有限变形理论及其在岩土工程中的应用
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摘要
随着矿产资源勘探、能源开发、交通运输、城市建设和地下工程的发展,工程的规模越来越大,所涉及的岩土力学的问题越来越复杂。很多工程用传统的小变形理论难以解决,因而有限变形(大变形)的理论及其工程应用越来越引起人们的注意,逐渐成为一个热点问题。
本文依托工程课题“复杂地质条件下地铁隧道群与大跨度隧道矿山法施工沉降预测及工法综合研究”,以有限变形理论在岩土工程中的应用为研究宗旨,重点是有限变形理论的研究,包括弹性理论和弹塑性理论。将岩土工程中常用的Mohr-Coulomb屈服准则与有限变形理论有机的结合在一起,提出应变软化模型,并通过用户子程序予以实现,最后利用工程实例进行验证。
本文的研究内容及获得的结论主要包括以下几个方面:
1.研究有限变形的弹性关系,找出常用各种应力、应变之间的相互关系。确定应力-应变之间的弹性关系以及应力率-应变率间的关系。
2.研究有限变形的弹塑性关系,正确描述有限变形的塑性变形。采用变分原理得到有限变形的平衡方程和边界条件。结合加法分解得到有限变形弹塑性的求解方法。基于有限变形弹塑性的求解方法,提出相应的有限元算法。实现了采用Mohr-Coulomb屈服准则,适用于岩土材料的有限变形弹塑性分析。
3.将材料常规单轴压缩全过程的应力-应变曲线转化为真实应力-真实应变的曲线,从而得到可用于大变形分析的切向弹性模量。引入内部状态参量-等效塑性应变,将材料粘聚力和模量看作等效塑性应变的函数,而泊松比和摩擦角保持不变,得到应变软化模型。
4.在材料力学特性、本构关系、屈服准则以及参数变化规律研究成果的基础上,以通用有限元软件ABAQUS为平台,编写USDFLD等用户子程序实现具体工程课题研究。
5.在上述研究成果的基础上,以某地铁隧道开挖为工程实例,分别采用小变形理论以及有限变形理论并考虑应变软化效应模拟隧道施工过程,为复杂地质条件下地铁隧道群与大跨度隧道矿山法施工进行沉降预测、沉降控制提供依据。计算结果与现场监测相对比,表明有限变形的计算结果更符合工程实际,验证了有限变形理论研究大变形的可行性,该模型可用于类似的岩土工程,为工程提供较为科学的依据。
本文的主要创新点如下:
1.采用Cauchy应力和对数应变以及对应的变化率,结合加法分解,正确描述了有限变形的塑性变形;实现了采用Mohr-Coulomb屈服准则,适用于岩土材料的有限变形弹塑性分析。
2.以有限变形的弹塑性理论为基础,引入内部状态参量-等效塑性应变,推导了粘聚力、变形模量与等效塑性应变之间的定量关系,得到适用于岩土工程大变形的应变软化模型。
3.基于Visual Fortran编写用户子程序,嵌入ABAQUS软件实现本构关系,通过对岩石标准试件的数值模拟,能够很好的模拟应变软化过程。根据某地铁隧道地表沉降变形大的特点,将本模型应用到工程中,模拟结果与实际情况具有很好的吻合性。
Now,with quickly developing of minerals exploration,energy development, communications and transport,urban construction,undergrounding engineering,the dimensions of these projects are more and more tremendous and problems involved in rock and soil mechanics are more and more complex.Many geotechnical engineering and projects can not be solved by the conventional theory of small deformation,so the theory of finite deformation(large deformation) and its application attract more and more researchors attention,and it is becoming a hot topic.
Founded by "research on forecasting settlement and construction process of drilling and blasting method for a group of tunnels and large span tunnel in the condition of complexly geological structure",and taken a certain tunnel as an engineering example,the hard core of this paper is the theory of finite deformation applied in geotechnical engineering,and the emphasis is studying on the theory including elastic and elasto-plastic theory.It is combined Mohr-Coulomb yield criterion common used in geotechnical engineering with the theory of finite deformation,and putted forward the strain softening model.The model is implemented by user subroutine,and verified by applied it to the horizontal subject in the last.From the research,the following conclusions were achieved:
1.Studying on the elastic finite deformation,relationships of all kinds of common stresses and strains are obtained.So the relatioship between stress and strain,stress ratio and strain ratio can be ascertained.
