Uncertainty in differential settlements of bridge foundations and retaining walls

ABSTRACT

In the bridge design specifications of the American Association of State Highway and Transportation Officials (AASHTO) using the Load and Resistance Factor Design (LRFD) method, the loads and resulting force effects are given two-letter designations, e.g. “SE” for “force effects due to settlement”. The SE load factor is used to develop factored values of the induced force effects such as moments and shears in a bridge structure due to foundation movements. In 2018 AASHTO committees voted to adopt calibrated values of the SE load factors that account for the uncertainty in predicted foundation movements from different analytical methods. However, additional uncertainty can occur in the differential settlements. This paper explores the additional uncertainty in differential settlements of bridge foundations and retaining walls using the datasets for two analytical methods that were used by AASHTO to develop the SE load factors for foundation settlement. Normalised probability exceedance charts (NPECs), that integrate the concept of reliability index and data correlation, have been developed and their application in bridge and wall design process is discussed for a variety of scenarios. Guidance is provided for the practical implementation of differential settlement in bridge analysis through an example problem.     

Development of analytical models to estimate the increase in pile capacity with time (pile setup) from soil properties

This paper presents the analyses of twelve prestressed concrete (PSC) instrumented test piles that were driven in different bridge construction projects of Louisiana in order to develop analytical models to estimate the increase in pile capacity with time or pile setup. The twelve test piles were driven mainly in cohesive soils. Detailed soil characterizations including laboratory and in situ tests were conducted to determine the different soil properties. The test piles were instrumented with vibrating wire strain gauges, piezometers, pressure cells that were monitored during the whole testing period. Several static load tests (SLTs) and dynamic load tests were conducted on each test pile at different times after end of driving (EOD) to quantify the magnitude and rate of setup. Measurements of load tests confirmed that pile capacity increases almost linearly with the logarithm of time elapsed after EOD. Case pile wave analysis program was performed on the restrikes data and was used along with the load distribution plots from the SLTs to evaluate the increase in skin friction capacity of individual soil layers along the length of the piles. The logarithmic linear setup parameter “A” for unit skin friction was calculated of the 70 individual clayey soil layers and was correlated with different soil properties such as undrained shear strength (S_u), plasticity index, vertical coefficient of consolidation (c_v), over consolidation ratio and sensitivity (S_t). Nonlinear multivariable regression analyses were performed, and three different empirical models are proposed to predict the pile setup parameter “A” as a function of soil properties. For verification, the subsurface soil conditions and setup information for additional 18 PSC piles collected from local database were used to compare the measured versus predicted “A” parameters from the proposed models, which showed good agreement.

     

Load–settlement behavior of rock-socketed drilled shafts using Osterberg-Cell tests

Osterberg-Cell (O-Cell) tests are widely used to predict the load–settlement behavior of large-diameter drilled shafts socketed in rock. The loading direction of O-Cell tests for shaft resistance is opposite to that of conventional downward load tests, meaning that the equivalent top load–settlement curve determined by the summation of the mobilized shaft resistance and end bearing at the same deflection neglects the pile-toe settlement caused by the load transmitted along the pile shaft. The emphasis is on quantifying the effect of coupled shaft resistance, which is closely related to the ratios of pile diameter to soil modulus (D/E_s) and total shaft resistance to total applied load (R_s/Q) in rock-socketed drilled shafts, using the coupled load-transfer method. The proposed analytical method, which takes into account the effect of coupled shaft resistance, was developed using a modified Mindlin’s point load solution. Through comparisons with field case studies, it was found that the proposed method reasonably estimated the load-transfer behavior of piles and coupling effects due to the transfer of shaft shear loading. These results represent a significant improvement in the prediction of load–settlement behaviors of drilled shafts subjected to bi-directional loading from the O-Cell test.     

Proposed nonlinear 3-D analytical method for piled raft foundations

The load distribution and deformation of piled raft foundations subjected to axial and lateral loads were investigated by a numerical analysis and field case studies. Special attention is given to the improved analytical method (YSPR) proposed by considering raft flexibility and soil nonlinearity. A load transfer approach using p–y, t–z and q–z curves is used for the analysis of piles. An analytical method of the soil–structure interaction is developed by taking into account the soil spring coupling effects based on the Filonenko-Borodich model. The proposed method has been verified by comparing the results with other numerical methods and field case studies on piled raft. Through comparative studies, it is found that the proposed method in the present study is in good agreement with general trend observed by field measurements and, thus, represents a significant improvement in the prediction of piled raft load sharing and settlement behavior.     

