Pile Behavior under Inclined Compressive Loads A Model Study

Pile Behavior under Inclined Compressive Loads A Model Study Soumya Roy Assistant Professor & PhD Candidate, Civil Engineering Department, Meghnad Saha Institute of Technology, Kolkata, West Bengal, India. e-mail: roy.shoummo@gmail.com Dr. Bikash Chandra Chattapadhyay Emeritus Professor, Civil Engineering Department, Bengal Engineering and Science University, Shibpur, Howrah, West Bengal, India. Dr. Ramendu Bikash Sahu Distinguished Professor, Civil Engineering Department, Jadavpur University, Kolkata, West Bengal, India e-mail: rbsahu_1963@yahoo.co.in ABSTRACT Pile used as the foundation in many cases may be subjected to inclined compressive loading condition. In such cases, overall behaviors of the piles are estimated from available conventional theoretical approaches. As there are limited experimental studies available on behavior of vertical piles subjected to inclined compressive loads, in this paper, an attempt has been made to study the behavior of single pile subjected to varying inclined load until failure with angle of applied load varying from 0 0 to 90 0 from vertical axis of pile through a rigorous experimental program. Increment of load inclination is kept small so as to facilitate a precise and detailed study of effect of load inclination on inclined load carrying capacity of a vertical pile. Axial, lateral and inclined load carrying capacity for pile of various slenderness ratios are predicted from available theories and compared with present study. Influence of vertical and lateral components of the loads on horizontal and vertical displacement of the pile head is discussed. Variation of ultimate load carrying capacity of vertical pile with angle of load inclination is also reported through polar diagrams. KEYWORDS: Pile foundation, inclined load, bearing capacity, model tests. INTRODUCTION Foundations of many structures are subjected to inclined compressive loads as in foundations of transmission towers, wind energy converter towers, offshore structures etc. In such cases, to increase the load carrying capacities of adopted foundations and also to decrease the corresponding settlements, piles may be employed. Besides, in the complex cases where the horizontal and vertical movements are generated along with the moments generated due to wind and seismic loads a pile foundation should satisfy the safety and serviceability conditions well. Normally the axial - 2187 -

Vol. 18 [2013], Bund. K 2188 loading of the pile is predominant. But in special cases like piles supporting offshore wind energy foundations or conductors, the axial, mostly vertical load is accompanied by a lateral (horizontal) load as pointed out by Lianyang Zang et al. (2005), Zadeh N.G. et al. (2011). Current design practice involves separate analysis of axial and lateral pile capacities and does not consider the interaction of vertical and horizontal load components in case of inclined loading conditions. Behavior of vertical piles under oblique load has been studied by several researchers. Meyerhof (1956) pointed out the deficiencies in assumptions of Terzaghi s theory (1943) for application to deep foundation in cohesionless soil and proposed higher values for bearing capacity factor, N q values which are much higher than those Terzaghi s bearing capacity factor. Based on modified bearing capacity factor values for deep foundations, Meyerhof (1960) proposed theoretical analysis of bearing capacity of rigid piles and retaining walls. Berezantev (1961) assumed a much simpler failure mechanism of pile foundation and proposed N q values based on actual slenderness ratio (L/d) ratio and angle of internal soil frictional resistance, values. Vesic (1967) proposed modified curves of N q versus for dense cohesionless soil deposits. Load displacement response of pile under oblique pull has been studied by Yoshimi (1964) for rigid piles using a subgrade modulus concept. The analysis has been further modified and extended by Ramanathan and Aiyer (1970) for flexible piles. In these studies it was assumed that the presence of an axial component of the pull has no influence on the normal deflection of the piles. Simplified methods to evaluate ultimate resistance under oblique pull have been attempted for vertical piles by Broms (1965), Meyerhof (1973), Poulos and Davis (1980), Chattopadhyay & Pise (1986) and for inclined piles by Flemings et al. (1985). Bearing capacity study of rigid piles based on 1 g experiments in sand and clay for vertical pile, batter pile and pile in group has been done by Saffery et al. (1961), Meyerhof et al. (1965, 1972, 1973 and 1981b). Behavior of vertical and batter piles subjected to inclined oblique loads have been reported by researchers like Das et al. (1976), Chari & Meyerhof (1983), Ismael (1989), Sastry & Meyerhof (1990,1995), Shahrour, et al. (1991), Amde et al. (1997), Chattopadhyay & Pise (1986). However, the comparative study by Lianyang Zang et al. (2005) has shown that these studies produced significantly different ultimate resistance values of single as well as pile group. Thus it becomes difficult for practicing engineers to select the appropriate method in practice. Analysis of piles subjected to inclined loading action is complicated due to large number of variables involved (Meyerhof & Ranjan, 1973). Further, experimental studies on behavior of single pile subjected to inclined compressive loads are limited. The effect of angle inclination of compressive load on horizontal deflection and vertical displacement of vertical piles of different length to diameter ratio are also rarely tested. Limited experimental results on vertical pile under central inclined loading by (Meyerhof G.G. et al. 1972) indicated that ultimate capacity of pile for a central inclined load at the head of a fully embedded pile, the limits of vertical and horizontal components, P v and P h, respectively, of ultimate capacity can be approximated by a semi-empirical relationship expressed as Pv PU 2 Ph PH 2 1 (1) where, P u and P H are the ultimate pile capacities under axial loading and horizontal loading respectively. Meyerhof (1976) showed that in cohesion less soil, the ultimate capacity of a vertical pile for axial load can be expressed as

