A Time-Dependent Model For Predicting The Response Of A Horizontally Loaded Pile Embedded In A Layered Transversely Isotropic Saturated Soil

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1 IOSR Journal of Mehanial and Civil Engineering (IOSR-JMCE) e-issn: ,p-ISSN: X, Volume 16, Issue 2 Ser. I (Mar. - Apr. 219), PP A Time-Dependent Model For Prediting The Response Of A Horizontally Loaded Pile Embedded In A Layered Transversely Isotropi Saturated Soil Oliver C. Waka 1, Jian-Fei Lu 2, Aayush Neupane 3, Shoaib Ahmed 4, Jaob Arku Ziama 5, 1 Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu, 21213, P.R. China 2 Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu, 21213, P.R. China 3 Department of Civil and Transportation Engineering, Hohai University, Nanjing, Jiangsu, 2111, P.R. China 4 Department of Civil Engineering, Jiangsu University, Zhenjiang, Jiangsu, 21213, P.R. China 5 Department of Arhiteture and Transportation, Liaoning Tehnial University, Fuxin, 123, P.R. China Correspondent Author: Oliver C. Waka Abstrat: A time-dependent model designed for estimating the response of a horizontally loaded pile in a layered saturated soil is presented in the present paper. The results of the present model are ompared with the results of existing solution; a better agreement is seen thereof, thus verifying this model. The present results show that the shear fore of the pile dereases with inreasing depth. The results also indiate that the displaement of the pile dereases as the depth inreases. In addition, the pore pressure along the pile-length vanishes to zero as the time inreases. This model shows the influene of the soil on a single horizontally loaded pile. When the depth of the soil inreases, the shear fore and displaement of the pile all derease signifiantly. Keywords: Foundation, horizontally loaded pile, layered saturated soil, Muki s pile method, Pile, Pile-soil Date of Submission: Date of aeptane: I. Introdution Pile foundations are designed to support high-rise buildings, brides and heavy laterally loaded strutures onstruted in soils not suitable for a shallow foundation system. The lateral and vertial fores ating on the pile are partiularly due to the ations of wind, earthquake and deadweight. [1-4], [5]. Dead loads from tall buildings supported on pile foundations are transferred through the piles to a deeper stratified soil medium. The seletion of the type and size of pile foundation to support a tall building involves the onsideration of fators that may influene the foundation. Some fators onsidered in the seletion proess of a suitable foundation type inlude the bearing apaity of soils, type of struture, distribution of loadings, durability requirements and onstrution osts. Furthermore, sine weak soils are reinfored with pile foundations to prevent exessive settlements of strutures, it is neessary to investigate the behavior of soils on whih strutures are ereted. Thus, the present study analyzes the interation between a laterally loaded pile and the saturated layered half-spae TISS. Apirathvoraku and Karasuhhi[5] used the fititious pile method to study the response of a irular ylindrial elasti pile embedded in a saturated elasti half-spae and subjeted to a moment at the top end. Niumpradit & Karadushi[6] used the Biot s theory ombined with the fititious pile method of [7] to aount for the influene of the displaement on the pile-soil interations. However, only final and initial solutions were obtained in the aforementioned studies. In spite of the available reports on pile-soil interation, studies on a single pile embedded in a layered TISS an be seldom found in the literature. Previous studies have only onsidered the pile-soil interation problems of a single layered transversely isotropi soil. The present study is an effort toward resolving the problem and losing the gap in the literature. This paper aims to apply Muki s formulation to the problem of a laterally loaded pile embedded in a layered transversely isotropi saturated soil to predit the response of the pile. The pile-soil problem is deoupled into a half-spae and a fititious pile. The layered TISS is handled as a three-dimensional medium, and the pile is regarded as a one-dimensional pile. The relationship between the layered TISS and the fititious pile is established with the approximation that the normal strain of the extended layered TISS along the axis of the pile is equal to the vertial strain of the fititious pile. Then, by ombining the fititious pile method and the basi solution of the layered TISS, the seond kind of Fredholm integral equation of the pile is established. Numerial results obtained by this study are ompared with the existing results to verify the present study. DOI: 1.979/ Page

