Response in piled raft foundation of tall chimneys under along-wind load incorporating flexibility of soil

Abstract

The present paper deals with the numerical analysis of tall reinforced concrete chimneys with piled raft foundation subjected to along-wind loads considering the flexibility of soil. The analysis was carried out using finite element method on the basis of direct method of soil-structure interaction (SSI). The linear elastic material behavior was assumed for chimney, piled raft and soil. Four different material properties of soil stratum were selected in order to study the effect of SSI. The chimney elevation and the thickness of raft of piled raft foundation were also varied for the parametric study. The chimneys were assumed to be located in terrain category 2 and subjected to a maximum wind speed of 50 m/s as per IS:875 (Part 3)-1987. The along-wind loads were computed according to IS:4998 (Part 1)-1992. The base moments of chimney evaluated from the SSI analysis were compared with those obtained as per IS:4998 (Part 1)-1992. The tangential and radial bending moments of raft of piled raft foundation were evaluated through SSI analysis and compared with those obtained from conventional analysis as per IS:11089-1984, assuming rigidity at the base of the raft foundation. The settlements of raft of piled raft foundation, deflection of pile and moments of the pile due to interaction with different soil stratum were also evaluated. From the analysis, considerable reduction in the base moment of chimney due to the effect of SSI is observed. Higher radial moments and lower tangential moments were obtained for lower elevation chimneys with piled raft resting on loose sand when compared with conventional analysis results. The effect of SSI in the response of the pile is more significant when the structure-foundation system interacts with loose sand.

Keywords

finite element method / piled raft / tall chimney / soil-structure interaction / along-wind load

Introduction

Annular raft foundations are more economical for tall reinforced concrete chimneys if the soil conditions are favorable. If the supporting soil is weak, then the addition of a limited number of piles will help to improve the ultimate load capacity and to reduce the settlement and differential settlement considerably. Such kind of foundation which combines shallow foundation (raft) and deep foundation (pile group) is generally known as piled-raft foundation. In piled raft foundations, the function of the rafts is to provide the required bearing capacity whereas the pile groups which also contribute sufficient bearing capacity control the settlements appreciably. There are various interactions involved in this foundation such as pile-to-pile, pile-to-raft, raft-to-super structure and pile-to-soil interactions. Therefore the analysis of such kind of foundation is complex.

Simplified solutions were formulated for the analysis and design of piled raft systems by Poulos and Davis [ 1]. This method only predicts the settlement of piled raft foundations. For the accurate design of piled raft systems, a proper estimation of load sharing between the raft and the pile group is required [ 2– 4]. Numerical methods were widely used by many researchers for the analysis and design of piled raft foundations. A numerical method for the approximate computation of influence factors for raft and piled raft foundations were proposed by Ta and Small [ 5] and concluded that if the supporting soil stratum is very stiff then the pile will take more loads than the raft. For the analysis of flexible piled-rafts, a boundary element formulation was presented by Mendonça and Paiva [ 6] in which all the interactions among the raft, the pile and the soil were considered. Analysis of vertically loaded piles supported on the multi-layered soil stratum was studied by many researchers using this method [ 7, 8]. The behavior of piled raft foundations embedded in different types of soils was studied by Zhang and Small [ 9] using finite element method subjected to both vertical and horizontal loads. A combination of finite element method and boundary element method was used in the study [ 10] to estimate the interaction between soil and piles, with or without rigid raft, subjected to horizontal and vertical loads. The finite difference method was utilized by Lin and Feng [ 11] for the analysis of piled raft on layered subsoil subjected to vertical loading. Poulos [ 12] critically reviewed a number of methods for the analysis of piled raft foundation and pointed out that the three dimensional numerical analysis is the most accurate method. Many recent researchers [ 13– 16] focused on the three dimensional analysis of piled raft systems. It is also seen that many recent research on piled raft foundation [ 17– 20] accounted only the settlement of piled raft foundation and interaction between various elements in this complex system.

