岩石弹塑性损伤MHC耦合模型及数值算法研究
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摘要
岩体工程大多数不是赋存于单一的地质环境中,而是处于复杂的多场环境下,如：应力场(Mechanical)、渗流场(Hydrological)、温度场(Thermal)以及水化学场(Chemical),它们之间的相互作用构成了国际岩石力学学会研究的热点问题,即“岩石多场耦合问题”。随着我国大规模的岩体工程建设,岩体工程在载荷和水-岩作用下的应力-渗流-化学(MHC)耦合问题日趋重要。本文以数值计算手段为主,试验手段为辅,以岩石弹塑性损伤MHC耦合问题为主要研究内容,以程序开发为线索层层递进最终实现问题的研究,揭示多场耦合之间的相互作用、破坏机理为研究目标,以大连地铁隧道工程、吉林抚松隧道工程、贵阳地铁隧道工程为背景,从而体现所做研究工作的理论价值和工程意义。
本文在国家自然科学基金资助项目(No.51079010：渗流-应力耦合海床基岩开挖损伤机理和模型研究)和大连海事大学全国优秀博士学位论文培育基金资助项目(No.2013YB03：海水作用下隧道围岩MHC损伤耦合机理试验及模型研究)下围绕“岩石弹塑性损伤MHC耦合问题”开展研究,具体将其细化为5个子问题进行研究,岩石超声损伤、冻胀力及渗透性试验,岩石弹塑性软化、损伤模型建立及数值算法,岩石弹塑性损伤MH耦合模型及程序实施,岩石弹塑性损伤MHC耦合模型及程序实施,同时为了准确的进行计算,解决复杂模型中参数无法确定的瓶颈,进行参数反演研究。具体开展以下研究工作：
(1)岩石压缩过程伴随着岩石微裂纹闭合、萌生、扩展和贯通等,宏观表现为岩石变形、破坏过程。在此过程中声波波速随着损伤、破坏表现出一定的变化规律,运用这种变化规律预测岩体工程结构稳定性有着重要的意义。从声波波速的角度出发,测试无受力和受力状态下干燥、饱水裂隙片岩的纵波波速,研究饱水天然裂隙片岩的波速特性及压缩全过程中波速随应变的变化规律,波速变化与岩石损伤、破裂之间的内在关系。同时进行受压饱水裂隙片岩断裂与损伤分析,基于张开型裂纹推导Drucker-Prager准则的尖端塑性区半径,以此反应压缩过程中产生的水压力对尖端塑性区的影响。关于岩石饱水冻胀力试验装置、环向渗流-应力耦合岩石渗透性试验装置还鲜见报道,为了研究岩石冻胀损伤及环向渗流-应力耦合下渗透性的变化规律问题,自主研制相应试验装置。采用饱水岩石冻胀力试验装置进行不同冻融温度、不同岩石含水率、不同冻融循环次数条件下岩石冻胀力测试试验。采用环向渗流-应力耦合岩石渗透性试验装置进行不同渗透压、不同轴压条件下岩石渗透性试验。
(2)搭建岩石弹塑性损伤MHC耦合程序框架,采用模块化的思想,分别针对各部分程序进行开发,然后按照一定的规则相互调用,以这种方式构成一个有机整体,为开展岩石多场耦合问题提供数值计算手段。基于von Mises本构模型、Drucker-Prager本构模型的完全隐式返回映射算法(Fully implicit return mapping algorithm)以及相对应的一致切线模量(Consistent tangent modulus),采用面向对象的编程方法,利用C++语言编制相应求解程序,作为主控力学程序基本部分。返回映射算法可避免预测应力漂移屈服面的现象,对于准静态变形条件下的本构方程可以获得准确的解,在迭代中使用Newton-Raphson法可获得近似平方的收敛速度,具有较高的精确性和稳定性。结果表明算法的优越性、程序的正确性和工程中的实用性,具有一定的理论价值和实际意义。将岩石弹塑性损伤MHC耦合程序嵌入到差异进化算法(Differential evolution algorithm,DE)中,开发智能反分析程序,对相关程序的计算效率、正确性等进行验证,并在实际工程中应用。
(3)岩石的软化、损伤特性对渗流场、化学场有重要影响,在展开岩石弹塑性损伤MHC耦合问题研究时,针对岩石软化、损伤特性进行研究,建立相应本构模型并开发求解程序。关于岩土工程材料应变软化问题及有限元对其数值计算时切线刚度矩阵负定造成求解困难的问题进行研究。首先,建立基于Drucker-Prager强度准则的岩石弹塑性应变软化本构模型。其次,考虑弧长法在判断切线刚度矩阵正定性导致效率低的缺点,在弹塑性增量有限元方程的迭代计算中尝试采用Newton-Raphson法和Arc-Length法(NR-AL法)联合迭代求解的思路,即在结构未达到极限荷载前采用Newton-Raphson迭代法,而当结构接近极限荷载时转换为Arc-Length法控制迭代,从而使结构越过峰值点进入软化区直至破坏,NR-AL法汲取了2者迭代求解中具有的优势。最后,利用C++语言对所建应变软化模型的本构求解和弹塑性增量有限元方程迭代求解过程给予程序实现,应用所编程序进行数值计算,分析Drucker-Prager理想弹塑性模型、应变软化模型、应变硬化模型计算的应力-应变曲线的区别,同时将应变软化模型计算结果与试验数据进行对比。研究结果表明所建应变软化本构模型可以较好地模拟岩石材料的峰后软化特性,能够揭示峰后应变软化特性和破坏机制,NR-AL法能够求解由于应变软化造成的负刚度问题,也克服了单独使用弧长法时判断切线刚度矩阵正定性效率低的缺点。
(4)在实际隧道施工过程中,隧道开挖引起地下岩体应力重分布使得围岩的微裂纹扩展损伤,并伴随有塑性流动变形。为研究损伤引起的刚度退化和塑性导致的流动两种破坏机制的耦合作用,从弹塑性力学和损伤理论的角度出发,同时引入修正有效应力原理来考虑孔隙水压力的作用,建立基于Drucker-Prager屈服准则的弹塑性损伤本构模型。针对该本构模型推导了孔隙水压力作用下弹塑性损伤本构模型的数值积分算法-隐式返回映射算法。大多数弹塑性损伤模型中涉及参数多且不易确定的问题,采用反分析方法获得损伤参数,解决损伤模型参数不易确定的难题。采用面向对象的编程方法使用C++语言编制了弹塑性损伤本构求解程序,并对所建弹塑性损伤模型和所编程序进行试验和数值两方面的验证；最后将其在吉林抚松隧道工程中进行应用,模拟了塑性区和损伤区的发展变化。研究结果表明所建立弹塑性伤损本构模型能够较好地描述岩石的力学性能、塑性和损伤变化趋势,所编程序能够进行实际工程问题的模拟,对现场施工给予一定的指导。同时基于Lemaitre等向硬化弹塑性损伤耦合本构模型,采用C++语言在Visual6.0环境下编制有限元本构求解程序,在塑性损伤修正步中求解返回映射方程时,选取一种简单的形式,只需迭代求解一个标量非线性方程,计算效率较高。通过缺口圆棒数值算例初步验证了程序的正确性。同时丰富了岩石弹塑性损伤MHC耦合程序中主控力学程序的本构模型,为研究岩石等材料损伤问题提供方法和途径。