Vol. 18 [2013], Bund. K 2189 P U P P (2) p s where, P p is the end bearing and P s is the shaft resistance of the pile and expressed as P p q A p DN 0. 5dN (3) K s P A tan 2 D s s (4) in which, A p and A s = the areas of pile point and shaft, respectively; D= the depth of embedment of the pile; d=diameter of pile; K s = the average coefficient of earth pressure on the shaft; N q, N are the bearing capacity factors; = the angle of skin friction; and = the average unit weight of the sand. The ultimate lateral resistance as given by Meyerhof et al. (1981a) can be expressed by Eqn. 4. P 0.12BD 2 H k b [5] where, B is the pile diameter and K b is the coefficient of net passive earth pressure for =0, approximately on the pile. Broms (1964) on the basis of measured maximum lateral earth pressure by Prakash S (1962), assumed that full passive resistance equal to three times the Rankine s passive earth pressure develops close to the location of center of rotation of pile under horizontal load applied at the free head of vertical short pile and expressed ultimate lateral load carrying capacity as P dl 2L 3 H K p where, = effective unit weight of soil; K p =Rankine s passive earth pressure coefficient. The theoretical reduction factor for determination of ultimate bearing capacity of a vertical pile subjected to an inclined load having load inclination angle with the vertical axis of the pile, was roughly given by the corresponding reduction factor for shallow foundations expressed as [6] Pv P U 1 0 90 J.B. Hansen (1970) also suggested the following relationships for the inclination factors, i q and i to be used for deriving value of P p as P p DN i 0. 5di N q q in which i q and i in cohesionless soil can be expressed as 2 A p [7] [8] i q 0.5P sin 1 cos U PU 5 [9]

Vol. 18 [2013], Bund. K 2190 i 0.7P sin 1 cos U PU Muhs and Weiss (1973) concluded that the ratio of vertical component P v of the ultimate load with inclination with the vertical to the ultimate load P U when the load is vertical is approximately given by: 5 [10] P V P U 1 tan 2 Poulos and Davis (1980) assumed that the ultimate axial and normal load carrying capacities of the pile are not seriously affected by the inclined soil surface relative to the pile axis. Fleming et al. (1985) suggested that for a general case when pile is subjected to load P, inclined at angle to the vertical as shown in Figure 1, axial failure will occur if [11] P cos P U and rotation failure or bending failure in vertical pile will occur if P sin P H [12] [13] WORK OBJECTIVE In the analytical approaches to predict the load-displacement responses of a pile under central inclined load, it is assumed that the lateral displacement of the pile head is independent of the vertical component of the inclined load. Similarly, while estimating the ultimate resistance it is considered that the vertical load factor of the inclined load does not influence the ultimate lateral resistance of the pile. The analytical approaches of Fleming et al. (1985), Poulos and Davis (1980) are not validated through rigorous experiments or field tests results. Reliability on any theoretical approach depends on agreement of estimated results with the experimental observations. However, for pile under inclined loads, very few test results are available. The present work provides results of model vertical pile tested under controlled conditions for load displacement and ultimate resistance under central inclined compressive loads. Present work was intended to study the assumed simple but rather complex behavior of a single pile-soil interaction mechanism under different inclined loading system. The test results are compared with the available limited theoretical approaches for pile under inclined compressive load. EXPERIMENTAL PROGRAM Dry brown uniformly graded Mogra sand obtained from sand mines of Hoogly district, West Bengal, India was used as soil medium. The physical properties of the sand are given in table 1. Rigid rough mild steel circular cross sections having outside diameter 20 mm and wall thickness 5mm with three types of length to diameter ratio viz. 10, 15, 20 were used as model piles. Surface of the pile is made rough by scratching the surface with iron paper followed by gluing mild steel powder carefully so that the outside diameter of the piles remain same.