All the above mentioned research focuses on the behavior of piled raft foundations neglecting the super structure. It is also noticed that generally the studies on tall chimneys including the standard codes of practice [ 21– 24] did not consider the effect of foundation and supporting soil. Chimneys are tall structures with slender and tapering geometry. Such unique geometry of super structure has its own contribution in the response of foundation. Super structure-foundation-soil interaction studies are required for the accurate prediction of the response both in the structure and foundation. Very few researchers [ 25, 26] studied the effect of SSI of chimney super structure with raft foundation. These studies used two different approaches for modeling the soil stratum namely winkler spring soil model [ 25] and elastic continuum soil model [ 26]. The two basic methods involved in the solution of soil-structure interaction problems are referred to as the direct method and substructure method. The entire structure-foundation-soil system is modeled and analyzed in a single step as per the direct method of SSI [ 27– 29]. This method can be easily implemented using a finite element method. In substructure approach [ 27, 30], the soil-structure system is divided into two substructures, the soil medium and the structures. The overall response in this method is based on the principle of superposition.

The present study deals with the three dimensional finite element analysis of tall reinforced concrete chimneys with piled raft foundation subjected to along wind load considering the flexibility of soil. The along wind load was estimated according to IS:4998 (Part 1)-1992 [ 23]. Linear material behavior of chimney, piled raft and soil were assumed. The analysis was done based on the direct method of soil-structure interaction. Parametric studies were conducted on chimneys of 100, 200 and 400 m heights considering the different material properties of soil stratum and different thickness of raft of piled raft foundation to understand the significance of SSI. Responses in the chimney and foundation were evaluated. The responses in the raft of piled raft foundation from the SSI analysis were compared with that obtained from the conventional analysis of annular raft foundation as per IS:11089-1984 [ 31] assuming rigidity at the base of foundation.

Modeling of chimney-piled raft-soil system

Idealization of chimney

Practical range of ratio of height to base diameter (slender ratio) of chimneys varies from 7 to 17 [ 24]. The chimney elevations of 100, 200 and 400 m with a slender ratio of 17 representing very slender chimneys were selected for the present study. The taper ratio (ratio of top diameter to base diameter) and ratio of diameter to thickness at base were considered as 0.6 and 35 respectively. The thickness at top of chimney was taken as 0.4 times the thickness at base but the minimum thickness at top was restricted to 0.2 m. All the above chimney parameters were selected based on the study conducted by Menon and Rao [ 24]. Details of different geometric parameters of chimneys are given in Table 1.

Configuration of piled raft foundation

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 wind sheild at ground level [ 32]. The ratio of outer diameter to thickness (D_o/t) of annular raft was taken as 12.5, 17.5 and 22.5 [ 25] to evaluate the influence of stiffness of raft. Piled raft foundations were designed for the moment and shear force at the base of chimney. For this, RC friction piles of 20 m length (l) and 1 m diameter were considered. For friction piles, the optimum spacing recommended is 3d where d is the diameter of the pile. Spacing (s) of 3d ensures that interference of stress zones of adjacent friction piles is minimum and results in a high group efficiency. Therefore, s/d of 3 was selected. Table 1 gives the details of different geometric parameters of raft and the total number of piles. Figure 1 shows the layout of piled raft foundation of 200 m tall chimney.

Material properties of chimney and foundation

M30 grade concrete and Fe 415 grade steel were selected as the materials for both chimney and piled raft. The modulus of elasticity for chimney was taken as 33.5 GPa as per IS:4998 (Part1)-1992 [ 23]. For piled raft foundation, the modulus of elasticity of 27.39 GPa was calculated corresponding to M30 grade concrete using the equation, E=\mathrm{5000}\sqrt{fck} as there is no IS code provides the modulus values directly. The poisson’s ratio and density of concrete were taken as 0.15 and 25 kN/m³ respectively for both chimney and piled raft foundation.

Soil property and material model

To study the effect of SSI, different properties of the soil stratum were considered. 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 mass density, elastic modulus, poisson’s ratio and coefficient of internal friction as per the refs [ 33, 34]. The properties of the soil stratum are given in Table 2. In this analysis, an elastic continuum finite element model [ 26, 28, 29] was assumed to represent the soil.