桥梁桩基主动托换中顶升荷载的简化计算

以福州地铁1号线盾构隧道下穿洗马桥的桩基主动托换工程为依托,针对桥梁上部结构-桩身-土体三者共同组成的复杂超静定结构,运用数值模拟方法和现场实测数据,分析了在不同顶升荷载作用下复杂超静定结构的内力与位移响应,重点讨论了托换过程中上、下部结构的相对刚度及其对顶升荷载的影响;根据顶升荷载作用点以下桩身轴力接近0的条件,确定了桥墩盖梁与薄壁桥台梁两种典型工况下的桩基顶升荷载分别为1 800 kN和2 600 kN。现场监测结果表明,顶升过程中上部结构的位移值和桩身轴力变化值,均与计算结果吻合较好。在此基础上,提出基于上、下部结构刚度比的顶升荷载简化计算方法,研究结果可为类似复杂超静定结构的桩基主动托换工程提供参考和借鉴。     

Calibration of resistance factor for design of pile foundations considering feasibility robustness

The resistance factor for pile foundations in load and resistance factor design (LRFD) is traditionally calibrated considering target reliability index (β_T) and statistics of load and resistance bias factors. However, the resistance bias factor is hard to quantify statistically. Consequently, the design obtained using the calibrated resistance factor can still miss β_T if the variation in resistance bias factor has been underestimated. In this paper, we propose a new resistance factor calibration approach to address this dilemma by considering “feasibility robustness” of design in the calibration process. Herein, the feasibility robustness is defined as a probability that the β_T requirement can still be satisfied even in the presence of uncertainty or variation in the computed bearing capacity. For illustration, LRFD approach for pile foundations commonly used in Shanghai, China is examined. Emphasis is placed on re-calibration of resistance factors at various feasibility robustness levels, with due consideration of the variation in the resistance bias factor. A case study is presented to illustrate the use of the re-calibrated resistance factors. The results show that the feasibility robustness is gained at the expense of cost efficiency; in other words, the two objectives are conflicting. To aid in the design decision-making, an optimal feasibility robustness level and corresponding resistance factors are suggested in the absence of a designer’s preference.     

Probabilistic analysis of load-settlement response from pile load tests

The evaluation of variability in ultimate pile capacity from the load-settlement data is useful in the context of code calibration and reliability based design in pile foundations. This paper examines the applicability of two non-linear analytical methods to calculate the load-settlement response of piles using actual test data in terms of percentage deviation from the measured capacity. The degree of agreement associated with each method with respect to field test data is quantified using two different failure criteria (FHWA and Eurocode) for determination of the ultimate load of pile. The analytical methods are used to quantify the variability associated with the soil-pile interface parameters and ultimate capacity using Monte Carlo simulations, which is useful in load-resistance factored/reliability design of pile foundations. Study reveals that variability depends on the method of analysis, percent deviation of prediction from measured values and failure criteria.     

Shear Load Transfer Characteristics of Drilled Shafts Socketed in Rocks

This paper presents a shear load transfer function and an analytical method for estimating the load transfer characteristics of rock-socketed drilled shafts subjected to axial loads. A shear load transfer (f–w) function of rock-socketed drilled shafts is proposed based on the constant normal stiffness (CNS) direct shear tests. It is presented in terms of the borehole roughness and the geological strength index (GSI) so that the structural discontinuities and the surface conditions of the rock mass can be considered. An analytical method that takes into account the coupled soil resistance effects is proposed using a modified Mindlin’s point load solution. Through comparisons with load test results, the proposed methodology is in good agreement with the general trend observed in in situ measurements and represents an improvement in the prediction of the shear behavior of rock-socketed drilled shafts.     