2 II. Types of foundation In Engineering, the design of foundation strutures is muh more ritial than that of the design of a superstruture. Defets found in a foundation are muh more diffiult to retify than any defets disovered in the superstruture. The properties of the soil under the foundation vary onsiderably. Although in most design ases, engineers assume that struture is rigid, so the ground pressures are uniform; in reality, soil deposits are not uniform. Soil varies with depth. Thus, when seleting and designing a foundation, it is neessary to onsider the types and environmental onditions of foundation as well as the strength and durability of the foundation to avoid failure. 2.1 Shallow foundations Shallow foundation is the type of foundation used when the soil medium below the footing is strong enough to withstand the loads from superstrutures. This type of foundation is the most ommonly used foundation. It is inexpensive and usually designed to support residential buildings as well as medium size strutures, where the bearing apaity of the soil meets design requirements. Usually, the settlement is omputed to determine immediate and long term effets. 2.2 Mat / Raft foundations Mat/Raft foundation, as the name suggests, is large in size and distributes weight from superstruture to a large area. This type of foundation an be used to support strutures of moderate height. Nevertheless, this foundation type is not suitable for high rise buildings, as this foundation annot form adequate soil resistane to ounter the effet of lateral loadings. The soil parameters used for designing this foundation type should be seleted arefully refleting the variation in both the soil vertial and horizontal diretions. The effet of new onstrution should be onsidered [8]. 2.3 Pile foundations Pile foundation is used when the soil below the footing is not suitable for a raft/mat foundation system. This type of foundation is designed as single piles or pile groups to reinfore the stratum of the weak soil and support the superstrutures. In addition, it is used to transfer vertial and imposed loads to the bearing soil stratum and resist lateral fores due to wind and earthquake. III. Governing equations and basi solution In this setion, the governing equations for the layered soil are introdued. Then the equations are used to derive the basi solution. The equilibrium equations are written as follows: rr zr rr r z r z r r zz zr zr, in whih zz, rr and as well as zr denote the total normal and shear stress, respetively. Then, the priniple of effetive stress for the saturated soil is expressed as follows: p, (2) T T where,,, ;,,, ; and p p p p rr zz zr rr zz zr stress, the effetive stress, and the pore pressure vetors, respetively.,,, T (1) represent the total IV. Formulation of the Fredholm integral equation for the single pile in a half spae soil This setion presents a horizontally loaded pile embedded in a layered transversely isotropi saturated soil and subjeted to a stati load and a shear fore at the top end as shown in Fig.1 the pile is used to exemplify the formulation proess of the integral equation for the pile. The Young s modulus of the fititious pile is obtained by subtrating the elasti modulus of the soil from the elasti modulus of the real pile, written as:, i 1,2 (3) E E E p b p vi where E and E p1 vi are the Young s moduli of the fititious pile orresponding to the real pile embedded in the first and seond layers of the soil, respetively; E is the elasti modulus of the real pile; E p s1 and E sb are respetively the elasti modulus of the first and seond soil layers. The shear fores and moment are written as: DOI: 1.979/ Page

3 t Q( t) Q() d t M( t) M() d Q (), (4) M () Q t the shear fore at the top and M () where (), (5) t is the bending moment of the pile. Q () t M () t d L z figure 1 Shemati of a single pile V. Numerial results and analyses First, numerial results omputed by the proposed model for the analysis of pile embedded in a layered TISS are presented. Then, the results of this model are ompared with those of existing solutions to validate the auray of the present model. Finally, a parametri study to investigate the effet of various parameters on the behavior of a single pile is arried. Some quantities used in this paper are defined as: z z, L R r, t L kt uz (z), u L L N N( z) L, 2 p pz ( ) Q / d, o 2 Q Q ( z) Q, M M ( z) Qd (6) in whih L, and k represent the referene length, the shear modulus and permeability, respetively. Furthermore, the quantities with asterisk namely z, R, u, N, displaement, pile axial fore, pore pressure, time, shear fore and the moment, aordingly. DOI: 1.979/ Page p, t Q and M denote the depth, radius, 5.1. Verifiation of the proposed model To verify the auray of the method used in this study, a numerial example is presented to show the final solution of the pile's response. The results obtained by the present model are ompared with the existing results presented by [5]as shown in Fig.2. The relevant parameters used are given as: the pile length-diameter ratio l/ d 2, the soil Poisson s ratio v.3 and the pile-soil Young s modulus ratio Ep / E. From the graphial representation thereof as depited in Fig. 2, it is easy to notie that as the time t approahes infinity, the pore pressure tends to zero, thereby validating the reliability of the proposed model. 5.2 Influene of the stratified property of the soil on the behavior of the pile In this setion, two examples with pile length L are presented to hek the effet of the stratified property of the soil on the response of the pile. The shear fore and displaement of the pile together with the 5 pore pressure of the soil at different times (seven days, t s) and (twenty-eight days,