2.Studying on the elasto-plastic finite deformation,plastic deformation of it is correctly expressed.The balance equations and boundary conditions of it are obtained by using variational principle.Combining additive decomposition of the streching and the deformation gradient,the method of solving plastic deformation of it is also obtained.Based on the above methods,relevantly finite element method is putted forward.So elato-plastic analysis of finite deformation is implemented which is appropriate to geotechnical engineering,adopted Mohr-Coulomb yield criterion.
3.Turned perfect complete stress-strain curve in uniaxial compression test into Cauchy stress- logarithmic strain curve,so the tangential modulus can be acquired which is available for analyzing large deformation.Internal state parameter- equivalent plastic strain is introduced,and taken cohesion force and modulus of material as a function of equivalent plastic strain,but Poisson's ratio and friction angle as constants,that is strain sfotening model.
4.Based on the result of material mechanic properties,constitutive relationship,yield criterion and parameters variant regular patterns,by using universally FE software ABAQUS, writing user subroutine USDFLD and embedding it into ABAQUS,the constitutive relationship of strain sftening model is implemented in order to apply it in practical projects.
5.Based on the result of above,taking a certain tube as a verification project,its construction process has been respectively simulated by small deformation method,finite deformation method and taken into account the effect of strain softening.That provides scientific foundation for forecasting,and controlling settlement for a group of tunnels and large span tunnel in the condition of complexly geological structure.By comparing the result of numerical simulation to measurement in situ,that is indicated the results of finite deformation is more coincided with the fact,and verified its feasibility to apply finite deformation theory in large deformation.So it is concluded that the strain softening model can be applied in similar project and provided scientific foundation for it.
The unique points of view in the dissertation are as follows:
Firstly,the plastic deformation of the finite deformation was exactly expressed by using the relationship between Cauchy stress and logrithmic strain,and corresponding ratio, combined additive decomposition of the streching and the deformation gradient.Then the elasto-plastic analysis of the finite deformation is implemented by taken Mohr -Coulomb yield criterion.
Secondly,based on the plastic deformation of the finite deformation,and introduced internal state parameter,equivalent plastic strain,a quantitative relationship between cohesion force,defomation modulus and equivalent plastic strain are derived.So,the strain softening model is obtained which is appropriate to geotechnical engineering.
Lastly,the model is implemented by user subroutines writed in Visual Fortran,and embedded in ABAQUS.It is efficiently simulated the course of strain softening,through modelling the test of standard specimen of rock.Because the settlement of tunnel was very large,the model was applied and good results were obtained in the tunnelling process.
本文依托工程课题“复杂地质条件下地铁隧道群与大跨度隧道矿山法施工沉降预测及工法综合研究”,以有限变形理论在岩土工程中的应用为研究宗旨,重点是有限变形理论的研究,包括弹性理论和弹塑性理论。将岩土工程中常用的Mohr-Coulomb屈服准则与有限变形理论有机的结合在一起,提出应变软化模型,并通过用户子程序予以实现,最后利用工程实例进行验证。
本文的研究内容及获得的结论主要包括以下几个方面:
1.研究有限变形的弹性关系,找出常用各种应力、应变之间的相互关系。确定应力-应变之间的弹性关系以及应力率-应变率间的关系。
2.研究有限变形的弹塑性关系,正确描述有限变形的塑性变形。采用变分原理得到有限变形的平衡方程和边界条件。结合加法分解得到有限变形弹塑性的求解方法。基于有限变形弹塑性的求解方法,提出相应的有限元算法。实现了采用Mohr-Coulomb屈服准则,适用于岩土材料的有限变形弹塑性分析。
3.将材料常规单轴压缩全过程的应力-应变曲线转化为真实应力-真实应变的曲线,从而得到可用于大变形分析的切向弹性模量。引入内部状态参量-等效塑性应变,将材料粘聚力和模量看作等效塑性应变的函数,而泊松比和摩擦角保持不变,得到应变软化模型。
4.在材料力学特性、本构关系、屈服准则以及参数变化规律研究成果的基础上,以通用有限元软件ABAQUS为平台,编写USDFLD等用户子程序实现具体工程课题研究。
5.在上述研究成果的基础上,以某地铁隧道开挖为工程实例,分别采用小变形理论以及有限变形理论并考虑应变软化效应模拟隧道施工过程,为复杂地质条件下地铁隧道群与大跨度隧道矿山法施工进行沉降预测、沉降控制提供依据。计算结果与现场监测相对比,表明有限变形的计算结果更符合工程实际,验证了有限变形理论研究大变形的可行性,该模型可用于类似的岩土工程,为工程提供较为科学的依据。
本文的主要创新点如下:
1.采用Cauchy应力和对数应变以及对应的变化率,结合加法分解,正确描述了有限变形的塑性变形;实现了采用Mohr-Coulomb屈服准则,适用于岩土材料的有限变形弹塑性分析。
2.以有限变形的弹塑性理论为基础,引入内部状态参量-等效塑性应变,推导了粘聚力、变形模量与等效塑性应变之间的定量关系,得到适用于岩土工程大变形的应变软化模型。
3.基于Visual Fortran编写用户子程序,嵌入ABAQUS软件实现本构关系,通过对岩石标准试件的数值模拟,能够很好的模拟应变软化过程。根据某地铁隧道地表沉降变形大的特点,将本模型应用到工程中,模拟结果与实际情况具有很好的吻合性。
Now,with quickly developing of minerals exploration,energy development, communications and transport,urban construction,undergrounding engineering,the dimensions of these projects are more and more tremendous and problems involved in rock and soil mechanics are more and more complex.Many geotechnical engineering and projects can not be solved by the conventional theory of small deformation,so the theory of finite deformation(large deformation) and its application attract more and more researchors attention,and it is becoming a hot topic.