The soil is a semi-infinite medium, an unbounded domain. For static loading, a fictitious boundary at a sufficient distance from the structure, where the response is expected to have died out from a practical point of view, was introduced. The width of soil taken for modeling was four times the diameter of foundation laterally. The bedrock was assumed to be at a depth of 30 m for all chimneys [ 29]. This leads to a finite domain for the soil which was modeled similar to the structure. The total discretized system, consisting of the structure and the soil was then analyzed [ 27].

Computation of along-wind load as per IS:4998 (Part 1)-1992

The chimneys are classified as class C structures located in terrain category 2 and subjected to a basic wind speed of 50 m/s. According to IS:875 (part 3)-1987 [ 35], terrain category 2 is an open terrain with well scattered obstructions having heights generally between 1.5 m and 10 m. There are two methods for estimating along-wind load for chimneys as per IS:4998 (Part 1)-1992 [ 23]. They are simplified method and random response method as follows.

Simplified method

The along-wind load or drag force per unit height (N/m) of the chimney at any level is calculated from the equation

(1) F_z=p_z.C_D.d_z,

where p_z = design wind pressure in N/m² at height z; z = height of any section of chimney from top of foundation in m; C_D = 0.8, drag co-efficient of chimney; d_z = diameter of chimney at height z in m.

Random response method

The along-wind load per unit height at any height z on a chimney is calculated from the equation

(2) F_z=F_{zm}+F_{zi},

where F_{zm} is the wind load in N/m height due to hourly mean wind (HMW) speed at height z; F_{zi} is the wind load in N/m height due to the fluctuating component of wind at height z.

(3) F_{zm}={\overline{p}}_z.C_D.d_z,

where {\overline{p}}_z is the design pressure at height z (N/m²) due to HMW, {\overline{p}}_z=\mathrm{0.6}{\overline{V}}_z^{\mathrm{2}} . {\overline{V}}_z = HMW speed in m/s.

(4) F_{zi}=\mathrm{3}·{\displaystyle \frac{\left(G-\mathrm{1}\right)}{H^{\mathrm{2}}}}·{\displaystyle \frac{z}{H}}·{\displaystyle \underset{\mathrm{0}}{\overset{H}{\int }}{F}_{zm}·z·\mathrm{d}z},

where G is the gust factor which is calculated from the equation.

(5) G=\mathrm{1}+g_f·r·\sqrt{B+{\displaystyle \frac{SE}{\beta }}},

where g_f = peak factor defined as the ratio of the expected peak value to RMS value of the fluctuating wind load; r = twice the turbulence intensity; B = background factor indicating the slowly varying component of wind load fluctuation; E = a measure of the available energy in the wind at the natural frequency of chimney S = size reduction factor; \beta = coefficient of damping of the structure; H = total height of the chimney in m.

The along-wind loads for all chimneys were estimated by both the methods. The base moment of chimneys obtained from both the methods are shown in Table 3. It is found that out of the two methods, the higher value of base moment of chimney was obtained from random response method. Therefore the wind load computed from random response method was applied along the height of chimney.

Finite element model

The finite element modeling and analyses were carried out by using the commercial finite element software ANSYS. In the finite element modeling, the chimney and raft of piled raft were modeled with SHELL63 elements defined by four nodes having six degrees of freedom at each node. The three dimensional soil stratum was modeled with SOILD45 elements with eight nodes having three translational degrees of freedom at each node. The pile was also modeled using SOILD45 elements. The surface-surface contact elements were used to form 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 ( \mu ) was defined between contact and target surfaces based on the angle of friction ( \phi ) given in Table2. The coefficient of friction between the pile and soil was taken as 0.577, 0.7, 0.839 and 1.0 for soil type S1, S2, S3 and S4 respectively using the formula, \mu =\tan \phi .