Vol. 18 [2013], Bund. K 2191 Table 1: Physical properties of Sand Property Value Specific gravity Uniformity coefficient, C U Coefficient of Curvature, C C Effective size, D 10 in mm Maximum dry density, max in gm/cc Minimum dry density, man in gm/cc Angle of internal friction in degree 2.65 1.25 0.96 0.45 1.545 1.431 41 Same method has been employed previously for making of rough piles by Chattopadhyay and Pise (1986). Pile is installed as fully embedded in sand bed. The tests were conducted in a steel tank of size 100 cm X 100 cm and 75 cm deep. Loads were applied on the top of the pile with load inclined at an angle () 0 0, 15 0, 30 0, 45 0, 60 0 and 90 0 with the vertical axis of the pile. Load was applied on the pile top at a desired angle of loading through a hand operated wheel axel arrangement. P P v P h P U P H Figure 1: Vertical pile under different loading condition A schematic view of the experimental assembly is shown in Figure 2. Placement density of the sand during testing was 1.52 gm/cc and the angle of shearing resistance was 41 0. Pile fixed in the pile cap which is a mild steel plate, was placed at the center of the tank. The horizontality of the top of the cap was checked with a level. Sand was poured in the tank through a funnel type hopper keeping the height of fall about 750 mm constant throughout the time of fall. This technique is reported to achieve good reproducible density by Pise (1983) and Chattopadhyay and Pise (1986). After half or more of the pile length has been embedded in sand, pile cap plates were very carefully removed. Further sand pouring was continued to top level surface. Pile fully embedded in sand in vertical position in model tank was subjected to inclined load at the free head. Loading was applied at the pile head by wheel axle arrangement for load inclination angle ranging from 0 0 to an angle of 60 0 with the vertical axis of the pile. Horizontal load at the free head was applied following the proposed procedure by Chattopadhyay and Pise (1986). Vertical and the horizontal displacements of the pile top were measured with dial gauges of sensitivity 0.002 mm. Loads were applied in small increments till the ultimate capacity of the pile was reached with little subsequent increment of the applied load. To check the repeatability of the results most of the tests were carried out thrice. Additionally, some more tests were also conducted in loose sand deposit by keeping of sand as 31 0 for precise comparison with the theoretical values.

Vol. 18 [2013], Bund. K 2192 Figure 2: Schematic diagram of experimental setup designed by Roy et al. (2012) EXPERIMENTAL RESULTS AND DISCUSSION Due to application of oblique load P on pile head, it is subjected to a vertical component, P v and a horizontal component, P h. From geometry, these components can be expressed as: P v = P cos [14] P h = P sin [15] From Eqn. [14] and Eqn. [15] it is seen that as increases, P v decreases and P h increases. Thus with the increase of tilt of load with the vertical direction the horizontal component dominates the vertical load component. Previous analytical and experimental approaches propose that depending on the relative magnitudes of the ultimate axial capacity and lateral ultimate resistance of a vertical pile, the axial component may attain critical value equal to ultimate load carrying capacity of pile axially. In this case, the horizontal component remains smaller than the ultimate horizontal load carrying capacity causing axial failure of the pile. However, if the horizontal component reaches the critical value equal to the ultimate horizontal capacity, while the axial component is less than the ultimate axial load capacity, plastic hinge formation takes place and bending failure will occur in long pile and in case of short pile translation failure in pile occurs. As thorough understanding of the complex pile soil interaction under inclined compressive load was intended, short rigid mild steel pile was selected. Results of load versus axial and normal movement of the pile head were plotted. Comparisons of obtained experimental results with the available theories are shown in Figure 10 to 12. Load-Vertical displacement diagrams Figure 3a, 4a, 5a, shows the vertical displacement of piles having L/d = 20, 10 and 15 under various inclination of load with the vertical pile axis. Failure was associated with noticeable peak