桩-网复合地基承载性状现场试验研究

桩-网复合地基是一种软弱地基处理方法,它能通过变形协调,充分发挥桩、网、土的各自作用,有效地控制工后沉降或差异沉降。为了解路堤荷载下桩-网复合地基工作机制,深入分析其沉降变形、荷载传递、桩土应力比和网的受力等性状,接桩体种类设计了两个试验区进行对比分析,研究成果表明,桩网复合地基可以有效减少沉降量;土工格栅的荷载传递能力强于土拱;土工格栅的最大应变出现在桩帽边缘,仅为1 %,最小应变则出现在桩间。试验结果为桩网复合地基理论研究和优化设计提供了依据。     

Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach

An analytical approach using a Winkler model is investigated to provide analytical solutions of settlement of a rectangular pile subjected to vertical loads in nonhomogeneous soils. For a vertically loaded pile with a rectangular cross section, the settlement influence factor of a normal pile in nonhomogeneous soils is derived from Mindlin's solution for elastic continuum analysis. For short piles with rectangular and circular cross sections, the modified forms of settlement influence factors of normal piles are produced taking into account the load transfer parameter proposed by Randolph for short circular piles. The modulus of subgrade reaction along a rectangular pile in nonhomogeneous soils is expressed by using the settlement influence factor related to Mindlin's solution to combine the elastic continuum approach with the subgrade‐reaction approach. The relationship between settlement and vertical load for a rectangular pile in nonhomogeneous soils is available in the form of the recurrence equation. The formulation of settlement of soils surrounding a rectangular pile subjected to vertical loads in nonhomogeneous soils is proposed by taking into account Mindlin's solution and both the equivalent thickness and the equivalent elastic modulus for layers in the equivalent elastic method. The difference of settlement between square and circular piles is insignificant, and the settlement of a rectangular pile decreases as the aspect ratio of the rectangular pile cross section increases. The comparison of results calculated by the present method for a rectangular pile in nonhomogeneous soils has shown good agreement with those obtained from the analytical methods and the finite element method. Copyright © 2014 John Wiley & Sons, Ltd.     

秦巴山区软岩地基桥桩承载性状试验研究

为了研究软岩地基桥桩的荷载传递性状、破坏机理,并获取在该地质条件下更为可靠的桩基计算参数,对秦巴山区软岩地基3根钻孔灌注试桩进行竖向静载试验。结果表明：秦巴山区软岩地基桥桩试桩荷载沉降曲线呈陡降型,实测竖向极限承载力为20 500kN,桩的破坏方式为桩身材料强度破坏;淤泥质亚黏土地层中的碎石起到一定的骨架作用,增强了此地层桩极限侧阻力,发挥极限侧阻力所需的桩土（岩）相对位移为4～8mm;强风化砾岩表现为加工软化型,发挥极限侧阻力所需的桩土（岩）相对位移为3～8mm;中风化砂砾岩表现为明显的加工硬化型,所需的桩岩相对位移大,且桩极限侧阻力的特征点不明显;淤泥质亚黏土地层桩侧阻力占总荷载的60%～70%,随着桩顶荷载的逐步加大,该地层桩侧阻力所占比例不断下降,而嵌岩段桩侧阻力所占比例逐渐上升,达到55%～65%,嵌岩段桩侧阻力沿桩深的分布曲线表现出非线性的特征;试桩为端承摩擦桩,桩端阻力约占桩顶荷载的20%左右,且未充分发挥,在上部结构允许的沉降范围内,适当增加桩端的沉降有利于端阻力的发挥;桩侧阻力先于端阻力发挥,建议单桩承载力设计时分别采用不同的端阻力和侧阻力安全系数。     

Lateral force and centroid location caused by horizontal and vertical surcharge strip loads on a cross‐anisotropic backfill

This work presents analytical solutions for determining lateral force (force per unit length) and centroid location caused by horizontal and vertical surcharge surface loads acting on a cross‐anisotropic backfill. The surcharge loading types are point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load, and downward nonlinear‐varying strip load. The planes of cross‐anisotropy are assumed parallel to the backfill ground surface. The proposed solutions, derived by integrating the lateral stress solutions (Int. J. Numer. Anal. Meth. Geomech. 2005; 29 :1341–1361), do not exist in literature. Clearly, the type and degree of material anisotropy, loading distance from the retaining wall, and loading types markedly impact the proposed solutions. Two examples are utilized to illustrate the type and degree of soil anisotropy, and the loading types on the lateral force and centroid location in the isotropic/cross‐anisotropic backfills generated by the horizontal and vertical uniform, upward linear‐varying and upward nonlinear‐varying strip loads. The parametric study results demonstrate that the lateral force and centroid location accounting for soil anisotropy, loading distance from the retaining wall, dimension of the loading strip, and loading directions and types differ significantly from those estimated using existing isotropic solutions. The derived solutions can be added to other lateral pressures, such as earth pressure or water pressure, required for stability and structural analysis of a retaining wall. Additionally, they can simulate realistically actual surcharge loading problems in geotechnical engineering when backfill materials are cross‐anisotropic. Copyright © 2007 John Wiley & Sons, Ltd.     