The chimney shell was discretised with element of 2m size along height and with divisions of 7.5° in the circumferential direction. The diameter and thickness of chimney shell were varied linearly along the entire height to generate the tapered geometry of chimney. The pile was discretised as 14 equal parts along the length of pile.

The lateral movements at the soil boundaries were restrained. All the movements were restrained at bed rock level. The nodes at the interface of bottom of raft and top of soil were completely coupled. Three dimensional finite element model of integrated 200m high chimney-piled raft-soil system generated using the ANSYS software is shown in Fig. 2. The finite element models of piled raft and that of a single pile are shown in Fig. 3. The wind load computed as per IS:4998 (Part 1)-1992 [ 23] was applied in the chimney as point loads at 10 m intervals along its height after suitably averaging the load above and below each section. The gravity load was also applied to the integrated chimney-foundation-soil system. This system was analyzed based on direct method of SSI by assuming the linear elastic material behavior of structure, foundation and soil.

Conventional analysis of annular raft foundation as per IS:11089-1984

The basic assumptions of conventional method of analysis of annular raft foundation given in IS:11089-1984 [ 31] are 1) The foundation is rigid relative to the supporting soil and the compressible soil layer is relatively shallow; and 2) The contact pressure distribution is assumed to vary linearly throughout the foundation. The cross sectional elevation and plan of chimney with annular raft foundation and the pressure distribution under annular raft are given in Fig. 4. As per IS:11089-1984, the non-uniform pressure distribution under annular raft is modified to uniform pressure distribution p, and is obtained as p₁+ 0.5 p₂, where p₁ is uniform pressure due to dead loads (V) and p₂ is pressure due to bending effects (M) as shown in Fig. 4. The formulae for circumferential and radial moments, M_t and M_r , respectively are given below.

(6) M_t={\displaystyle \frac{p{a}^{\mathrm{2}}}{\mathrm{16}}}\left[\left\{\mathrm{4}\left(\mathrm{1}+{\displaystyle \frac{b^{\mathrm{2}}}{r^{\mathrm{2}}}}\right)\left({\log }_{\mathrm{e}}{\displaystyle \frac{a}{c}}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}-{\displaystyle \frac{c^{\mathrm{2}}}{\mathrm{2}{a}^{\mathrm{2}}}}\right)\right\}+{\displaystyle \frac{r^{\mathrm{2}}}{a^{\mathrm{2}}}}-{\displaystyle \frac{\mathrm{4}{b}^{\mathrm{2}}}{a^{\mathrm{2}}}}\left\{{\log }_{\mathrm{e}}{\displaystyle \frac{r}{a}}+{\displaystyle \frac{\mathrm{3}}{\mathrm{4}}}\left({\displaystyle \frac{\mathrm{1}}{\mathrm{3}}}+{\displaystyle \frac{a^{\mathrm{2}}}{b^{\mathrm{2}}}}+{\displaystyle \frac{a^{\mathrm{2}}}{r^{\mathrm{2}}}}\right)-{\displaystyle \frac{a^{\mathrm{2}}+r^{\mathrm{2}}}{a^{\mathrm{2}}-b^{\mathrm{2}}}}\cdot {\displaystyle \frac{b^{\mathrm{2}}}{r^{\mathrm{2}}}}{\log }_{\mathrm{e}}{\displaystyle \frac{a}{b}}\right\}\right].