Vol. 18 [2013], Bund. K 2193 values for = 0 0 and = 15 0 for all the L/d ratio of pile. However, for greater values of, failure load were taken where load settlement curves becomes almost parallel to vertical settlement axis. (a) Axial displacement (b) Lateral displacement Figure 3: Load versus displacement of pile head (d = 20 mm, L = 450 mm) (a) Axial displacement (b) Lateral displacement Figure 4: Load versus displacement of pile head (d = 20 mm, L = 300 mm)

Vol. 18 [2013], Bund. K 2194 (a) Axial Movement (b) Lateral Movement Figure 5: Load versus displacement of pile head (d = 20 mm, L = 200 mm) It is further seen that for a particular axial movement of the pile the load bearing capacity of the pile increases as L/d ratio increases. From Eqn. [15] it can be proposed that for a particular value of inclined load magnitude, the vertical component P v, decreases with increase in. If the vertical movement and the vertical settlement of pile are assumed to be independent of load inclination angle i.e. independent of the normal component of the inclined load, to cause an equal vertical movement, equal magnitude vertical component to that of load at purely vertical case would be same. To verify this, plots of vertical component versus vertical settlement of pile head are drawn in Figure 6(a,b) and Figure 7 for all pile slenderness ratios at load inclination angle of 15 0, 30 0 and 45 0 respectively. All these applied inclined loads have vertical components, P v. The curves of vertical component of the load versus vertical settlement of the pile at 15 0, 30 0 and 45 0 are different from pile s vertical settlement under axial loading condition (at = 0 0 ) i.e. when no horizontal components are present. This indicates that presence of lateral component of the applied load modifies the vertical load displacement response. Further it is observed from, Figure 3a, 4a and 5a, the presence of horizontal component of the applied load, when the inclination of loading with the vertical axis of pile approaches an angle around 15 0 caused an increase in vertical load carrying capacity of the pile. Result obtained indicated similar trend reported by Chattopadhyay and Pise (1986) where an increase in uplift capacity of vertical pile was revealed nearer to the 22 0 angle of pull with the vertical axis of pile.

Vol. 18 [2013], Bund. K 2195 (a) L = 400mm, d = 20mm (b) L = 300mm, d=20mm (c) L= 200mm, d = 20 mm Figure 7: Vertical Component versus axial settlement of pile Load-Horizontal displacement diagrams For all test conditions the horizontal movement of the pile head are plotted against the applied inclined load in Figure 3b,4b,5b. From these figures it is seen that for a particular horizontal movement of the pile head the magnitude of the load carrying capacity increases with the increase in the L/d ratio of pile. From Eqn. 16 it is seen that for a particular value of inclined load magnitude, the lateral component P h, increases with the increase in. If the lateral displacement is assumed to be dependent on the normal component only and independent of axial component of the inclined load, to cause an equal lateral movement, magnitude of the load component would be same required for pure horizontal loading. Typical plots of horizontal components of the applied inclined load versus horizontal deflection of the pile head are shown in Figure 8 (a.b.c) for chosen L/d ratio. It is seen that the load deflection curves at = 15 0, 30 0 and 45 0 i.e. when vertical components are present are different for = 90 0, i.e. when there is no vertical component acting on the pile head thereby indicating the influence of the vertical load component on the lateral load-displacement response of the pile head. This shows a significant effect of presence of vertical component of the

Vol. 18 [2013], Bund. K 2196 inclined load. However, with the increase of load inclination angle with the vertical axis of the pile the lateral deflection increases noticeably. Similar results have been reported by Nima Ghashghaee Zadeh et. al. (2011). (a) L= 400 mm, d = 20mm (b) L= 300 mm, d = 20 mm (c) L= 200 mm, d = 20 mm Figure 8: Lateral Component of Load versus lateral settlement of pile head (a) Loose sand (b) Dense sand Figure 9: Polar load carrying capacity diagram for vertical pile of diameter 20mm for various L/d ratio and applied load

