适用于饱和黏土循环动力分析的边界面塑性模型及应用
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摘要
嵌入式海洋结构诸如桩基、吸力锚、桶型基础以及拖曳锚等，往往处于极其复杂和恶劣的海洋环境条件，通常需深嵌于海床土以提供承载性能。因此，该类结构及其周围的海洋土体将直接或间接地承受由风、浪、流等导致的长期、持续、低频循环载荷的作用。海洋土尤其是海洋软土的非线性动力特性在循环载荷下将发生一系列演变，进而会引起嵌入式海洋结构循环承载性能的巨大变化。鉴于此，本文建立了适用于该类结构循环承载力评估的数值分析模型。
首先，基于临界状态理论建立了能合理反映饱和黏土循环稳定和循环退化动力特性的无弹性域边界面塑性模型。以应力反向点作为边界面的广义各向同性硬化中心，提出了广义各向同性硬化准则。低应力水平下，边界面随着广义各向同性硬化中心的运动在应力空间中达到循环稳定状态；高应力水平下，引入与塑性偏应变有关的损伤变量实现边界面的收缩，以模拟土体循环刚度和强度的退化。该模型包含两类参数，即临界状态参数和塑性模量形函数参数，均具有明确的物理意义。对于单调加载事件的模拟，仅需要临界状态参数；对于循环加载事件的计算，需由常规室内试验测定动剪切模量和阻尼比，进而确定形函数参数。结合大量的国内外试验，对边界面模型进行考察，涉及的因素包括土质、固结水平、应力水平、加载方式（单向、双向循环，应力和应变控制）以及超固结比等，结果表明，该模型对等压固结饱和黏土的循环稳定和循环退化特性均能较为合理地反映。
其次，通过分离土体初始各向异性和后继各向异性在本构模型中的描述，即土体初始各向异性由边界面的初始旋转模拟，而后继应力诱发各向异性由广义各向同性硬化准则中的运动硬化部分确定，克服了原模型无法反映土体初始各向异性的缺陷；设计一系列简单加载、复杂加载的静、动力数值试验，并与解析解和试验数据进行了对比，验证了该种分离初始和后继各向异性描述做法的合理性；在不增加模型参数及复杂性的前提下，实现了等向硬化、运动硬化和旋转硬化准则功能的结合；分别基于广义Mises准则三维化方法和SMP准则变换应力法将该模型推广至三维应力空间，首次实现了SMP变换应力法在循环动力边界面塑性模型中的应用；对比分析了两种三维化方法在边界面模型中的应用性能。弥补了目前国际范围内针对循环动力本构模型三维化方法对比研究的缺乏。
再次，建立了可以反映土体循环稳定和循环退化的三维各向异性边界面塑性模型的隐式和显式积分格式，并将其开发进ABAQUS软件；针对常规隐式回映积分算法需要映射回归当前应力点、子增量步显式积分算法需要修正当前应力点至屈服面上，而无弹性域边界面模型内无屈服面的矛盾，修正了传统隐、显式积分算法，提高了该两种算法在无弹性域边界面塑性模型中的应用能力；结合饱和土体静、动三轴试验和刚性浅基础承载力边值问题，从精确性、稳定性、高效性方面对这两种积分格式在无弹性域边界面中的性能进行对比分析；给出两种积分算法在无弹性域边界面模型中的详细流程，具有极强的可重复性；由于本文建立的边界面塑性模型包含了各向同性硬化、运动硬化和旋转硬化等弹塑性模型要素，能够代表较为广泛的弹塑性本构模型，因此针对该模型的积分算法和数值开发对同类模型具有指导意义。
最后，针对目前已有的四种极限承载力确定标准，不能同时适用于不同类型的载荷—位移曲线的问题，对嵌入式海洋结构的各类载荷—位移曲线进行了系统研究，建议了具有普适性的极限承载力确定标准；采用本文建立的边界面塑性模型，基于ABAQUS平台，以法向承力锚（Vertically Loaded Plate Anchor, VLA）为例，开展了嵌入式海洋工程结构循环承载力分析，结果表明VLA表现出三种典型循环承载特性：循环稳定、循环次稳定和循环退化；VLA-海床土耦合系统的循环刚度也表现出相应的三种典型特性；针对VLA循环破坏时的两种典型位移曲线，建议了循环承载力的确定标准；考察了载荷均值、载荷幅值、载荷周次对循环承载力的影响；建议了嵌入式海洋结构循环承载力的分析流程，以此作为综合评估循环载荷作用下结构稳定性的基本依据。
The embedded offshore structures, such as the pile anchor, suction caissonanchor, the suction bucket foundation and the drag anchor, which need to withstandunder the extremely complicated ocean environment, are often deeply embedded inthe seabed to keep their stability and functionality. Inevitably, the embedded offshorestructure and its surrounding soil are subjected to the long-term, low-frequency cyclicloading caused by the winds, waves and currents. Hence, the evolvement of the cyclicbehavior of the seabed soil could induce the great change of the bearing capacity ofthe embedded offshore structures. With regard to the problem, a dynamic model forassessing the cyclic bearing capacity of the embedded offshore structures is presentedin the paper.
