Model Pile Groups Under Oblique Pullout Loads – an Investigation

Experimental investigations on model pile groups of configuration, 1 × 1(single pile), 3 × 1, 2 × 2 for embedment length to diameter ratio, L/d = 38, were conducted in uniform dry medium dense Ennore sand. The spacing of piles in the groups varied from 3 to 6 pile diameter. Soil–pile friction angles were δ = 16° and 28°. The pile groups were subjected to oblique pulling loads at angles θ = 0°, 30°, 60° and 90° with the vertical central axis of the groups. The load–displacement response, oblique ultimate pulling resistances have been qualitatively and quantitatively studied. The inclinations of the load, at which maximum oblique resistance for the groups were observed, have been reported. Predictions of ultimate resistance of pile groups under uplift, lateral and oblique pulling loads have been carried out respectively by the methods of Patra and Pise (2002) (Electronic Journal of Geotechnical Engineering, 8, Bundle B), Patra and Pise (2001) (Journal of Geotechnical and Geoenvironmental Engineering ASCE, 127(6), 481–487) and Chattopadhyay and Pise (1986c) (Proceedings of IST East Asian Conference on Struct Engineering and Const., Vol. 1, pp. 1632–1641). A comparison of the measured values of the Writers and others with the predicted values showed reasonable agreement.     

Numerical study of group effects for pile groups in sands

The OpenSees finite element framework was used to simulate the response of 3×3 and 4×3 pile groups founded in loose and medium dense sands. Several numerical static pushover tests were conducted to investigate the interaction effects for pile groups. The results were then compared with those from centrifuge study. It is shown that our simulations can predict the behaviour of pile groups with good accuracy. Special attention was given to the three dimensional distribution of bending moment. It was found that bending moment develops in the plane perpendicular to the loading direction. In addition, bending moment data from simulations was used to derive p–y curves for individual piles, which were used to illustrate different behaviour of individual piles in the same group. Copyright © 2003 John Wiley & Sons, Ltd.     

Explicit extension of the p–y method to pile groups in sandy soils

The method of “p–y” curves has been extensively used, in conjunction with simplified numerical methods, for the design and response evaluation of single piles. However, a straightforward application of the method to assess the response of pile groups is questionable when the group effect is disregarded. For this reason, the notion of p-multipliers has been therefore introduced to modify the “p–y” curves and account for pile group effect. The values proposed for p-multipliers result from pile group tests and are limited to the commonly applied spacing of 3.0 D and layout less than 3 × 3, restricting the applicability of the method to specific cases. With the aim of extending the applicability of the “p–y” method to pile groups, the authors have already proposed a methodology for estimating the “p _G–y _G” curves of soil resistance around a pile in a group for clayey soils. A complementary research allowing for the estimation of the “p _G–y _G” curves for sandy soils is presented in this paper. The well-known curves of soil resistance around the single pile in sandy soils are appropriately transformed to allow for the interaction effect between the piles in a group. Comparative examples validate the applicability and the effectiveness of the proposed method. In addition, the method can be straightforwardly extended to account for varying soil resistance, according to the particular location of a pile in a group. It can therefore be used in a most accurate manner in estimating the distribution of forces and bending moments along the characteristic piles of a group and therefore to design a pile foundation more accurately.     

Uplift Capacity of Single Bent Pile and Pile Group Considering Arching Effects in Sand

In this paper an analytical method has been proposed to predict the net ultimate uplift capacity of the single bent pile and pile group with a bent embedded in sand considering arching effects. Arching develops due to relative compressibility of sand relative to pile which activates the soil-pile friction. The method takes into consideration the embedded length (L), diameter of the pile (d), bent angle, surface characteristics of pile, group configuration, spacing of the pile group and the soil properties. Log spiral failure surface with parabolic arch shape was assumed in the analysis. Theoretical investigation for uplift capacity was been carried out for the single bent pile and group of pile (2 × 1, 2 × 2) embedded in sand. The variable used in the analysis were embedded length to pile diameter (L/d = 15, 20 and 25), spacing in the group (3d, 4d and 6d) and angle of bent (6°, 14° and 20°). Typical charts for evaluation of net ultimate uplift capacity for pile groups are presented through the figures. Comparison of theoretical results shows good agreement with established experimental results.     

