非共面复合加载条件下桶形基础稳定性研究

采用荷载-位移联合搜索方法,对于饱和软黏土地基上裙板式桶形基础在水平荷载H、力矩M与扭矩T的非共面复合加载条件下的稳定性进行了比较系统的三维有限元分析,主要探讨了在不同荷载空间内桶形基础的破坏包络轨迹。在分析中,地基土服从基于Tresca屈服准则的理想弹塑性本构关系。计算结果表明,与传统共面复合加载情况相比,非共面复合加载条件下桶形基础的破坏包络面形状有较大差异。非共面复合加载情况下,包络面形状不依赖于基础埋深比,可用简单的圆或椭圆方程进行描述。根据有限元计算结果,将已有的三自由度破坏包络面方程扩展到六自由度复合加载空间内,进而初步建议了一个六自由度破坏包络面方程,并对于实际工程中常用的桶形基础埋深比,给出了方程中偏心度参数取值的确定方法。该方程可用来合理评价复杂荷载条件下软黏土地基上桶形基础承载力。     

Combined loading of caisson foundations in cohesive soil: Finite element versus Winkler modeling

The undrained response of massive caisson foundations to combined horizontal, vertical and moment loading is parametrically investigated through a series of 3D finite element analyses. The parameters are: (a) the embedment ratio (D/B), (b) the factor of safety against initial vertical loading (FS_V) and (c) the ratio of the overturning moment to the horizontal force applied at the top of the caisson (M/Q). Emphasis is given on: (i) the identification of all possible failure mechanisms in M–Q–N space, (ii) the developed stress distributions along the caisson walls for various load levels up to complete failure conditions. The results are then used as a feedback for calibrating the parameters of a generalized four-type spring model, originally proposed by Gerolymos and Gazetas (2006), through a genetic algorithm-based optimization procedure. The predictions of the Winkler model compare very well with the FE results, not only at the local response level (in terms of stress distributions along the caisson shafts), but at a global response level (in terms of force–displacement curves and M–Q–N failure envelopes at the top of the caisson) as well. Contrary to established lateral soil resistance theories, it is shown that both the ultimate horizontal soil reaction and resisting moment per unit depth do not solely depend on the strength properties of soil and geometry of the caisson but are also functions of the applied load ratio M/Q and initial soil yielding due to vertical loading. Interesting conclusions are also drawn regarding the transition from the elastic to the ultimate limit state (hardening). Quantifying through analytical expressions the contribution of each of the two basic lateral resisting mechanisms to the response of the caisson, a classification method for embedded foundations is then proposed. The capabilities of the Winkler model are further demonstrated through comparison with FE analysis of the caisson cyclic lateral response.     

复合加载条件下沉箱基础稳定性的三维效应

联合采用swipe加载模式与固定位移比加载模式,对于吸力式沉箱基础在水平荷载H与力矩M的复合加载条件下的稳定性进行比较系统的三维有限元分析,主要探讨了基础埋深与直径之比、地基土不排水强度的非均质性对于基础在H-M荷载空间内的破坏包络轨迹的影响,揭示了地基在不同荷载分量组合条件下的失稳破坏机制,并与平面应变假定下得到的结果进行了比较。计算结果表明：平面应变与三维情况下基础的破坏包络面形状有较大差异,分析基础稳定性时,必须考虑其三维效应。在三维情况下,非均质土中埋深与直径之比较小的基础的破坏包络面仍然会向负方向倾斜,已有的包络面方程明显高估这种情况下沉箱基础在正向水平荷载与力矩联合作用下的承载力,从而导致基础设计偏于不安全。     

Undrained capacity of a surface circular foundation under fully three-dimensional loading

Circular foundations are widely employed in offshore engineering to support facilities and are generally subjected to fully three-dimensional loading due to the harsh offshore environmental load and complex operational loads. The undrained capacity of surface circular foundations on soil with varying strength profiles and under fully three-dimensional loading is investigated and presented in the form of failure envelopes that obtained from finite element analyses. The combined ultimate limit state of circular foundations is defined as the two-dimensional failure envelopes in resultant H-M loading space accounting for the vertical load and torsion mobilisation. The effects of vertical load and torsion mobilisation, soil shear strength heterogeneity and loading angle from moment to horizontal load on the shape of normalised H-M failure envelopes are explored. A series of expressions are proposed to describe the shape of failure envelopes obtained numerically, enabling essentially instantaneous generation of failure envelopes and optimisation of a circular foundation design based on constraint of any input variable through implementation in an automated calculation tool. An example application is ultimately provided to illustrate how the proposed expressions may be used in practice.     