Vol. 18 [2013], Bund. K 2197 Ultimate load carrying capacity of pile under applied inclined load Experimental results for single vertical piles under various inclinations of compressive loads are shown in Figure 9 in the form of polar load carrying capacity diagram, which gives the ultimate load carrying capability of a vertical pile for different directions of applied load. The nature of the polar curves in Figure 9a and b for different slenderness ratio of pile embedded in different densities of sand bed is found to analogous. The curve of Figure 9 reveals that the inclined load carrying capacity of a vertical free standing pile increase initially up to an angle close to 15 0 irrespective of density of sand bed and pile slenderness ratio. Similar test results have been also reported by Chattopadhyay and Pise (1986) for uplift pile capacity, where piles were embedded in different densities of sand bed and by Zadeh N.G. et. al. (2011) for piles in layered clay and sand bed under inclined compressive load studied through pressure- displacement (p-y curves) Winkler foundation analytical model. Figure 10: Ultimate axial capacity of versus L/d ratio from various studied Comparisons of experimental and theoretical values of ultimate load axial capacity of axially loaded vertical piles The various theoretical values of axial capacity and the capacity obtained from the present study have been shown in Figure 10. The experimental values of the ultimate load carrying capacity of piles have been compared with the available theoretical values. Theoretical capacities of the pile were predicted based on the analysis of Berezentsev (1961), Vesic (1967) and Meyerhof (1960) and is tabulated in Table 2. Experimental values of load carrying capacities of piles were found be closer to the predicted values for Berezentev and Vesic s theory. However, results for Meyerhof s theory are found to in close proximity to the experimental results at a higher L/d ratio. Table 2: Experimental and theoretical values of P U Length of L/d Theoretical ultimate axial resistance in N Experimental Pile in cm Meyerhof (in N) Berezantev Vesic (in N) Values (N) (in N) 20 10 127 145 153 147 30 15 225 243 248 255 40 20 315 325 356 348

Vol. 18 [2013], Bund. K 2198 Figure 11: P from present study versus P from theoretical methods for L/d = 20 (a) pile in dense sand bed; (b) pile in loose sand deposit. Comparisons of experimental and theoretical values of ultimate inclined load carrying capacity of vertical piles Typical plot of the ultimate inclined capacity of a vertical pile, P (for L/d = 20) from various theoretical approaches and the value predicted from present study has been shown in Fig. 11. P has been plotted against inclination of load application using polar diagram to give a comprehensive view of effect of inclination and also to facilitate a comparative study of the obtained test results with theories of several authors. Variation of P in both the densities of sand bed shows the prominent effect of load component of an inclined load on the vertical and lateral load carrying capacity of pile. Theoretical values for P are calculated from Eqn. 1, Eqn. 7 and Eqn. 8 and have been plotted against. To facilitate a comparative study through above equations, theoretical P are calculated for = 31 0. Rigorous experimental values of P showed that most of the theoretical values are conservative for dense sand deposits. Polar plots however reveal that all the theoretical approaches have over simplified the effect of both the vertical and horizontal load components of an inclined load. Hence the maximum load carrying capacity of a pile occurs for an inclination of the load at value of 15 0 (/12), which is not reflected from the previous studies. Significant increase in the inclined load carrying capacity of the vertical pile at lesser values of is due to lateral component s influence on the value of earth pressure coefficient k in Eqn. 3. Comparing the experimental vertical component, P v = P cos of an inclined compressive load P, with the ultimate axial capacity of pile P U for different load inclination, shown in Figjure 12 indicates that ratio of Pv/P U initially increases at lesser values of and gradually decreases following a nonlinear path with increase of. However, previous theoretical approaches over simplified the variation of the Pv/P U ratio with for conveniently analyzing the complex pile-soil interaction under inclined compressive loading condition. Some values of P found from Meyerhof