(7) M_r={\displaystyle \frac{p{a}^{\mathrm{2}}}{\mathrm{16}}}\left[\left\{\mathrm{4}\left(\mathrm{1}-{\displaystyle \frac{b^{\mathrm{2}}}{r^{\mathrm{2}}}}\right)\left({\log }_{\mathrm{e}}{\displaystyle \frac{a}{c}}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}-{\displaystyle \frac{c^{\mathrm{2}}}{\mathrm{2}{a}^{\mathrm{2}}}}\right)\right\}+{\displaystyle \frac{\mathrm{3}{r}^{\mathrm{2}}}{a^{\mathrm{2}}}}-{\displaystyle \frac{\mathrm{4}{b}^{\mathrm{2}}}{a^{\mathrm{2}}}}\left\{{\log }_{\mathrm{e}}{\displaystyle \frac{r}{a}}+{\displaystyle \frac{\mathrm{3}}{\mathrm{4}}}\left(\mathrm{1}+{\displaystyle \frac{a^{\mathrm{2}}}{b^{\mathrm{2}}}}-{\displaystyle \frac{a^{\mathrm{2}}}{r^{\mathrm{2}}}}\right)+{\displaystyle \frac{a^{\mathrm{2}}-r^{\mathrm{2}}}{a^{\mathrm{2}}-b^{\mathrm{2}}}}\cdot {\displaystyle \frac{b^{\mathrm{2}}}{r^{\mathrm{2}}}}{\log }_{\mathrm{e}}{\displaystyle \frac{a}{b}}\right\}\right].

For

For r>c ,

(8)

(9)

where a and b are the outer and inner radius of annular raft respectively, r is the radial distance to any point in raft and c is the radius of chimney windshield at base.

The tangential and radial bending moments at various radial locations in the raft were computed from the conventional analysis considering fixity at the base of foundation (as per IS 11089) and compared with the results obtained from finite element method considering the flexibility at the base of the foundation (SSI). The percentage variation of maximum values of the tangential and radial moment in the raft considering SSI from those obtained from conventional method of analysis was computed. The tangential and radial moments in the raft obtained from conventional analysis as per IS:11089-1984 [ 31] are designated as IS11089 in graphs. The settlement of piled raft obtained from SSI analysis was checked with the maximum permissible limit of settlement of raft as per IS:1904-1986 [ 36]. According to IS:1904, the maximum permissible settlement for raft foundation on sand is 0.075 m.

Results and discussions

Three dimensional finite element analysis was carried out to study the effect of SSI on reinforced concrete chimney with piled raft foundations subjected to along wind load. The responses in terms of base moment of chimney, tangential and radial bending moment in raft of piled raft, settlement of raft of piled raft, deflection of pile and bending moment of pile were evaluated. The effects of different parameters such as stiffness of soil, stiffness of raft and chimney elevations on the above responses were studied.

Effect of stiffness of soil

To study the effect of SSI, four types of soils were selected namely S1, S2, S3 and S4 representing loose sand, medium sand, dense sand and rock respectively. The variations in base moment of chimney, the bending moments and settlement of the raft and the deflection and bending moment of pile were evaluated from the SSI system.

Variation in the base moment of chimney

Along-wind load and the resulting base moment of chimney were computed as per IS:4998 (Part 1)-1992 based on two methods cited under Section 2.5, considering the fixity at the base of the chimney. Since the maximum base moment was obtained from the random response method, the wind load computed from this method was applied to the SSI system and analyzed to find the base moment of chimney with flexible base. This base moment obtained for chimney with flexible base was compared with that obtained for chimney with fixed base. The variations of base moment evaluated from both cases are shown in Table 3. It is found that the base moment of chimney increases with increase in stiffness of supporting soil. It is also seen that the base moment obtained from the analysis of chimney with piled raft foundation resting on rock is much lower than that obtained from chimney with fixed base. The base moment of the 100 m chimney supported on loose sand as evaluated from the SSI analysis has a reduction of 88% from that estimated from the chimney with fixed base.

Variation of tangential moment in raft

The maximum tangential moment location in raft of piled raft foundation is at the leeward side of raft. According to the conventional analysis of annular raft foundation, the location of maximum tangential moment is always at the inner edge of the raft and it decreases drastically toward the outer edge of the raft. The representative graphs of tangential moments at various radial locations in the leeward side, from inner to outer edge of the raft of 100, 200 and 400 m chimneys are shown in Fig. 5. From the SSI analysis of chimney-piled raft-soil system, it is observed that the tangential moment in the raft increases with decrease in stiffness of the supporting soil. The raft of foundation is rigid when it interacts with loose sand and it shows flexible behavior as it interacts with rock. It is also found that the maximum value of tangential moment in the raft is obtained at the chimney windshield location in the raft (r/a = 0.43 for 100 m chimney, r/a = 0.46 for 200 m chimney and r/a = 0.4 for 400 m chimney) when the SSI effect is considered. Sudden variation of moment in the raft occurs at the pile locations due to the moment distribution to piles. This variation is more in the raft of 400 m chimney. The contour of the tangential moment in the raft of 200 m chimney (D_o/t = 12.5) from SSI analysis is shown in Fig. 6. It is seen that the area of raft in the highest tangential moment range in the leeward side of raft is more when it interacts with soil type S1. This area reduces when the supporting soil stiffness increases from S1 to S4.