复合加载模式下单桩复合筒型基础地基承载力包络线研究

海上风力发电机属于高耸结构物,其地基基础不仅要承受上部结构传递的竖向荷载V、水平荷载H,更要抵抗巨大的弯矩荷载M。单桩复合筒型基础是新型的海上风力发电机基础型式,建立复合加载模式下单桩复合筒型基础地基的破坏包络线,并据此评价其稳定性是地基基础设计的重要手段。在Swipe加载方法和固定位移比加载方法的基础上,通过数值分析研究了不排水饱和软黏土中单桩复合筒型基础在V-H、V-M、H-M和V-H-M加载模式下的地基承载力包络线,开展了室内模型试验,验证了数值分析结果的可靠性。研究表明,V-H和V-M加载模式下地基承载力包络线具有对称性,而H-M加载模式下呈非对称性;V-H-M加载模式下地基承载力包络线的形状受弯矩荷载M的影响显著,表现为随着弯矩荷载的增加,V-H平面内的破坏包络线逐渐缩小。实际工程中,可根据受力状态与破坏包络面的相对关系,评价单桩复合筒型基础的稳定性。     

Undrained capacity of surface foundations with zero-tension interface under planar V-H-M loading

Undrained capacity of strip and circular surface foundations with a zero-tension interface on a deposit with varying degrees of strength heterogeneity is investigated by finite element analyses. The method for simulating the zero-tension interface numerically is validated. Failure envelopes for strip and circular surface foundations under undrained planar V-H-M loading are presented and compared with predictions from traditional bearing capacity theory. Similar capacity is predicted with both methods in V-H and V-M loading space while the traditional bearing capacity approach under-estimates the V-H-M capacity derived from the numerical analyses due to superposition of solutions for load inclination and eccentricity not adequately capturing the true soil response. An approximating expression is proposed to describe the shape of normalised V-H-M failure envelopes for strip and circular foundations with a zero-tension interface. The unifying expression enables implementation in an automated calculation tool resulting in essentially instantaneous generation of combined loading failure envelopes and optimisation of a foundation design as a function of foundation size or material factor. In contrast, the traditional bearing capacity theory approach or direct numerical analyses for a given scenario requires ad-hoc analyses covering a range of input variables in order to obtain the ‘best’ design.     

The influence of load inclination on the undrained bearing capacity of strip footings on slopes

The effect of inclined loading on the bearing capacity of foundations on horizontal ground surface is well established and both the exact solution and simpler empirical equations are available for the calculation of the failure loads. However, for footings on or near slopes complete solutions are available only for vertical loading. This paper investigates the influence of inclined loading on the horizontal and vertical failure loads. The finite element, upper bound plasticity and stress field methods are used to examine a wide range of geometries and soil properties. The methods are first validated against known solutions for two special cases and are subsequently employed to investigate the effect of the geometrical and material properties on the failure loads and the bearing capacity load interaction diagram. Based on this investigation an empirical equation is proposed for the load interaction diagram for undrained inclined loading of footings on or near slopes.     

Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic medium

In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd.     

复合加载情况下双层地基极限承载力研究

在复合加载情况下精确求解层状非均质地基的极限承载力,具有很强的工程实用与理论参考价值。基于土体极限平衡理论与通用有限元软件ABAQUS,针对复合加载情况下上硬下软的双层不排水饱和软黏土地基的极限承载力,进行了大量的数值计算,得出了上层土临界深度Hcr的计算公式、竖向极限承载力Pv的计算公式以及复合加载情况下地基破坏时的破坏包络面方程。研究结果表明：上层土临界深度Hcr取决于土层间强度比Su1/Su2;竖向极限承载力Pv与破坏包络面取决于土层间强度比Su1/Su2、上层土深度H1与基础型式。     

复合加载情况下非均质地基上条形基础的极限承载力研究

复合加载情况下精确求解非均质地基上条形基础的极限承载力以及评价影响极限承载力的相关因素,具有很强的工程实用与理论参考价值。基于极限平衡原理,在Mohr-Coulomb破坏准则的基础上,将非均质地基上条形基础极限承载力问题等价为一个边界待定的泛函极值问题。利用变分原理得到与平衡方程相等价的积分约束条件以及相应的欧拉方程与横截条件。引入问题边界条件,利用VC++6.0编制了数值计算程序,求得了复合加载情况下非均质地基破坏时的滑裂面函数与破坏包络曲线。从理论上研究了土体内摩擦角、土体黏聚力、土层强度比与地下水位变化等因素对地基破坏包络曲线的影响。研究结果表明,其解答是地基极限承载力真实解的某一最小上限。     

Effects of boundary conditions and partial drainage on cyclic simple shear test results—a numerical study