Response of Pile Groups Driven in Sand Subjected to Combined Loads

Although the loads applied on piles are usually a combination of both vertical and lateral loads, very limited experimental research has been done on the response of pile groups subjected to combined loads. Due to pile–soil–pile interaction in pile groups, the response of a pile group may differ substantially from that of a single pile. This difference depends on soil state and pile spacing. This paper presents results of experiments designed to investigate pile interaction effects on the response of pile groups subjected to both axial and lateral loads. The experiments were load tests performed on model pile groups (2 × 2 pile groups) in calibration chamber sand samples. The model piles were driven into the sand samples prepared with different relative densities using a sand pluviator. The combined load tests were performed on the model pile groups subjected to different axial load levels, i.e., 0 (pure lateral loading), 25, 50, and 75% of the ultimate axial load capacity of the pile groups, defined as the load corresponding to a settlement of 10% of the model pile diameter. The combined load test results showed that the bending moment and lateral deflection at the head of the piles increased substantially for tests performed in the presence of axial loads, suggesting that the presence of axial loads on groups of piles driven in sand is detrimental to their lateral capacity.     

U.S.G.5. II Revisited*

Based on the most recent compilation of analytical data, a new set of “usable values” is calculated for six of the best known silicate rock reference samples produced by the U.S. Geological Survey. The latest version of the “best laboratories” method is described and results are compared with other recently published values.     

Accuracy of Laser Ablation U-Pb Zircon Dating: Results from a Test Using Five Different Reference Zircons

Using a state‐of‐the‐art 193 nm‐LA‐MC‐ICP‐MS system and with careful control of analytical procedures, the long term external reproducibility and accuracy of the ages Phanerozoic zircons measured over a period of months using calibrator bracketing for the ²⁰⁶Pb/²³⁸U and ²⁰⁷Pb/²⁰⁶Pb ages were ca. 1% (2 RSD) if a single reference zircon was used for the matrix‐matched calibration. When different reference zircons were used for the calibration, suspicious systematic shifts in the obtained ages were observed and thus a reduction in the overall accuracy of the dating method became obvious. Such shifts were within a few percent range of the U‐Pb and Pb/Pb ages and seemed to vary independently of zircon age and composition. A “test of accuracy” experiment was conducted reducing instrumental effects as far as possible by analysing five different reference zircons mounted on a single mount eight times during the same session. An identical protocol was used for all analyses, with unchanged instrument parameters and with ion beam intensities kept as identical as possible. For data reduction, every zircon served consecutively as the reference zircon for calibration, with the others in the batch treated as unknowns. The known reference age and the four calculated ages obtained using the four other RMs for calibration were then compared. Even using such a strict analytical protocol, shifts in ²⁰⁶Pb/²³⁸U, ²⁰⁷Pb/²³⁵U and ²⁰⁷Pb/²⁰⁶Pb ratios were still present. They varied non‐systematically and ranged from ?4.35% to 3.08% for the investigated age range (1065 Ma to 226 Ma). Assuming the absence of instrumental effects (i.e., memory, dead‐time correction, non‐linearity of ion counters and interdetector calibration, crystallographic orientation, ablation cell geometry and setup, gas flows), the observed shifts were attributed to matrix and/or ablation related effects. It is proposed that non‐spectral matrix effects in the Ar plasma torch resulted in non‐uniform signal enhancement (or depression?) leading to shifts both in elemental and Pb isotopic ratios. Additionally, the ablated particle size distribution could be an important factor controlling plasma conditions and thus mass bias and fractionation. Until such effects are well understood and controlled, it would seem that any LA‐ICP‐MS zircon U‐Pb and ²⁰⁷Pb/²⁰⁶Pb age determination cannot be meaningfully interpreted at below a ca. 3% to 4% (2 RSD) confidence level.     