The maximum tangential moment in raft obtained from conventional analysis and the percentage variations of maximum tangential moment obtained by SSI analysis from the conventional method are tabulated in Table 4. It is observed that SSI effect causes considerable reduction in moments computed as per the basic assumption that the foundation is rigid according to the conventional method. The tangential moment in raft of 100 and 200 m chimney founded on loose sand is decreased by 51% ‒ 79% from the conventional analysis whereas this reduction is only 23% in the case of 400 m chimney founded on same soil type. An increase of 18% of tangential moment in raft (D_o/t = 12.5) of 400 m chimney resting on loose sand from the conventional analysis is seen. This is the single case in which the tangential moment from SSI analysis is higher than that from the conventional analysis and is due to the relatively very rigid response of the thick and large raft of a very tall chimney interacting with soft soil. In general, the conventional method of analysis gives conservative results.

Variation of radial moment in raft

The variation of radial moment at various radial locations in the leeward side from center to outer edge of the raft of 100, 200 and 400 m chimneys from SSI analysis and conventional analysis subjected to along-wind load are shown in Fig. 7. It is seen that the pattern of variation of radial moment in raft is same for both the cases. The maximum radial moment in the raft occurs at the chimney windshield location (r/a = 0.40 to 0.46) in the leeward side. Conventional analysis also exhibited the maximum radial moment in raft at windshield location. The radial moment in the raft increases with decrease in soil stiffness. There is a sudden increase of moment in the raft at the pile locations especially in the case of 400 m chimney. The contour of the radial moment in the raft of 200 m chimney (D_o/t = 12.5) from SSI analysis is shown in Fig. 8. It is observed that the area of raft with maximum radial moments in the leeward side decreases with increase in soil stiffness.

The percentage variation of maximum radial moment in raft with flexible base from that of conventional method is shown in Table 5. It is observed that the radial moments are reduced due to the inclusion of the effect of stiffness of the underlying soil, especially for the case of higher elevation chimneys (H= 400 m) with raft having less thickness (D_o/t = 17.5 and 22.5). The same chimney with raft of higher thickness (D_o/t = 12.5) resting on loose sand shows an increase in radial moment of 11% from that predicted from the conventional analysis. In the case of 100 m chimney, the radial moment in the raft (D_o/t = 12.5) resting on loose sand is increased by 33% from that of conventional analysis which is contributed due to the higher rigidity of the thick raft. It is also found that in the case of 200 m chimney, the maximum radial moment in the raft increases considerably for soil type S1 and S2 from that estimated by conventional analysis.

Settlement of raft

The settlement at various radial locations of the raft (D_o/t = 12.5) of 100, 200 and 400 m chimneys from SSI analysis is shown in Fig. 9. It is observed that as the soil type varies from rock to loose sand, the settlement of the raft increases. The settlement pattern shows that the raft settles non-uniformly with maximum displacement at chimney wind shield location in the raft on the leeward side of the chimney with flexible base. The maximum settlement is seen from the inner edge to outer edge of the raft of lower elevation chimneys (H = 100 m and H = 200 m; D_o/t = 12.5) resting on loose sand. This is more clear from the contour of the settlement of the raft of 200m chimney (D_o/t = 12.5) shown in Fig. 10. It is seen that the maximum settlement of raft is concentrated at wider areas in the leeward side when it interacts with loose sand. This area of large settlement reduces with increase in the stiffness of soil. There is not much raft deformation for soil type S3 and S4 as the raft behaves as equally rigid while interacting with these soil types.