Nonlinear Response of Single Piles in Sand Subjected to Lateral Loads using k hmax Approach

This paper presents results of analysis of full-scale pile load test data of 14 piles embedded in either loose or medium dense sands. The analysis was performed using two methods, p–y curve approach and a more recently developed k_hmax approach. Comparison of the results obtained using both the methods is also presented. A step-by-step analysis procedure is presented for predicting lateral load deflection response of single piles in sand using the k_hmax approach. The results presented show that the k_hmax approach has promise over the p–y curve approach because of its simplicity and the fact that it provides upper- and lower-bound curves, which are valuable guides to making engineering decisions. For loose sands, a new range of k_hmax values is recommended to better predict the lateral load–deflection response of single piles.     

An experimental study on static and dynamic bending behaviour of piles in soft clay

Static and dynamic lateral load tests were carried out on model aluminium single piles embedded in soft clay to study its bending behaviour. Model aluminium piles with length to diameter ratios of 10, 20, 30 and 40 were used. Static lateral load tests were conducted on piles by rope and pulley arrangement upto failure and load–deflection curves were obtained. Dynamic lateral load tests were carried out for different magnitudes of load ranging from 7 to 30 N at wide range of frequencies from 2 to 50 Hz. The load transferred to the pile, pile head displacement and the strain variation along the pile length were measured using a Data Acquisition System. Safe static lateral load capacity for all piles is interpreted from load–deflection curves. Dynamic characteristics of the soil–pile system were arrived from the acquired experimental data. The soil–pile system behaves predominantly in nonlinear fashion even at low frequency under dynamic load. The displacement amplitude under dynamic load is magnified by 4.5–6.5 times the static deflection for all piles embedded in soft clay. But, the peak magnification factor reduces with an increase in the magnitude of lateral load mainly because of increase of hysteretic damping at very soft consistency. The maximum BM occurs at the fundamental frequency of the soil–pile system. Even the lower part of the pile affects the pile head response to the inertial load applied at the pile head. The maximum dynamic BM is magnified by about 1.5 times the maximum static BM for model piles in tested consistency of clay. The maximum dynamic BM occurs at a depth of about 1.5 times the depth of maximum static BM for model piles, which indicates an increase of active pile length under dynamic load.     

抗滑桩应变特征与内力非线性研究

为探究抗滑桩实际内力与变形间的规律,特别是桩土相互作用下桩体受力、变形、稳定性等特征,通过抗滑桩大型物理模型试验,结合MATLAB拟合推导实现从桩表面应变散点数据到桩身挠度分布的求解。对比同桩长不同加载条件与同加载条件不同桩长两种情况下桩表面应变、桩身弯矩、剪力及挠度,分析抗滑桩的应变特征与内力变化规律。研究表明:单调与循环加载条件下抗滑桩工作阶段划分为三阶段,即未开裂阶段、混凝土开裂-钢筋屈服阶段、钢筋屈服-桩体破坏阶段。未开裂阶段一、二级荷载下由于土的压密性桩体略微回弹,桩表面应变、桩身弯矩、受荷段剪力及挠度出现较小的负值（绝对值约为破坏时的1%）。混凝土开裂-钢筋屈服阶段应变、弯矩、剪力、挠度增速明显加快。钢筋屈服-桩体破坏阶段应变、弯矩、剪力、挠度呈非线性增长,桩体的破坏模式均为弯剪破坏。随着自由端长度的增加,破坏时应变、弯矩增大,而剪力减小,破坏时应变增长约10%,弯矩增长约3%,剪力减少约20%;相对于单调加载,循环加载下最大弯矩值和最大挠度均有增大,最大弯矩增长约2%,最大挠度增长约1%。     

Field testing of one-way and two-way cyclic lateral responses of single and jet-grouting reinforced piles in soft clay