Vol. 18 [2013], Bund. K 2199 (1976), Hansen (1970) and Muhs and Weiss theory (1973) and that obtained from the present detailed experimental study have been tabulated in Table 3. Figure 12: Ultimate axial capacity of versus L/d ratio from various studied Table 3: Experimental and theoretical values of P for L/d = 20 L/d ratio Angle of load Theoretical values of P (N) Experimentally inclination, Meyerhof Hansen Muhs & Weiss obtained, P (N) 20 41 0 30 220 170 140 252 15 270 260 180 375 45 140 120 80 170 20 31 0 30 120 110 95 170 15 230 210 170 260 45 78 69 61 120 Comparisons of experimental and theoretical values of lateral load capacity of vertical piles The experimental values of the ultimate lateral resistance ( = 90 0 ) of piles have been compared with the theoretical values predicted from Brom s (1964), Brom s (1965) and Meyerhof s (1973) analysis in Table 4. The theoretical values of the ultimate lateral resistance are also estimated through Hyperbolic Response method (HR method), log log mthod (LL method) Chattopadhyay and Pise (1986) and from one of the most recent theory proposed by Lianyang Zang et al. (2005). Ultimate lateral resistance predicted through HR method, LL method and from method proposed by Zang et. al. (2005) has been tabulated in Table 5. Table 4: Experimental values and theoretical values of ultimate lateral resistance Theoretical ultimate lateral resistance in N L/d ratio Broms Broms (1964)* (1965)** Meyerhof (1973) 40 20 115 191 71 125 30 15 64 107 55 67 20 10 29 47 18 33 *Passive pressure mobilized = 3 times Rankine s passive earth pressure **Passive pressure mobilized = 5 times Rankine s passive earth pressure Length of pile in cm Experimental value in N

Vol. 18 [2013], Bund. K 2200 Length of pile in cm Table 5: Theoretical values of ultimate lateral resistance L/d ratio Theoretical ultimate lateral resistance in N HR method LL method Zang et. al. (2005) 40 20 145 130 180 30 15 55 65 77 20 10 17 28 52 The lateral load deflection curves as obtained from the experiments are shown in Figure 13 for various slenderness ratio of pile embedded in dense sand bed. As the load deflection relation is hyperbolic, ultimate lateral resistance has been predicted through the process as described in Chattopadhyay and Pise (1986). A similar method for predicting ultimate load for pile subjected to the inclined compressive load has been attempted by Chin (1970). Plot of ratio of horizontal deflection with applied load and deflection of pile head is shown in Figure 14. For the convenience of the comparative study, theoretical values are also predicted through LL method as suggested by Pise (1983). Ultimate lateral load is extrapolated as the lateral load corresponding to pile head deflection equal to pile diameter. The concept has been reported to give good results as proposed by Polous H.G. et al. (1980). Applied lateral loads and the corresponding deflections for the piles tested to failure are shown in Figure 15. The estimated values compared reasonably well with the predicted values of Brom s (1964) as well with the results of the present experimental program. Figure 13: Lateral load versus lateral deflection

Vol. 18 [2013], Bund. K 2201 Figure 14: Ultimate lateral resistance through HR method It is observed from Figure 16 that Brom s (1964) produces conservative value where as Brom s (1965) over estimates the lateral capacity which has also been pointed by Chattopadhyay and Pise (1986). Meyerhof s method estimates to some extent conservative value at smaller slenderness ratio but higher slenderness ratio prediction of lateral resistance is under estimated. This may be due to the fact that his theory gives good results for short rigid piles. Calculated lateral resistance from HR method correctly reflects the increment of lateral resistance with the increase of slenderness ratio but however it gave higher value of ultimate resistance at higher L/d ratio. Whereas, Zang et al. (2005) gives higher values of ultimate lateral resistance at higher slenderness ratio and the values are more than the results obtained from the present study. However, values predicted from LL method gives comparatively closer values to the experimental values for all the pile slenderness ratios. Figure 15: Ultimate lateral resistances from LL method

Vol. 18 [2013], Bund. K 2202 Figure 16: Ultimate lateral resistance of pile from various studies including present study SUMMARY AND CONCLUSION A rigorous experimental program was undertaken to study the ultimate inclined load carrying capacity of vertical single pile. Angle of load inclination was varied from 0 0 to 90 0 with a small angular interval difference of 15 0 upto 60 0 with the vertical axis of pile with an intention of studying the response of vertical and horizontal deflection of pile head against the inclined applied load. Experimental values of ultimate vertical load carrying capacity, lateral load carrying capacity including the inclined load carrying capacity of pile embedded in different densities of sand are compared with the predicted values from available theoretical approaches. Salient conclusions that can be drawn from the present study are as follows: The vertical settlement and the lateral deflection of pile under inclined compressive load depend on both axial and normal components of the applied load. The load-vertical displacement and the load-lateral movement of pile head (in direction of load) curve revealed that they are unequal with the curves obtained for the case of applied purely vertical load (=0 0 ) and pure lateral load(=90 0 ). Hence, the neglecting the component effect of an inclined load in proposing ultimate inclined load carrying capacity would be erratic and the assumption that the normal displacement of the pile is only dependent on the normal component and the axial displacement only on the axial component of the pull are not valid. Polar diagrams of the present study showed that all the theoretical approaches have minimized the effect of both the vertical and horizontal load components of an inclined load. There is a considerable increase in inclined load bearing capacity of a pile in in the vicinity of value = 15 0 (/12). Increase in the inclined load carrying capacity of the vertical pile at lesser values of is due to lateral component s influence on the value of earth pressure coefficient k in Eqn. 4. Comparisons of the experimental vertical component, P v = P cos of an inclined compressive load P, with the ultimate axial capacity of pile P U for different load inclination,, indicates that