The maximum settlements obtained from the SSI analysis are shown in Table 6. From the SSI analysis, it is seen that the settlements of raft of all chimneys are less than the permissible settlement of 0.075 m as per IS:1904-1986. The maximum settlement obtained is 54 mm corresponding to H = 400 m, D_o/t = 22.5 and soil type S1.

Variation of deflection of pile

The piles were considered as fixed headed piles because of the very stiff raft at top. The variations of vertical and lateral deflection of piles due to the effect of SSI were evaluated. Three piles namely P1, P2 and P3 were selected from the leeward side of entire chimney-piled raft-soil system in which P1 represents the outermost pile, P2 is located near to the chimney windshield location and P3 represents an inner most pile. The location of P1, P2 and P3 piles and the variation of bending moment, lateral and vertical deflection in these piles are shown in Fig. 11. It is obvious that the lateral deflection of P3 is less than that of P1 and P2 and the maximum lateral deflection is in pile P1. The magnitude of lateral deflection of pile is negligibly small when it interacts with loose sand. The vertical deflection of P2 and P3 are greater than that of P1since they are located closer to the chimney base. The pile P2 was selected to study the effect of SSI. The variation of vertical deflection of pile in 100 and 400 m chimneys due to the effect of supporting soil type is shown in Fig. 12. It is seen that the vertical deflection of pile increases with decrease in stiffness of soil. The maximum vertical deflection is observed at the top of the pile and it decreases toward the bottom of pile. The vertical deflection of pile is very less when it interacts with soil type S3 and S4.

Variation of bending moment of pile

From Fig. 11, it is seen that the pile P1 which lies in the outermost pile ring in the leeward side has the maximum bending moment. The variation of bending moment of pile P1 due to the effect of SSI is shown in Fig. 13. It is observed that the bending moment of pile increases with decrease in stiffness of soil. The maximum bending moment is observed at the top of the pile. It is also noted that the variation of bending moment below one fifth of the length from the top of pile is negligible for all supporting soil types except for soil type S1. The maximum bending moment of pile P1 is tabulated in Table 7. Due to SSI effect, the maximum bending moment at the pile top is the highest in soil type S1.

Effect of stiffness of raft

The effect of stiffness of raft was investigated by considering three D_o/t ratios (D_o/t = 12.5, 17.5, and 22.5) for the raft of piled raft foundation. Base moment of chimney increases with increase in D_o/t ratio. The stiffness of the foundation is less for higher D_o/t ratios of the raft and therefore it results higher base moment of chimney. The base moment of 100 m chimney with flexible base from that of same chimney with fixed base reduces by 88% for D_o/t = 12.5 and 70% for D_o/t = 22.5 but these variations for 400 m chimney are 99.84% and 99.51% for D_o/t = 12.5 and D_o/t = 22.5 respectively. Thus the variation of base moment of chimney with variations in stiffness of raft is considerable for lower elevation chimneys (H = 100 m) and negligible for higher elevation chimneys (H = 400 m).

It is seen that the maximum tangential and radial moment in raft increases with decrease in D_o/t ratio. This is due to the rigid behavior of the raft for lower values of raft thickness ratio. The reduction in tangential moments in raft as D_o/t varies from 12.5 to 17.5 is 13%‒25% whereas the reduction is of 9%‒16% when it varies from 17.5 to 22.5. In the case of radial moment in raft, the reduction in moments between the two consecutive ratios i.e., between D_o/t = 12.5 and 17.5 and between D_o/t = 17.5 and 22.5 are 29%‒36% and 19%‒26% respectively. The settlement of raft increases with increase in the D_o/t ratio. The maximum variation of settlement in raft with D_o/t ratio of 17.5 and 22.5 from that of D_o/t = 12.5 is 11% and 20% respectively for 400 m chimney. All the above variations of responses with respect to different D_o/t ratios correspond to chimney-foundation system resting on soil type S1.