Firstly, within the critical state framework, a new bounding surface plasticitymodel without elastic region suitable for capturing the cyclic shakedown anddegradation of saturated clay is developed. By taking the stress reversal point as thegeneralized homological center, the generalized hardening rule is proposed. Withmovement of the generalised homological centre, at lower stress amplitudes, thecyclic process ends at a steady state, and cyclic shakedown is reached. At higher stressamplitudes, a damage parameter related to the accumulated deviatoric plastic strain isincorporated into the form of the bounding surface, which is hence able to contract tomodel degradations in stiffness and strength. The model requires the critical stateparameters and the hardening modulus parameters, all of them have clear physicalmeanings. For the monotonic loading, only the former is needed, for the cyclicloading, the latter should be calibrated by the laboratory tests related with the dynamicshear modulus and the damping ratio. The developed model is validated throughundrained isotropic cyclic triaxial tests in normally consolidated and overconsolidatedsaturated clay under both one-way and two-way loadings. Both cyclic shakedown anddegradation are well reproduced by the model.
Secondly, by describing the initial anisotropy and stress-induced anisotropyseparately, i.e., the former is taken into account through adopting an inclinedbounding surface at the start of shearing loading but without further rotation in the subsequent shearing event and the latter is considered by the kinematic role of thegeneralised hardening rule, the proposed model is improved to reflect the effects ofinitial anisotropy. A series of simple monotonic loading test and complicated cyclicloading tests are carried out. By compared with the analytical and experimental results,the rationality and efficiency of the assumption are verified. Thus, without increasingany model parameter and complexity, the functionality of the isotropic, kinematic androtational hardening rule are included in the newly proposed bounding surface model.Furthermore, the new anisotropic bounding surface model is generalised to3-D stressspace by the Von-Mises criterion method and the transformed stress method based onthe SMP criterion, respectively. In addition, The comparative analysis of the twomethods is systematically carried out to compensate for the lack in the study ofgeneralising the2-D model to3-D stress space for the constitutive model for cyclicbehaviour of saturated clay.
Thirdly, the proposed bounding surface model in the paper is integrated by theimplicit return mapping and the sub-stepping integration schemes respectively andimplemented into ABAQUS. Two necessary modifications have been made for theimplicit and the sub-stepping integration schemes when applied to the boundingsurface model without elastic region. Because there is no yield surface in the type ofthe model, which the conventional implicit algorithm returns the stress state back to,or the sub-stepping integration corrects the drift of the stress state to. The applicabilityof the two integrations to the type model without the yield surface is enhanced.Furthermore, the comparative studies on the accuracy, robustness and efficiency of thetwo integrations for this kind of the bounding surface model are carried out both onthe soil element level and a coupled analysis of a rigid square footing on a normallyconsolidated saturated clay. In addition, the procedures of the two integrationalgorithms are given in detail, which can be highly reproduced. It should be noted thatthe model is a representative of a class bounding surface model with vanishing elasticregion which includes the typical model characteristics, i.e., the isotropic, kinematicand rotational hardening, the integrations for the model does provide a guidance forthe similar work.
Finally, due to that the existing criterion of the ultimate bearing capacity can not suitable for different types of load-displacement curves, a new criterion is establishedbased on the systematical analysis on all types of load-displacement curves. Byadopting the bounding surface model which has implemented in ABAQUS, the cyclicbearing capacity of the embedded offshore structure (the Vertically Loaded Anchor,VLA) is investigated. It shows that VLA has three typical types of displacementresponses under cyclic loading, i.e., the cyclic shakedown, the cyclic hypo-shakedownand the cyclic degradation. The stiffness of the coupled embedded offshorestructure-soil system shows the similar characteristics correspondingly. A criterion fordetermining the cyclic bearing capacity of the embedded offshore structure isproposed. The effects of the mean value and amplitude of the cyclic loading as well asthe number of cycles are investigated. The procedure for assessing the cyclic bearingcapacity is developed, which can be used for further evaluating the stability of theembedded offshore structures.
