to El Centro (1940) ground motion. The material properties of the soil and geometric properties of the chimney and raft of piled raft foundation were varied to understand the significance of SSI. The responses such as radial and tangential bending moment in raft and settlement of raft were considered for study. The absolute maximum bending moment in raft from SSI analysis is compared with that obtained from conventional analysis.
The following conclusions are drawn from the present study. The tangential moment in raft obtained from the dynamic SSI analysis is less than that obtained from the conventional analysis. The pattern of tangential moments in the raft obtained from the three-dimensional dynamic SSI analysis and that obtained from conventional analysis are different. The effect of SSI is more on the radial moment of raft of piled raft foundation of chimney. The dynamic SSI effect is more prominent in 100 m and 200 m chimney as compared to 400 m chimney. The higher modes of SSI system are also significant in determining the response in the raft.
The authors declare that they have no conflict of interests.