It is observed that (Table 7) the maximum bending moment of pile (P1) increases with increase in the D_o/t ratio only when the chimney with piled raft foundation interacts with loose sand. Maximum variation is observed for that of 200m chimney and the variations are 69% and 112% respectively for D_o/t = 17.5 and 22.5 from that of D_o/t = 12.5. In the case of medium sand, the bending moment of pile increases when the D_o/t ratio increases from 12.5 to 17.5 but it decreases when the D_o/t ratio increases from 17.5 to 22.5 except for 200 m chimney. It indicates that the effect of SSI in the response of bending moment of pile is significantly considerable for loose sand only. Generally it is seen that the bending moment of pile due to the interaction with soil type S3 and S4 is more for D_o/t ratio of 12.5.

Effect of height of chimney

The effect of SSI with increase in height of chimney was investigated by considering chimneys of three different heights (H = 100, 200 and 400 m). It is observed that the variation of base moment of chimney with flexible base from that of chimney with fixed base is more for 400 m chimney when compared to 100 m chimney. The tangential moments in the raft of 100 and 200 m chimney founded on soil type S1 is significantly less than that obtained from the conventional method but this reduction is less in 400 m chimney. In the case of radial moment in raft, the effect of SSI is more for 100 and 200 m chimneys as compared to 400 m chimneys. In general the effect of SSI is less in very tall chimneys except when it is founded on soil type S1.

Conclusions

SSI analysis was conducted for tall reinforced concrete chimneys with piled raft foundation subjected to along wind load. The analysis was carried out using three dimensional finite element analysis based on direct method of SSI. Equivalent static along-wind load were estimated as per IS:4998 (Part 1): 1992 and applied to chimneys along the height. Four different soil types, three different raft thicknesses based on different ratios of diameter to thickness of raft of piled raft foundation and three different chimney elevations were considered in order to study the effect of SSI. The base moment of chimney, the tangential and radial bending moment in raft, settlement of the raft, deflection and bending moment of pile were studied. The base moment of chimney evaluated from the SSI analysis was compared with that obtained according to IS:4998 (Part 1): 1992. The analysis of annular raft foundation was also carried out from conventional method of analysis as per IS:11089-1984, assuming the rigidity at the base of the foundation. The percentage variation was computed for maximum values of moments in the raft foundation obtained through SSI analysis from conventional method of analysis. The settlement of raft obtained from SSI analysis was verified with maximum permissible settlement of raft foundation on sand as per IS:1904-1986. The variation of deflection and bending moment of pile due to the effect of SSI were also investigated.

It is seen that all the maximum responses are obtained at the leeward side of integrated chimney-piled raft-soil system. The base moment of chimney increases with increase in stiffness of supporting soil type whereas the responses in raft and pile increase with decrease in stiffness of soil. The stiffness of raft significantly affects the responses in chimney, raft and pile.

The following general observations are drawn from the along-wind analysis of chimney-piled raft-soil system:

1) The base moments of chimneys are considerably reduced due to the effect of interaction with loose sand.

2) The maximum tangential and radial bending moment in the raft is obtained at the chimney windshield location in the leeward side from the SSI analysis whereas from the conventional analysis, the maximum tangential moment is obtained at inner edge of the raft and radial moment is obtained at the chimney windshield location in the raft.

3) In general, the maximum tangential moment in raft evaluated from the SSI analysis is less than that computed from conventional method.

4) The radial moments in raft of 100 and 200 m chimneys resting on loose sand are 33%–65% more than the moments obtained by the conventional analysis.

5) The effect of soil-structure interaction in the response of the pile is significant when the structure-foundation system interacts with loose sand.

6) The effect of thickness of raft of piled raft foundation is significant in the responses of lower elevation chimneys resting on loose sand.

7) Effect of SSI is negligible in very tall chimneys except when it is founded on loose sand.

Incorporating SSI effect in the analysis of RC chimneys founded on medium or loose sand leads to economic design as compared to the conservative conventional method of analysis. Hence it is beneficial to analyze tall RC chimneys considering the geotechnical features of construction site.

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