首先，基于临界状态理论建立了能合理反映饱和黏土循环稳定和循环退化动力特性的无弹性域边界面塑性模型。以应力反向点作为边界面的广义各向同性硬化中心，提出了广义各向同性硬化准则。低应力水平下，边界面随着广义各向同性硬化中心的运动在应力空间中达到循环稳定状态；高应力水平下，引入与塑性偏应变有关的损伤变量实现边界面的收缩，以模拟土体循环刚度和强度的退化。该模型包含两类参数，即临界状态参数和塑性模量形函数参数，均具有明确的物理意义。对于单调加载事件的模拟，仅需要临界状态参数；对于循环加载事件的计算，需由常规室内试验测定动剪切模量和阻尼比，进而确定形函数参数。结合大量的国内外试验，对边界面模型进行考察，涉及的因素包括土质、固结水平、应力水平、加载方式（单向、双向循环，应力和应变控制）以及超固结比等，结果表明，该模型对等压固结饱和黏土的循环稳定和循环退化特性均能较为合理地反映。
其次，通过分离土体初始各向异性和后继各向异性在本构模型中的描述，即土体初始各向异性由边界面的初始旋转模拟，而后继应力诱发各向异性由广义各向同性硬化准则中的运动硬化部分确定，克服了原模型无法反映土体初始各向异性的缺陷；设计一系列简单加载、复杂加载的静、动力数值试验，并与解析解和试验数据进行了对比，验证了该种分离初始和后继各向异性描述做法的合理性；在不增加模型参数及复杂性的前提下，实现了等向硬化、运动硬化和旋转硬化准则功能的结合；分别基于广义Mises准则三维化方法和SMP准则变换应力法将该模型推广至三维应力空间，首次实现了SMP变换应力法在循环动力边界面塑性模型中的应用；对比分析了两种三维化方法在边界面模型中的应用性能。弥补了目前国际范围内针对循环动力本构模型三维化方法对比研究的缺乏。
再次，建立了可以反映土体循环稳定和循环退化的三维各向异性边界面塑性模型的隐式和显式积分格式，并将其开发进ABAQUS软件；针对常规隐式回映积分算法需要映射回归当前应力点、子增量步显式积分算法需要修正当前应力点至屈服面上，而无弹性域边界面模型内无屈服面的矛盾，修正了传统隐、显式积分算法，提高了该两种算法在无弹性域边界面塑性模型中的应用能力；结合饱和土体静、动三轴试验和刚性浅基础承载力边值问题，从精确性、稳定性、高效性方面对这两种积分格式在无弹性域边界面中的性能进行对比分析；给出两种积分算法在无弹性域边界面模型中的详细流程，具有极强的可重复性；由于本文建立的边界面塑性模型包含了各向同性硬化、运动硬化和旋转硬化等弹塑性模型要素，能够代表较为广泛的弹塑性本构模型，因此针对该模型的积分算法和数值开发对同类模型具有指导意义。
最后，针对目前已有的四种极限承载力确定标准，不能同时适用于不同类型的载荷—位移曲线的问题，对嵌入式海洋结构的各类载荷—位移曲线进行了系统研究，建议了具有普适性的极限承载力确定标准；采用本文建立的边界面塑性模型，基于ABAQUS平台，以法向承力锚（Vertically Loaded Plate Anchor, VLA）为例，开展了嵌入式海洋工程结构循环承载力分析，结果表明VLA表现出三种典型循环承载特性：循环稳定、循环次稳定和循环退化；VLA-海床土耦合系统的循环刚度也表现出相应的三种典型特性；针对VLA循环破坏时的两种典型位移曲线，建议了循环承载力的确定标准；考察了载荷均值、载荷幅值、载荷周次对循环承载力的影响；建议了嵌入式海洋结构循环承载力的分析流程，以此作为综合评估循环载荷作用下结构稳定性的基本依据。
The embedded offshore structures, such as the pile anchor, suction caissonanchor, the suction bucket foundation and the drag anchor, which need to withstandunder the extremely complicated ocean environment, are often deeply embedded inthe seabed to keep their stability and functionality. Inevitably, the embedded offshorestructure and its surrounding soil are subjected to the long-term, low-frequency cyclicloading caused by the winds, waves and currents. Hence, the evolvement of the cyclicbehavior of the seabed soil could induce the great change of the bearing capacity ofthe embedded offshore structures. With regard to the problem, a dynamic model forassessing the cyclic bearing capacity of the embedded offshore structures is presentedin the paper.