Piles supporting transmission towers, offshore structures (such as wind turbines), or infrastructures in seismic areas are frequently subjected to either one-way or two-way cyclic lateral loadings. Relatively little attention, however, has been paid to compare and understand the effects of different loading regimes (one-way or two-way cycling) on lateral responses of piles in soft clay. For this reason, a series of field tests in soft clay are carried out to compare one-way and two-way cyclic responses of single piles and of jet-grouting reinforced piles. The field tests reveal that the single pile subjected to two-way cycling experiences much more rapid degradation in lateral stiffness and capacity, but accumulates much smaller residual pile deflection (δ _p), than the single pile under one-way cycling. This is because the reverse part of the two-way cycling also generates plastic strain, causing additional softening and strength reduction in the soil surrounding the pile. After each cycling, non-zero bending moment (i.e. locked in moment, or M _L) is retained in the single piles, and the M _L increases with the δ _p. The one-way cycling leads to two times larger M _L than the two-way cycling, as it causes greater δ _p. The maximum M _L in the pile after one-way cycling can be up to 40% of the maximum bending moment induced during the previous cyclic loading stage. After application of jet-grouting surrounding the upper part of the single pile, it greatly reduces degradation of lateral pile stiffness, accumulation of δ _p and therefore development of M _L. Compared to the field measurements, the API (API RP 2A-WSD, recommended practice for planning, designing, and constructing fixed offshore platform-working stress design, 21st edn. API, Washington, 2000) code underestimates the lateral stiffness of the pile under one-way cycling, while overestimates that of the pile under two-way cycling, leading to a non-conservative prediction of bending moment in the latter pile.     

Influence of seismic motions on behavior of piles in liquefied soils

In the present study an analytical procedure based on finite element technique is proposed to investigate the influence of vertical load on deflection and bending moment of a laterally loaded pile embedded in liquefiable soil, subjected to permanent ground displacement. The degradation of subgrade modulus due to soil liquefaction and effect of nonlinearity are also considered. A free headed vertical concrete elastic nonyielding pile with a floating tip subjected to vertical compressive loading, lateral load, and permanent ground displacement due to earthquake motions, in liquefiable soil underlain by nonliquefiable stratum, is considered. The input seismic motions, having varying range of ground motion parameters, considered here include 1989 Loma Gilroy, 1995 Kobe, 2001 Bhuj, and 2011 Sikkim motions. It is calculated that maximum bending moment occurred at the interface of liquefiable and nonliquefiable soil layers and when thickness of liquefiable soil layer is around 60% of total pile length. Maximum bending moment of 1210 kNm and pile head deflection of 110 cm is observed because of 1995 Kobe motion, while 2001 Bhuj and 2011 Sikkim motions amplify the pile head deflection by 14.2 and 14.4 times and bending moment approximately by 4 times, when compared to nonliquefiable soil. Further, the presence of inertial load at the pile head increases bending moment and deflection by approximately 52% when subjected to 1995 Kobe motion. Thus, it is necessary to have a proper assessment of both kinematic and inertial interactions due to free field seismic motions and vertical loads for evaluating pile response in liquefiable soil.     

Effect of Slope on <Emphasis Type="Italic">p</Emphasis>-<Emphasis Type="Italic">y</Emphasis> Curves for Laterally Loaded Piles in Soft Clay

Pile foundations are often subject to lateral loading due to various forces on a variety of structures like high rise buildings, transmission towers, power stations, offshore structures and highway and railway structures. The present investigation is to study the effect of slopes on p-y curves (where p is the static soil reaction and y is the pile deflection) due to static lateral loading in soft clay (Consistency index I_c = 0.42). A series of laboratory model tests were carried out on the instrumented model pile on sloping ground (slopes of 1V:1H, 1V:1.5H, 1V:2H, 1V:3H and 1V:5H) and with varying embedment length to diameter ratio (L/D) of 20, 25 and 30. From the experimental results, the bending moment curves along the pile shaft are double differentiated to obtain the soil resistance (p) and double integrated to obtain the deflection (y) using curve fitting method. New p-y curves for piles located on crest of soft clay with different sloping ground surface under static lateral loading are developed. Moreover, the effect of sloping angles on proposed p-y curves was studied.     

Response of 1 × 2 pile group under eccentric lateral loading

A large scale model test of a 1 × 2 pile group was conducted in silts to investigate its behavior under eccentric lateral loading. The model pile group consisted of two well instrumented steel piles and was installed in a large soil tank with a close spacing of three-pile diameters on centers. The test results revealed that the eccentricity of lateral loads had limited effect on the overall performances of the 1 × 2 pile group, but significantly contributed to the unevenness of internal forces of the individual piles. The coupling effect between the lateral deflection and torque gave rise to the substantial increase in the torsional resistance of individual piles within the group, comparing to that of a torsionally loaded single pile. The contribution provided by the torsional resistances of individual piles in resisting the external torque continually decreased when the applied lateral load increased. In addition, a three-dimensional finite-element analysis for the pile group was performed and the simulated response was found to be in good agreement with the measured test results. Based on the same model, more cases with different loading conditions were further analyzed. It could be concluded from the analyses that the layout of individual piles within the group obviously affected the behavior of the 1 × 2 pile group under eccentric lateral loads.     