4 6 t s) are given. A layered half-spae of three layers with different Young s moduli is used here. Three different ases are onsidered. Case A orresponds to a softer middle layer with shear moduli ratios as: : : 5:1:5. Case B represents a homogeneous soil. Case C denotes a harder middle layer with v1 v2 v3 shear moduli ratio given as: v 1 : v2 : v3 2 :3: 2. The stiffness ratio 2.5 is onstant in the examples. Moreover, the soil parameters used in the examples are given in Table 1. The pile parameters are presented as the pile length L 2 m ; the pile radius and Young s modulus are held onstant, R.25 m, and 9 Ep 2.61 Pa. In similar way, the thikness, shear modulus v and oeffiient of permeability k h of the first layer of the soil are given as the referene length L, shear modulus and oeffiient of permeability k, aordingly. Fig. 3 (a) shows that the depth inreases with dereasing shear fore of the pile for Case C and inreases with inreasing shear of the pile for Case A. However, Fig. 3 (b) shows that in the ase of the softer middle layer(case A), the shear fore inreases with inreasing depth, while the depth inreases with dereasing shear fore for the harder middle layer (Case C). Moreover, Fig. 4 shows that for the harder middle layer Case C, the displaement of the pile is larger than that of (Case A). As shown in Fig. 5 (a) and (b), the pore pressure of the soil along the pile length gets larger for Case A and gets muh smaller in Case C. In addition, the pore pressure of the soil dereases with time in the ase of the homogeneous layer (Case B). From Fig. 3 and 4, the shear fore and displaement of the pile derease with inreasing depth and also inrease with inreasing time. On the other hand, in Fig. 5, the pore pressure of the soil tends to zero as the time inreases. Table 1 Parameters and values of the soil used in the example Layer h /m v / Pa h -3 1 hv / N m k w v number k / m s h Case A Case B Case C v Figure 2 Comparison with existing results for the shear fore of the pile DOI: 1.979/ Page

5 Figure 3 Variation of the pile shear fore along the depth at time (a) 5 Days and (b) 25 Days Figure 4 Variation of the pile displaement along the depth at time (a) 5 Days and (b) 25 Days Figure 5 Variation of the pore pressure at the pile length along the depth at time (a) 5 Days and (b) 25 Days VI. Conlusion In this study, the soil is regarded as a three-layered transversely isotropi saturated soil with two overlying layers and one underlying layer half-spae. Numerial results of the present model are validated through omparison with the results of existing solutions. Numerial results of this paper show that time has a huge influene on the pore pressure of the soil. As validated, over a long period of time, the pore pressure along the pile-length vanishes to zero. This model is suitable for estimating the response of a horizontally loaded pile undergoing small defletion. DOI: 1.979/ Page

6 Referenes [1]. Z. Y. Ai, Y. F. Chen, and X. B. Jiang, "Behavior of laterally and vertially loaded piles in multi-layered transversely isotropi soils," Applied Mathematial Modelling, vol. 51, pp , 217. [2]. J. Booker and J. Small, "A method of omputing the onsolidation behaviour of layered soils using diret numerial inversion of Laplae transforms," International Journal for Numerial and Analytial Methods in Geomehanis, vol. 11, pp , [3]. S. Lee, Y. Kog, and G. Karunaratne, "Laterally loaded piles in layered soil," Soils and foundations, vol. 27, pp. 1-1, [4]. S. Yimsiri and K. Soga, "Cross-anisotropi elasti parameters of two natural stiff lays," Géotehnique, vol. 61, p. 89, 211. [5]. V. Apirathvoraku and P. Karasudhi, "Quasi-stati bending of a ylindrial elasti bar partially embedded in a saturated elasti halfspae," International Journal of Solids and Strutures, vol. 16, pp , 198. [6]. B. Niumpradit and P. Karasudhi, "Load transfer from an elasti pile to a saturated porous elasti soil," International journal for numerial and analytial methods in Geomehanis, vol. 5, pp , [7]. R. Muki and E. Sternberg, "On the diffusion of an axial load from an infinite ylindrial bar embedded in an elasti medium," International Journal of Solids and Strutures, vol. 5, pp , [8]. H. G. Poulos, "Tall building foundations: design methods and appliations," Innovative Infrastruture Solutions, vol. 1, p. 1, 216. Oliver C. Waka. A Time-Dependent Model For Prediting The Response Of A Horizontally Loaded Pile Embedded In A Layered Transversely Isotropi Saturated Soil. IOSR Journal of Mehanial and Civil Engineering (IOSR-JMCE), vol. 16, no. 2, 219, pp DOI: 1.979/ Page