Gravity-induced stresses near axisymmetric topography of small slope

An approximate, analytical solution is found for the gravity-induced stresses in the neighbourhood of an axisymmetric topographic feature on an elastic half-space. The solution is in the form of a perturbation expansion in powers of the characteristic slope, ?. The leading order problem, at O(1), is for a distributed normal load on a plane half-space. The O(?) correction is due to a distributed shear traction. The vertical variation of the near-surface stress perturbation and the rotation of the principal stress directions are O(?) effects, and thus include contribution s of like order from both the normal and shear loads. The method requires general solutions for axisymmetric, normal and shear tractions of arbitrary radial distribution, and these are found in terms of Hankel transforms.     

Active and passive arching stresses in c′-ϕ′ soils: A sensitivity study using computational limit analysis

Vertical soil arching, commonly known as the “trapdoor mechanism,” is a pervasive phenomenon in various geotechnical applications that can be evaluated through a variety of analytical and numerical approaches, most of which exist due to a variety of proposed arching mechanisms, many of which are focused on either purely frictional or cohesive soils. This study investigates the realized arching mechanisms and associated loads for trapdoors under both active and passive arching conditions in c′-ϕ′ soils through a series of dimensionless charts using both upper and lower bound limit analyses. An associated sensitivity analysis demonstrates that arching loads are highly dependent on collapse mechanism, a function of not only geometry, but soil shear strength, with cohesion affecting the realized mechanism and arching loads.     

层状地基群桩沉降计算的剪切位移解析算法

考虑群桩的“束缚作用”,基于剪切位移法的理论,提出了竖向荷载作用下用于层状地基大规模群桩沉降分析的简捷实用的解析算法。以单桩位移积分方程为基础,导出了桩顶位移与轴力和桩底位移与轴力之间的关系,考虑桩-桩相互作用,得出了计算群桩沉降的柔度矩阵方程。推导过程中,桩被分成任意n段,因此该方法可以用于地基土任意分层的群桩沉降计算。算例分析表明,该方法与边混合法和界元法有较好的一致性。     

桩-土-承台结构在波浪力作用下的力学效应分析

在港口桥梁工程和海洋工程中,一般将桩从桩-土-承台结构中分离出来,单独计算波浪力对桩的作用。在提出波浪力作用下桩-土-承台结构相互作用模型的基础上,结合工程算例,进行了桩-土-承台结构在波浪力作用下桩的荷载和弯矩计算分析,结果表明：在不考虑波浪力的情况下,计算结果跟规范方法较为接近,验证了桩-土相互作用模型的适用性。在此基础上迭加波浪力,将波浪力和桩-土-承台作为一个完整的系统研究,随着承台所受外力、波浪力、桩侧地基土的变化,分析了桩-土-承台结构在波浪力作用下的受力效应。     

竖向力与水平向力同时作用下管桩的性状研究

用解析方法研究了管桩在轴向力和水平向力（倾斜力）联合作用下的受力及变形性状。在高层建筑、桥梁工程、海洋工程、新型海堤护岸等工程中桩基自由长度上作用土压力、风荷载、波浪荷载等荷载型式,基桩经常在竖向、水平向荷载同时作用下工作。国内外学者通过大量试验和理论研究得出了计算竖向、水平向荷载下基桩内力和挠度的半经验公式以及张氏法公式。为了分析竖向、水平向荷载同时作用下自由荷载的作用,在现行m法假设的基础上,从弹性桩的挠曲微分方程出发,导出了任意自由荷载作用下桩任意截面的水平变位、倾角、弯矩、剪力和地基反力计算表达式。桩的挠曲微分方程是分段函数,包括地上部分和地下部分桩,相应的内力和变位求解也分为两段。最后通过一个算例分析了桩顶竖向荷载、桩顶水平力和自由荷载对桩身的受力性状各参数的影响。计算结果表明, 桩顶水平力对桩身最大弯矩和桩顶水平变位的影响最大,而桩周内外摩阻力及桩身自重对桩身受力性状影响较小。