Owing to imperfect boundary conditions in laboratory soil tests and the possibility of water diffusion inside the soil specimen in undrained tests, the assumption of uniform stress/strain over the sample is not valid. This study presents a qualitative assessment of the effects of non‐uniformities in stresses and strains, as well as effects of water diffusion within the soil sample on the global results of undrained cyclic simple shear tests. The possible implications of those phenomena on the results of liquefaction strength assessment are also discussed. A state‐of‐the‐art finite element code for transient analysis of multi‐phase systems is used to compare results of the so‐called ‘element tests’ (numerical constitutive experiments assuming uniform stress/strain/pore pressure distribution throughout the sample) with results of actual simulations of undrained cyclic simple shear tests using a finite element mesh and realistic boundary conditions. The finite element simulations are performed under various conditions, covering the entire range of practical situations: (1) perfectly drained soil specimen with constant volume, (2) perfectly undrained specimen, and (3) undrained test with possibility of water diffusion within the sample. The results presented here are restricted to strain‐driven tests performed for a loose uniform fine sand with relative density D_r=40%. Effects of system compliance in undrained laboratory simple shear tests are not investigated here. Copyright © 2004 John Wiley & Sons, Ltd.     

Bearing capacity of strip footings on <Emphasis Type="Italic">c</Emphasis>–<Emphasis Type="Italic">φ</Emphasis> soils with square voids

The presence of underground voids has an adverse influence on the performance of shallow foundations. In this study, the bearing capacity and failure mechanism of footings placed on cohesive-frictional soils with voids are evaluated using discontinuity layout optimization. By introducing a reduction coefficient, a set of design charts that can be directly applied to the classical bearing capacity formulation is presented. The results indicate that the undrained bearing capacity with voids is sensitive to soil weight and cohesion, as both the bearing capacity and stability issues exist in the problem. The failure mechanism is directly related to a variety of soil properties, the locations of single voids, and the horizontal distance between two voids. The presence of voids has a more dominant effect on c–φ soils compared to that on undrained soil. An interpretation of the critical and adverse locations for single-void and dual-void cases with various soil strengths is presented.     

力矩与水平荷载联合作用下裙板式基础破坏包络面研究

联合采用swipe加载模式、固定位移比与固定荷载比加载模式,对于裙板式浅基础在水平荷载与力矩荷载的复合加载条件下的承载性能进行比较系统的平面应变有限元分析,主要探讨了裙板式基础埋深、地基土不排水强度的非均质性对于基础破坏包络面的影响,揭示了地基在水平和力矩荷载的不同组合条件下的失稳破坏机制。同时,对于两种swipe加载模式的有效性进行了比较。计算结果表明：对于非均质土,当裙板式基础埋深与宽度之比大于0.3时,破坏包络面产生正方向倾斜;当埋深与宽度之比小于0.3时,基础的破坏包络面出现负方向倾斜。而在均质土中,基础的破坏包络面没有出现负方向倾斜。     

破坏包络面理论在多基础系统中的应用研究

由多个分离基础组成的多基础系统是常用的海洋结构基础型式。基于破坏包络面理论,分析了砂土地基多基础系统的失效模式,建立了相应的承载力计算方法,并验证了计算方法的可行性。对比分析了单一基础和多基础系统不同荷载路径下的荷载安全系数,探讨了破坏包络面理论与分项系数法相结合的基础承载力计算方法。失效模式的分析表明,由于水平荷载的增大,四腿平台结构迎浪侧基础首先到达破坏包络线,其失效模式属于滑动失稳,但由于基础间的运动约束,其并不会出现真正的滑移破坏。随着水平荷载进一步地增大,迎浪侧基础承担的水平和竖向荷载不断减小,导致背浪侧基础受到不断增大的荷载。最终,背浪侧基础也到达破坏包络线,多基础系统失效。分析表明,荷载路径对基础的荷载安全系数有决定性的影响,计算基础的荷载安全系数需指明相应的荷载路径。鉴于破坏包络面的大小和形状取决于众多因素,基础设计时需采用特定工况下的破坏包络面进行承载力计算。     

Material stability analysis of rock joints

For prediction of rockfalls, the failure of rock joints is studied. Considering these failures as constitutive instabilities, a second‐order work criterion is used because it explains all divergence instabilities (flutter instabilities are excluded). The bifurcation domain and the loading directions of instabilities, which fulfill the criterion, are determined for any piecewise linear constitutive relation. The instability of rock joints appears to be ruled by coupling features of the behavior (e.g., dilatancy). Depending on the loading parameters, instabilities can lead to failure, even before the plastic limit criterion. Results for two given constitutive relations illustrate the approach. Some given loading paths are especially considered. Constant volume (undrained) shear and τ‐constant paths are stable or not depending on the link between the deviatoric stress and strain along undrained paths, as found for soils. Some unstable loading paths are illustrated. Along these paths, failure before the plastic limit criterion is possible. The corresponding failure rules are determined. Copyright © 2012 John Wiley & Sons, Ltd.     