Analysis of creep settlement of pile groups in linear viscoelastic soil

This paper presents the analysis of creep settlement of pile groups for line pile groups, square pile groups, and rectangular pile groups undergoing creep settlements over a period of time. The soil is treated as a viscoelastic material and is modeled using a three-parameter viscoelastic model. The damping component (dashpot) takes care of the permanent time-dependent deformations in three-parameter viscoelastic model. An approach suggested by Mindlin has been employed to calculate the stress distribution along the pile length in a group. The viscoelastic problem is converted into an elastic problem by the application of Laplace transform. Results in the form of variation of interaction factors for parameters such as pile length to diameter ratio, pile spacing, Poisson's ratio, and modulus ratio have been presented. Comparison has been made between interaction factors for piles groups undergoing immediate settlements and creep settlements. Finally, a typical predictive example has been presented for a 3 × 3 pile group showing creep settlement. The load rearrangement due to creep settlements causes about 5% to 35% increase in base resistance over time. Interaction factors for pile groups (2 × 1, 3 × 1, 2 × 2, and 3 × 2) undergoing creep settlement is about 15% to 55% higher than the interaction factors considering only the immediate settlements for pile group spacing less than or equal to 5d.     

Experimental investigation of the behavior of pile groups in sand under different loading rates

The behavior of pile groups in sand under different loading rates is investigated. A total of 60 tests were conducted in the laboratory using model steel piles embedded in a medium dense sand. The model piles have an outside diameter of 25 mm and embedment length of 500 mm. Five different configurations of pile groups (2 × 1, 3 × 1, 2 × 2, 2 × 3, 3 × 3) with center to center spacing between the piles of 3d, 6d and 9d (d is the pile diameter) were tested. The piles were subjected to axial compressive loads under four different loading rates: 1.0, 0.5, 0.1 and 0.05 mm/min. Test results indicated that the axial compressive capacity of pile group increases with the loading rate such that the pile capacity versus logarithm of loading rate data plot approximately along a straight line. The slope of this line increases as the number of piles in a group increases and it decreases by increasing the spacing between piles in a group.     

Excess heat capacity and entropy of mixing along the chlorapatite–fluorapatite binary join

The heat capacity at constant pressure, C _p, of chlorapatite [Ca₅(PO₄)₃Cl – ClAp], and fluorapatite [Ca₅(PO₄)₃F – FAp], as well as of 12 compositions along the chlorapatite–fluorapatite join have been measured using relaxation calorimetry [heat capacity option of the physical properties measurement system (PPMS)] and differential scanning calorimetry (DSC) in the temperature range 5–764 K. The chlor-fluorapatites were synthesized at 1,375–1,220°C from Ca₃(PO₄)₂ using the CaF₂–CaCl₂ flux method. Most of the chlor-fluorapatite compositions could be measured directly as single crystals using the PPMS such that they were attached to the sample platform of the calorimeter by a crystal face. However, the crystals were too small for the crystal face to be polished. In such cases, where the sample coupling was not optimal, an empirical procedure was developed to smoothly connect the PPMS to the DSC heat capacities around ambient T. The heat capacity of the end-members above 298 K can be represented by the polynomials: C _p^ClAp = 613.21 − 2,313.90T ^−0.5 − 1.87964 × 10⁷ T ⁻² + 2.79925 × 10⁹ T ⁻³ and C _p^FAp = 681.24 − 4,621.73 × T ^−0.5 − 6.38134 × 10⁶ T ⁻² + 7.38088 × 10⁸ T ⁻³ (units, J mol⁻¹ K⁻¹). Their standard third-law entropy, derived from the low-temperature heat capacity measurements, is S° = 400.6 ± 1.6 J mol⁻¹ K⁻¹ for chlorapatite and S° = 383.2 ± 1.5 J mol⁻¹ K⁻¹ for fluorapatite. Positive excess heat capacities of mixing, ΔC _p^ex, occur in the chlorapatite–fluorapatite solid solution around 80 K (and to a lesser degree at 200 K) and are asymmetrically distributed over the join reaching a maximum of 1.3 ± 0.3 J mol⁻¹ K⁻¹ for F-rich compositions. They are significant at these conditions exceeding the 2σ-uncertainty of the data. The excess entropy of mixing, ΔS ^ex, at 298 K reaches positive values of 3–4 J mol⁻¹ K⁻¹ in the F-rich portion of the binary, is, however, not significantly different from zero across the join within its 2σ-uncertainty.     