Vol. 18 [2013], Bund. K 2203 ratio of P v /P U initially increases at lesser values of and gradually decreases following a nonlinear path with increase of. Hence, the reduction factors for predicting the inclined load carrying capacity for deep foundations are generally over safe. Ultimate axial, lateral and inclined load carrying capacity of vertical pile are estimated from different methods and are compared with the experimental results. Experimental values of lateral load carrying capacity are mostly closer to LL method for all pile slenderness ratio and ultimate theoretical axial load resistance values predicted using Berezentsev s and Vesic s theory are closer to pile capacity when loaded to ultimate failure load. But values of P calculated from limited semiemperical and approximate relations scatter by a considerable amount from the obtained experimental results. Polar diagrams of the present work show that P is related to a continuous function to the angle of inclination of applied load and its normal and axial components which was however simplified and not validated by rigorous experimental and field tests in the previous studies. REFERENCES 1. Amde, A.M., Chini, S.A. & Mafi, M. (1997) Model study of H-piles subjected to combined loading, Geotechnical and Geological Engineering, Vol. 15, pp. 343-355. 2. Berezantsev, U.G. (1961) Load Bearing Capacity and Deformation of Piled Foundations, 5 th International Conference in Soil Mechanics and Foundation Engineering. 3. Broms, B.B. (1964) Lateral Resistance of Piles in Cohesionless Soil, Journal of Soil Mechanics and Foundation Div., ASCE, Vol. 90, No. SM3, 27-63. 4. Broms, B.B. (1965) Discussion to paper by Y. Yoshimi., Journal of Soil Mechanics and Foundation Engineering Division, ASCE, Vol. 91, No.4, pp 199-205. 5. Chari, T.R. & Meyerhof, G.G. (1983) Ultimate Capacity of single rigid piles under inclined loads in sand, Canadian Geotechnical Journal, Vol. 20, pp. 849-854. 6. Chattopadhyay, B.C. & Pise, P.J., (1986) Ultimate Resistance of Vertical Piles to Oblique Pulling Loads, Proc. 1 st East Asian Conference on Structural Engineering and Construction, Bangkok, pp 1632-1641. 7. Chin, F.K. (1970) Estimation of Ultimate Load on Piles not Carried to Failure, Proc. 2 nd S.E. Asian Conference on Soil Engineering. 8. Das, B.M., Seeley,G.R. & Raghu, D. (1976) Uplift Capacity of Model Piles under Oblique Loads, Journal of the Geotechnical Engineering Division, ASCE, Vol. 102, No. (9), pp. 1009-1013. 9. Fleming, W. G. K., Weltman, A. J., Randolph, M. F. & Elson, W.K., (1985) Pilling Engineering, Survey University Press, Galsgow and London. 10. Hansen, J.B., (1970) A revised and Extended Formula for Bearing Capacity, Bulletien No. 28, Copenhagen, Danish Geotechnical Institute. 11. Ismael, N.F. (1989) Field Tests on Bored Piles Subject to axial and Oblique Pull, Journal of Geotechnical Engineering, Vol. 115, No. 11, pp. 1588-1598. 12. Lianyang, Zhang, Francisco Silva, and Ralph Grismala, (2005) Ultimate Lateral Resistance to Piles in Cohesionless Soils, Journal of Geotechnical and Geo

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Vol. 18 [2013], Bund. K 2205 29. Vesic, A.S.(1967) A Study of Bearing Capacity of Deep Foundations, Final Report Georgia Institute of Technology, Atlanta, USA. 30. Yoshimi, Y. (1964) Piles in Cohesionless Soil subject to Oblique Pull, Journal of the Soil Mechanics and Foundations Division, ASCE, 90(6), pp. 11-24. 2013, EJGE