Bearing strength surface for bridge caisson foundations in frictional soil under combined loading

The problem of estimating the bearing capacity of massive caisson foundations in frictional soil under combined vertical (N), horizontal (Q) and moment (M) loading is examined numerically by means of three-dimensional finite element analyses. The analysis is performed with due consideration to the foundation’s depth-to-width ratio (D/B), the magnitude of the vertical load and the caisson-soil contact interface conditions. The constitutive law for soil behavior is appropriately validated against experimental results from 1-g small-scale tests, available in the literature. The ultimate limit states are presented in the form of a bearing strength surface in dimensionless and normalized form, while detailed discussion is provided on the physical and geometrical interpretation of the kinematic mechanisms that accompany failure. A generalized closed-form expression for the failure envelope in M–Q–N space is then fitted to the numerical results with use of an appropriately trained artificial neural network. An upper-bound limit equilibrium solution for a certain failure mechanism (designated as the “sliding” mechanism) associated with maximum horizontal bearing capacity is also developed for verification purposes. One of the originalities of the paper lies with respect to the post-failure response of the caissons, where it is shown that the incremental displacement vector is accurately reproduced by assuming normality on the bearing strength surface irrespective of the considered plastic flow rule (associative or non-associative) at the microscale (soil element).     

复合加载模式下地基失效机制研究

在土体极限平衡定理的基础上,利用有限元数值分析软件ABAQUS对复合加载模式下地基失效机制进行了详细地研究。结果表明,竖向荷载V控制着地基破坏滑裂面的深浅程度,水平荷载H和力矩荷载M造成了地基破坏模式的非对称性;文中提出的前倾勺形破坏模式和后仰勺形破坏模式,合理地解释了H-M荷载空间中破坏包络面的非对称性,并给出了H-M荷载空间中不同的地基失效模式与荷载分量间的关系和地基土体中出现极限力矩荷载时的经验判断公式。     

条形荷载下不排水土坡破坏模式判定及极限承载力估算

为了确定边坡放置地基的极限承载力,采用弹-理想塑性有限元,分析了不排水土坡(u=0)的坡肩上放置条形基础的地基极限承载力。结果表明,不排水土坡地基极限承载力仍可沿用Terzaghi水平地基极限承载力计算公式qu=cuNc。不考虑重度条件下,土坡地基的破坏模式类似于水平地基破坏模式,承载力系数Nc与极限分析法计算的结果一致;考虑重度条件下,可用土坡实际状态的Taylor数与其极限状态的Taylor数的差值N作为判别指标,当该值较小时将发生边坡破坏模式,较大时发生地基破坏模式,找出了两种破坏模式的N分界点,确定了Nc与N的关系,建立起坡肩作用条形荷载下不排水土坡极限承载力计算公式。     

The effective stress concept and the evaluation of changes in pore air pressure under jacketed isotropic compression tests for dry sand based on the 2‐phase porous theory

The effective stress concept for solid‐fluid 2‐phase media was revisited in this work. In particular, the effects of the compressibility of both the pore fluid and the soil particles were studied under 3 different conditions, i.e., undrained, drained, and unjacketed conditions based on a Biot‐type theory for 2‐phase porous media. It was confirmed that Terzaghi effective stress holds at the moment when soil grains are assumed to be incompressible and when the compressibility of the pore fluid is small enough compared to that of the soil skeleton. Then, isotropic compression tests for dry sand under undrained conditions were conducted within the triaxial apparatus in which the changes in the pore air pressure could be measured. The ratio of the increment in the cell pressure to the increment in the pore air pressure, m, corresponds to the inverse of the B value by Bishop and was obtained during the step loading of the cell pressure. In addition, the m values were evaluated by comparing them with theoretically obtained values based on the solid‐fluid 2‐phase mixture theory. The experimental m values were close to the theoretical values, as they were in the range of approximately 40 to 185, depending on the cell pressure. Finally, it was found that the soil material with a highly compressible pore fluid, such as air, must be analyzed with the multi‐phase porous mixture theory. However, Terzaghi effective stress is practically applicable when the compressibilities of both the soil particles and the pore fluid are small enough compared to that of the soil skeleton.     

倾斜与偏心荷载作用下裙板式基础破坏包络面研究

联合采用Swipe加载模式与固定位移比加载模式,对裙板式浅基础在倾斜与偏心荷载两种加载条件下的承载性能进行了比较系统的平面应变有限元分析,主要探讨了裙板式基础埋深、地基土不排水强度的非均质性对基础在竖向荷载V与水平荷载H、竖向荷载V与弯矩M加载平面内的破坏包络面的影响,揭示了地基在不同荷载分量组合条件下的失稳破坏机制。结果表明,基础埋深与地基土强度的非均质性对于地基失稳模式有较大影响,但V-H和V-M平面内的破坏包络面形状具有较好的归一化特性,并分别建议了裙板式基础在倾斜和偏心荷载作用下的破坏包络面方程。