基于能量耗散原理的土与结构接触面模型研究及应用
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摘要
土与结构接触面的力学行为是土与结构相互作用的微观反映,其主要以土与混凝土接触面为代表,它涉及到岩土工程的诸多领域。详细研究接触面的力学行为并建立相应的本构模型具有重要的理论意义和实用价值。本文从基础试验、接触面单元、接触面本构模型等方面对土与混凝土接触面的力学行为进行了系统的研究;建立了基于能量耗散假定的3参数应力应变模型,进而建立了接触面正反向剪切本构模型;最后在岩土工程中推广了新3参数应力应变模型的应用,并通过数学严格证明了新3参数应力应变模型与传统模型的关系,主要内容如下:
(1) 通过多种接触面直剪试验,分析了接触面抗剪强度参数随接触类型和土体含水率变化的规律,指出了接触面的力学行为与结构的亲水性密切相关。
(2) 进行了土与混凝土接触面4个含水率、4个正向剪切比的正反向单剪试验,研究了不同含水率与正向剪切比对接触面反向抗剪强度的影响规律,观察了接触面剪切破坏的位置。
(3) 分析试验数据,基于热力学原理和能量耗散假定,得到了接触面应力～应变曲线的控制微分方程,建立了更为适用的接触面3参数应力～应变新模型;给出了其相应的拟合评价体系,通过多种试验数据对3参数模型进行了验证;从能量耗散和微分方程的角度,分析了本文3参数模型与2参数模型的关系,引用数学特征“半值收敛指数”指出了传统模型在理论和数学上的不足。
(4) 基于能量耗散的接触面应力应变3参数模型,建立了接触面正向剪切模型。
(5) 在接触面正反向单剪试验的基础上,明确提出了“临界正向剪切比”的概念;建立了基于能量耗散原理的接触面正反向剪切本构模型。
(6) 从能量耗散的机理出发,将本文3参数应力应变模型推广到土体本构模型和膨胀土的膨胀变形、桩极限承载力的增长、垃圾填埋封顶沉降、软土地基工后沉降等一类岩土工程课题的表征中;最后统一了这类课题的本质:具有相同的基于能量耗散的控制微分方程,并从理论上证明了其各自传统模型的缺陷。
(7) 从数学上严格证明了2参数双曲线模型、指数曲线模型均是3参数模型的特例;采用2种方法证明了初始导数、极限值对应相等的情况下,指数曲线模型、2参数双曲线模型分别是3参数模型的上界、下界;采用3种方法证明了指数曲线模型数值大于对应的2参数双曲线模型数值。
Soil-concrete interface determines the behavior of many geotechnical structures, and it is the micro-representive of soil-structure interaction. Therefore, proper understanding of the interface shearing mechanisms and establishing its good constitutive model are essential in both theory aspect and practical aspect. In this paper, soil-concrete interface behavior is comprehensively studied including laboratory tests, interface element and interface constitutive law, and a new constitutive model considering previous shear ratio is proposed based on laboratory tests and some potential energy dissipating theory postulates. The mew-built 3-parameter model is generalized to some geotechnical subjects. Finally, pure mathematic analysis on relationship between the new model and traditional models are conducted. The main contents can be summarized as follows:(1) According to direct shear tests on four kinds of interface types, analysis on interface behavior changed with soil water content and contacted structure is conducted, and conclusion that interface behavior depends closely on structure hydrophilic nature is made.(2) Improved simple shear tests on soil-concrete interface, considering four soil water contents and four previous shear ratios, are accomplished, and interface behaviors under different soil water contents and previous shear ratios are analyzed in details. Shear failure position of the interface is recorded, too.(3) Combined with tests results and potential energy dissipating theory postulates, control differential equation for interface stress-strain relationship is developed, and a new 3-paramenter model for it is established. Appraisal factor for the 3-paramenter model is presented and fitting accuracy of the new model is proved by many laboratory tests results. Form potential energy dissipating theory and control differential equation angles, the relationships between the 3-paramenter model and corresponding traditional models are discussed, and mathematics "half value index" is used to point out deficiency of traditional models in both mathematics and mechanical theory.(4) A new interface constitutive model neglecting previous shear ratio is presented on the basis of above established 3-parameter stress-strain model.(5) Based on improved simple shear tests on soil-concrete interface, the concept "critical previous shear ratio" is put forward, then a new interface constitutive model based on potential energy dissipating theory considering previous shear ratio is proposed.(6) Form potential energy dissipating principle and control differential equation angles, the developed 3-parameter model is generalized to constitutive model of soil itself
and to one kind time effect geotechnical subject, including expansive deformation of expansive soil, time-dependent ultimate bearing capacity of pile, post-settlement of municipal refuse landfill and post-settlement of soft foundation. Finally, the nature of this kind subject is indicated that they have same control differential equation, and deficiency of their traditional models in both mathematics and mechanical theory is analyzed, too.(7) According pure mathematic proof, conclusion that 2-parameter hyperbolic model and exponential model are both simplified types of the new 3-parameter model is made. Two mathematic methods are presented to prove that 2-parameter hyperbolic model and exponential model are the superior limit and lower limit of the corresponding new 3-parameter model respectively. Three mathematic methods are put forward to confirm that the value of exponential model is larger than that of corresponding 2-parameter hyperbolic model.