斜坡桩水平循环特性模型试验及有限杆单元解

为了揭示斜坡效应和循环弱化效应共同影响下的斜坡桩水平循环特性,进行了不同循环次数、荷载幅值及坡度下的单向水平循环加载试验,并将水平静载试验作为对照,揭示了桩顶位移、桩身弯矩及地基反力等变化规律。综合考虑二阶效应及桩-土相互作用的影响,对单元刚度矩阵进行了改进,提出了有限杆单元解。将理论预测曲线等与实测曲线及幂级数法计算结果进行了对比,验证了有限杆单元解的合理性。结果表明：桩身弯矩及位移均随循环次数非线性增加,最大弯矩位置逐渐从无量纲深度z_α=1.25下移到z_α=1.75;桩顶无量纲位移y0,α与循环次数n之间的关系符合幂函数y0,α=An0.11;当荷载幅值由20 N增加到40 N时,最大无量纲弯矩由0.010增加到0.029,位置均保持在z_α=1.7附近;当坡度由30°增加到60°时,最大无量纲弯矩由0.011(z_α=1)增加到0.025(z_α=2.5)。     

A modulus‐multiplier approach for non‐linear analysis of laterally loaded pile groups

A modulus‐multiplier approach, which applies a reduction factor to the modulus of single pile p–y curves to account for the group effect, is presented for analysing the response of each individual pile in a laterally loaded pile group with any geometric arrangement based on non‐linear pile–soil–pile interaction. The pile–soil–pile interaction is conducted using a 3D non‐linear finite element approach. The interaction effect between piles under various loading directions is investigated in this paper. Group effects can be neglected at a pile spacing of 9 times the pile diameter for piles along the direction of the lateral load and at a pile spacing of 6 times the pile diameter for piles normal to the direction of loading. The modulus multipliers for a pair of piles are developed as a function of pile spacing for departure angle of 0, 90, and 180sup>/sup> with respect to the loading direction. The procedure proposed for computing the response of any individual pile within a pile group is verified using two well‐documented full‐scale pile load tests. Copyright © 2006 John Wiley & Sons, Ltd.     

High-pressure X-ray diffraction study of ε-FeOOH

An in situ synchrotron X-ray diffraction study was carried out on ε-FeOOH at room temperature up to a pressure of 8.6 GPa using the energy-dispersive method. The linear compressibility was determined to be β _a  = 1.69(3) × 10⁻³ GPa⁻¹, β _b  = 2.86(6) × 10⁻³ GPa⁻¹, and β _c  = 1.73(5) × 10⁻³ GPa⁻¹. The b-axis of the unit cell is more compressible than the a and c axes. The pressure–volume data were fitted to a third-order Birch–Murnaghan equation of state. The best fit was found using a room temperature isothermal bulk modulus of K ₀ = 126(3) GPa and its pressure derivative K′ = 10(1).     

Evaluation of Curve Fitting Techniques in Deriving p–y Curves for Laterally Loaded Piles

The p–y method is one of the most popular methods for the analysis and design of laterally loaded piles. The mathematical relationship it provides between the bending moment, which can be easily measured at strain gauges along the pile, and the soil resistance and lateral pile displacement, facilitates the construction of p–y curves. Numerical techniques are required to fit smooth continuous curves to the discrete bending moment data in order to improve the accuracy of subsequent differentiation and integration operations. Due to the lack of guidance on the optimum positioning of strain gauges and the reliability and accuracy of curve fitting methods, a unifying study, inclusive of small (0.61 m) and large (3.8 and 7.5 m) diameter piles in clay, was carried out using 18 strain gauge layouts and cubic spline, cubic to quintic B-spline and 3rd to 10th degree global polynomial techniques. Bending moment data was obtained using 3D finite element analysis. Through a comprehensive evaluation, the cubic and cubic B-spline methods were found to be consistently accurate in deriving p–y curves for both the small and large diameter piles.     