Firstly, within the critical state framework, a new bounding surface plasticitymodel without elastic region suitable for capturing the cyclic shakedown anddegradation of saturated clay is developed. By taking the stress reversal point as thegeneralized homological center, the generalized hardening rule is proposed. Withmovement of the generalised homological centre, at lower stress amplitudes, thecyclic process ends at a steady state, and cyclic shakedown is reached. At higher stressamplitudes, a damage parameter related to the accumulated deviatoric plastic strain isincorporated into the form of the bounding surface, which is hence able to contract tomodel degradations in stiffness and strength. The model requires the critical stateparameters and the hardening modulus parameters, all of them have clear physicalmeanings. For the monotonic loading, only the former is needed, for the cyclicloading, the latter should be calibrated by the laboratory tests related with the dynamicshear modulus and the damping ratio. The developed model is validated throughundrained isotropic cyclic triaxial tests in normally consolidated and overconsolidatedsaturated clay under both one-way and two-way loadings. Both cyclic shakedown anddegradation are well reproduced by the model.
Secondly, by describing the initial anisotropy and stress-induced anisotropyseparately, i.e., the former is taken into account through adopting an inclinedbounding surface at the start of shearing loading but without further rotation in the subsequent shearing event and the latter is considered by the kinematic role of thegeneralised hardening rule, the proposed model is improved to reflect the effects ofinitial anisotropy. A series of simple monotonic loading test and complicated cyclicloading tests are carried out. By compared with the analytical and experimental results,the rationality and efficiency of the assumption are verified. Thus, without increasingany model parameter and complexity, the functionality of the isotropic, kinematic androtational hardening rule are included in the newly proposed bounding surface model.Furthermore, the new anisotropic bounding surface model is generalised to3-D stressspace by the Von-Mises criterion method and the transformed stress method based onthe SMP criterion, respectively. In addition, The comparative analysis of the twomethods is systematically carried out to compensate for the lack in the study ofgeneralising the2-D model to3-D stress space for the constitutive model for cyclicbehaviour of saturated clay.
Thirdly, the proposed bounding surface model in the paper is integrated by theimplicit return mapping and the sub-stepping integration schemes respectively andimplemented into ABAQUS. Two necessary modifications have been made for theimplicit and the sub-stepping integration schemes when applied to the boundingsurface model without elastic region. Because there is no yield surface in the type ofthe model, which the conventional implicit algorithm returns the stress state back to,or the sub-stepping integration corrects the drift of the stress state to. The applicabilityof the two integrations to the type model without the yield surface is enhanced.Furthermore, the comparative studies on the accuracy, robustness and efficiency of thetwo integrations for this kind of the bounding surface model are carried out both onthe soil element level and a coupled analysis of a rigid square footing on a normallyconsolidated saturated clay. In addition, the procedures of the two integrationalgorithms are given in detail, which can be highly reproduced. It should be noted thatthe model is a representative of a class bounding surface model with vanishing elasticregion which includes the typical model characteristics, i.e., the isotropic, kinematicand rotational hardening, the integrations for the model does provide a guidance forthe similar work.
Finally, due to that the existing criterion of the ultimate bearing capacity can not suitable for different types of load-displacement curves, a new criterion is establishedbased on the systematical analysis on all types of load-displacement curves. Byadopting the bounding surface model which has implemented in ABAQUS, the cyclicbearing capacity of the embedded offshore structure (the Vertically Loaded Anchor,VLA) is investigated. It shows that VLA has three typical types of displacementresponses under cyclic loading, i.e., the cyclic shakedown, the cyclic hypo-shakedownand the cyclic degradation. The stiffness of the coupled embedded offshorestructure-soil system shows the similar characteristics correspondingly. A criterion fordetermining the cyclic bearing capacity of the embedded offshore structure isproposed. The effects of the mean value and amplitude of the cyclic loading as well asthe number of cycles are investigated. The procedure for assessing the cyclic bearingcapacity is developed, which can be used for further evaluating the stability of theembedded offshore structures.
引文
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