(1) 通过多种接触面直剪试验,分析了接触面抗剪强度参数随接触类型和土体含水率变化的规律,指出了接触面的力学行为与结构的亲水性密切相关。
(2) 进行了土与混凝土接触面4个含水率、4个正向剪切比的正反向单剪试验,研究了不同含水率与正向剪切比对接触面反向抗剪强度的影响规律,观察了接触面剪切破坏的位置。
(3) 分析试验数据,基于热力学原理和能量耗散假定,得到了接触面应力～应变曲线的控制微分方程,建立了更为适用的接触面3参数应力～应变新模型;给出了其相应的拟合评价体系,通过多种试验数据对3参数模型进行了验证;从能量耗散和微分方程的角度,分析了本文3参数模型与2参数模型的关系,引用数学特征“半值收敛指数”指出了传统模型在理论和数学上的不足。
(4) 基于能量耗散的接触面应力应变3参数模型,建立了接触面正向剪切模型。
(5) 在接触面正反向单剪试验的基础上,明确提出了“临界正向剪切比”的概念;建立了基于能量耗散原理的接触面正反向剪切本构模型。
(6) 从能量耗散的机理出发,将本文3参数应力应变模型推广到土体本构模型和膨胀土的膨胀变形、桩极限承载力的增长、垃圾填埋封顶沉降、软土地基工后沉降等一类岩土工程课题的表征中;最后统一了这类课题的本质:具有相同的基于能量耗散的控制微分方程,并从理论上证明了其各自传统模型的缺陷。
(7) 从数学上严格证明了2参数双曲线模型、指数曲线模型均是3参数模型的特例;采用2种方法证明了初始导数、极限值对应相等的情况下,指数曲线模型、2参数双曲线模型分别是3参数模型的上界、下界;采用3种方法证明了指数曲线模型数值大于对应的2参数双曲线模型数值。
Soil-concrete interface determines the behavior of many geotechnical structures, and it is the micro-representive of soil-structure interaction. Therefore, proper understanding of the interface shearing mechanisms and establishing its good constitutive model are essential in both theory aspect and practical aspect. In this paper, soil-concrete interface behavior is comprehensively studied including laboratory tests, interface element and interface constitutive law, and a new constitutive model considering previous shear ratio is proposed based on laboratory tests and some potential energy dissipating theory postulates. The mew-built 3-parameter model is generalized to some geotechnical subjects. Finally, pure mathematic analysis on relationship between the new model and traditional models are conducted. The main contents can be summarized as follows:(1) According to direct shear tests on four kinds of interface types, analysis on interface behavior changed with soil water content and contacted structure is conducted, and conclusion that interface behavior depends closely on structure hydrophilic nature is made.(2) Improved simple shear tests on soil-concrete interface, considering four soil water contents and four previous shear ratios, are accomplished, and interface behaviors under different soil water contents and previous shear ratios are analyzed in details. Shear failure position of the interface is recorded, too.(3) Combined with tests results and potential energy dissipating theory postulates, control differential equation for interface stress-strain relationship is developed, and a new 3-paramenter model for it is established. Appraisal factor for the 3-paramenter model is presented and fitting accuracy of the new model is proved by many laboratory tests results. Form potential energy dissipating theory and control differential equation angles, the relationships between the 3-paramenter model and corresponding traditional models are discussed, and mathematics "half value index" is used to point out deficiency of traditional models in both mathematics and mechanical theory.(4) A new interface constitutive model neglecting previous shear ratio is presented on the basis of above established 3-parameter stress-strain model.(5) Based on improved simple shear tests on soil-concrete interface, the concept "critical previous shear ratio" is put forward, then a new interface constitutive model based on potential energy dissipating theory considering previous shear ratio is proposed.(6) Form potential energy dissipating principle and control differential equation angles, the developed 3-parameter model is generalized to constitutive model of soil itself
and to one kind time effect geotechnical subject, including expansive deformation of expansive soil, time-dependent ultimate bearing capacity of pile, post-settlement of municipal refuse landfill and post-settlement of soft foundation. Finally, the nature of this kind subject is indicated that they have same control differential equation, and deficiency of their traditional models in both mathematics and mechanical theory is analyzed, too.(7) According pure mathematic proof, conclusion that 2-parameter hyperbolic model and exponential model are both simplified types of the new 3-parameter model is made. Two mathematic methods are presented to prove that 2-parameter hyperbolic model and exponential model are the superior limit and lower limit of the corresponding new 3-parameter model respectively. Three mathematic methods are put forward to confirm that the value of exponential model is larger than that of corresponding 2-parameter hyperbolic model.
引文
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