Load–Deflection response of transversely isotropic piles under lateral loads

In general, pile materials are assumed to be isotropic during the analysis of the load–deflection response of piles under lateral loads. However, commonly used materials such as reinforced concrete and timber as well as potentially promising new pile materials such as fiber reinforced polymers are typically transversely isotropic materials. Experimental studies have shown that transversely isotropic materials have a high ratio of section longitudinal modulus to the section in‐plane shear modulus (E_zz/G_xz) compared to the value for isotropic materials. The high modulus ratio leads to a more significant shear deformation effect in beam bending. To account for the shear deformation effect, the Timoshenko Beam Theory has been adopted in deriving the solutions for the load–deflection response of transversely isotropic piles under lateral loads instead of the Classical (Euler–Bernoulli) Beam Theory. The load–deflection responses depend on the shear effect coefficient, the lateral soil resistance, the embedment ratio, and the boundary conditions. The deflection of the pile, if the shear deformation effect is considered, is always larger than if it is neglected. Copyright © 2000 John Wiley & Sons, Ltd.     

Behavior of epidote at high pressure and high temperature: a powder diffraction study up to 10 GPa and 1,200 K

The thermo-elastic behavior of a natural epidote [Ca_1.925 Fe_0.745Al_2.265Ti_0.004Si_3.037O₁₂(OH)] has been investigated up to 1,200 K (at 0.0001 GPa) and 10 GPa (at 298 K) by means of in situ synchrotron powder diffraction. No phase transition has been observed within the temperature and pressure range investigated. P–V data fitted with a third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 458.8(1)ų, K _T0 = 111(3) GPa, and K′ = 7.6(7). The confidence ellipse from the variance–covariance matrix of K _T0 and K′ from the least-square procedure is strongly elongated with negative slope. The evolution of the “Eulerian finite strain” vs “normalized stress” yields Fe(0) = 114(1) GPa as intercept values, and the slope of the regression line gives K′ = 7.0(4). The evolution of the lattice parameters with pressure is slightly anisotropic. The elastic parameters calculated with a linearized BM-EoS are: a ₀ = 8.8877(7) Å, K _T0(a) = 117(2) GPa, and K′(a) = 3.7(4) for the a-axis; b ₀ = 5.6271(7) Å, K _T0(b) = 126(3) GPa, and K′(b) = 12(1) for the b-axis; and c ₀ = 10.1527(7) Å, K _T0(c) = 90(1) GPa, and K’(c) = 8.1(4) for the c-axis [K _T0(a):K _T0(b):K _T0(c) = 1.30:1.40:1]. The β angle decreases with pressure, β_P(°) = β_P0 −0.0286(9)P +0.00134(9)P ² (P in GPa). The evolution of axial and volume thermal expansion coefficient, α, with T was described by the polynomial function: α(T) = α₀ + α₁ T ^−1/2. The refined parameters for epidote are: α₀ = 5.1(2) × 10⁻⁵ K⁻¹ and α₁ = −5.1(6) × 10⁻⁴ K^1/2 for the unit-cell volume, α₀(a) = 1.21(7) × 10⁻⁵ K⁻¹ and α₁(a) = −1.2(2) × 10⁻⁴ K^1/2 for the a-axis, α₀(b) = 1.88(7) × 10⁻⁵ K⁻¹ and α₁(b) = −1.7(2) × 10⁻⁴ K^1/2 for the b-axis, and α₀(c) = 2.14(9) × 10⁻⁵ K⁻¹ and α₁(c) = −2.0(2) × 10⁻⁴ K^1/2 for the c-axis. The thermo-elastic anisotropy can be described, at a first approximation, by α₀(a): α₀(b): α₀(c) = 1 : 1.55 : 1.77. The β angle increases continuously with T, with β_T(°) = β_T0 + 2.5(1) × 10⁻⁴ T + 1.3(7) × 10⁻⁸ T ². A comparison between the thermo-elastic parameters of epidote and clinozoisite is carried out.