Founded by "research on forecasting settlement and construction process of drilling and blasting method for a group of tunnels and large span tunnel in the condition of complexly geological structure",and taken a certain tunnel as an engineering example,the hard core of this paper is the theory of finite deformation applied in geotechnical engineering,and the emphasis is studying on the theory including elastic and elasto-plastic theory.It is combined Mohr-Coulomb yield criterion common used in geotechnical engineering with the theory of finite deformation,and putted forward the strain softening model.The model is implemented by user subroutine,and verified by applied it to the horizontal subject in the last.From the research,the following conclusions were achieved:
1.Studying on the elastic finite deformation,relationships of all kinds of common stresses and strains are obtained.So the relatioship between stress and strain,stress ratio and strain ratio can be ascertained.
2.Studying on the elasto-plastic finite deformation,plastic deformation of it is correctly expressed.The balance equations and boundary conditions of it are obtained by using variational principle.Combining additive decomposition of the streching and the deformation gradient,the method of solving plastic deformation of it is also obtained.Based on the above methods,relevantly finite element method is putted forward.So elato-plastic analysis of finite deformation is implemented which is appropriate to geotechnical engineering,adopted Mohr-Coulomb yield criterion.
3.Turned perfect complete stress-strain curve in uniaxial compression test into Cauchy stress- logarithmic strain curve,so the tangential modulus can be acquired which is available for analyzing large deformation.Internal state parameter- equivalent plastic strain is introduced,and taken cohesion force and modulus of material as a function of equivalent plastic strain,but Poisson's ratio and friction angle as constants,that is strain sfotening model.
4.Based on the result of material mechanic properties,constitutive relationship,yield criterion and parameters variant regular patterns,by using universally FE software ABAQUS, writing user subroutine USDFLD and embedding it into ABAQUS,the constitutive relationship of strain sftening model is implemented in order to apply it in practical projects.
5.Based on the result of above,taking a certain tube as a verification project,its construction process has been respectively simulated by small deformation method,finite deformation method and taken into account the effect of strain softening.That provides scientific foundation for forecasting,and controlling settlement for a group of tunnels and large span tunnel in the condition of complexly geological structure.By comparing the result of numerical simulation to measurement in situ,that is indicated the results of finite deformation is more coincided with the fact,and verified its feasibility to apply finite deformation theory in large deformation.So it is concluded that the strain softening model can be applied in similar project and provided scientific foundation for it.
The unique points of view in the dissertation are as follows:
Firstly,the plastic deformation of the finite deformation was exactly expressed by using the relationship between Cauchy stress and logrithmic strain,and corresponding ratio, combined additive decomposition of the streching and the deformation gradient.Then the elasto-plastic analysis of the finite deformation is implemented by taken Mohr -Coulomb yield criterion.
Secondly,based on the plastic deformation of the finite deformation,and introduced internal state parameter,equivalent plastic strain,a quantitative relationship between cohesion force,defomation modulus and equivalent plastic strain are derived.So,the strain softening model is obtained which is appropriate to geotechnical engineering.
Lastly,the model is implemented by user subroutines writed in Visual Fortran,and embedded in ABAQUS.It is efficiently simulated the course of strain softening,through modelling the test of standard specimen of rock.Because the settlement of tunnel was very large,the model was applied and good results were obtained in the tunnelling process.
引文
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