(5)在地下水渗流场、应力场、损伤场的耦合作用下,更易造成隧道围岩坍塌或涌水等灾害。首先,将围岩材料视作各向同性连续介质,采用基于前文Drucker-Prager准则建立岩石弹塑性损伤本构模型进行数值求解。其次,根据岩石处于弹塑性状态时渗透系数动态演化公式,建立岩石弹塑性损伤MH耦合模型,并给出三场耦合情况下的数值求解迭代方法。同时针对耦合模型中涉及参数较多且不易测定的问题,基于前文差异进化算法原理建立的智能反分析方法,对耦合模型中的损伤参数进行反演。最后,利用C++语言编制相应的岩石弹塑性损伤MH耦合程序,利用所编程序进行以下计算：①分别采用弹性模型和弹塑性损伤模型进行隧道围岩位移场、应力场的计算。②不考虑力学作用的情况下进行孔隙水压力、渗流量的计算。③采用所建耦合模型计算得到隧道围岩应力场、渗流场以及损伤场的相互影响规律。研究结果表明所建立的耦合模型通过应力、渗流和损伤的相互作用更能够真实地反映出岩石材料的宏观破坏现象,所编计算程序能够模拟地下水渗流场、应力场、损伤场之间的耦合特性,为受地下水影响严重的工程建设提供了方法。采用上述所建模型及程序对大连地铁海事大学试验线路过河段隧道施工过程中的围岩稳定性进行计算。
(6)关于岩石MHC耦合的研究相对较少,这其中大多数是围绕试验展开的,涉及岩石MHC耦合模型及相关数值程序方面的研究相对较少,如何建立岩石应力-渗流-化学耦合作用的定量关系和数学模型,仍是一个亟待解决的问题和难题。考虑应力场、渗流场、化学场三者的耦合作用,根据力学损伤变量和水化学损伤变量推导岩石弹塑性MHC耦合损伤变量。①基于已有试验研究得出的水化学损伤与超声波速之间的经验公式给出水化学损伤变量的动态演化规律。以耦合损伤变量代替力学损伤变量,采用所编制的弹塑性损伤MH耦合程序进行数值计算,此耦合属于单向耦合方式,只能够反映出水化学场对应力场、渗流场的作用。②基于水化学动力学的计算,采用孔隙度的形式给出水化学损伤变量,将岩石弹塑性损伤MH耦合程序与水化学动力学软件phreeqc结合,开发岩石弹塑性损伤MHC耦合程序,此耦合方式属于松弛耦合方式,通过耦合损伤变量将化学场与应力场、渗流场联系起来,能够反映三场之间的相互作用及影响,采用该程序对受水化学溶液作用影响的问题进行模拟计算。最后对贵阳地铁1号线下穿南明河段隧道进行数值模拟。
Most rock engineerings are not occur in a single geological environment, but in a more complex environment, such as:mechanical field (Mechanical, M), hydrological field (Hydrological, H), thermal field (Thermal, T) and chemical field (Chemical, C). The interaction between them constitutes the hot issues of international society for rock mechanics, namely "multi-field coupling problems of rock". The mechanical-hydrolo-gical-chemical (MHC) coupling problem of rock engineering under the action of load and water-rock has become important increasingly with the large-scale construction of rock engineering in China. In this paper, the numerical calculation method as the priority, the test means as the auxiliary, the elastoplastic damage and MHC coupling problem as the main research content, the program development as clue to research of implementation issues layer of progressive, the interaction between multi-field coupling, failure mechanism as the research target, Dalian subway tunnel engineering, Jilin FuSong tunnel engineering, Guiyang subway tunnel engineering as the background in order to reflect the significance and the value of research work.
Based on the national natural science fund project (No.51079010:Research of Damage Mechanism and Model of Seabed Rock Excavation with the Mechanical-Hydrological Coupling) and the excellent doctor dissertation fund project of Dalian Maritime University (No.2013YB03:MHC and Damage Coupling Mechanism Test and the Model Research of Tunnel Surrounding Rock under the Action of Seawater), to carry out the research around "the rock elastoplastic damage and MHC coupling problem." Specific to divide it into5subproblems, rock ultrasonic damage, frost heaving force and permeability test, rock elastoplastic softening, damage model establishment and numerical algorithm, rock elastoplastic damage and MH coupling model and program implementation, rock elastoplastic damage and MHC coupling model and program implementation. At the same time, the parameter inversion problem is studied in order to accurately calculate and solve the bottleneck of parameters uncertain in complex model. Mainly in the following research work:
(1) Compression process of rock with micro crack closure, initiation, extension and penetration, the macro performance deformation and failure process of rock. Acoustic wave velocity as the change law of damage, destruction in the process, using the change law to predict the stability of rock engineering structural has important significance. Testing acoustic wave velocity without stress state and stress state under the dry and saturated fractured schist and wave velocity vary with compressional strain response from the perspective of acoustic wave velocity. Full water wave characteristics of rock and the relationship between the change of wave speed and rock damage, fracture are analyzed. At the same time, fracture and damage of the full water schist are analyed, the tip of the radius of plastic zone of Drucker-Prager criterion is deduced. About fill water rock frost heaving force test device, the report of the ring seepage-stress coupling of rock permeability testing device is also rare. In order to study the frost heaving damage and the change rule of permeability of rock under the ring seepage-stress coupling, the corresponding test apparatus are developed. Different freezing and thawing temperature, moisture content of rock, frost heaving force under the conditions of different freeze-thaw cycles test are conducted using the saturated rock frost heaving force test device. Permeability tests are conducted under the conditions of different osmotic pressure and axial compression using the ring seepage-stress coupling device.
(2) Set up elastoplastic damage and MHC coupling application framework of rock, each part of the program is developed separately adopting the idea of modularization, and then call each other according to certain rules, constitute an organic whole in this way which provide the numerical calculation method for multi-field coupling problems of rock. The corresponding solving program is compiled using C++language and using object-oriented programming method, based on fully implicit return mapping algorithm (Fully implicit return mapping algorithm) of von Mises constitutive model and Drucker Prager constitutive model as well as the corresponding to the Consistent tangent modulus (Consistent tangent modulus). It is the dominant mechanical basic parts program. Return mapping algorithm can avoid the drift phenomenon of the trial stress, and achieve the accurate solution of the constitutive equation on the condition of the quasi-static deformation, a quadratic convergence rate when using the Newton-Raphson iteration scheme, higher accuracy and stability. The results show that the superiority of the algorithm, and the correctness and the practicality of the program. The coupling procedure of the rock elastoplastic damage and MHC is embedded in differential evolution algorithm (Differential evolution algorithm, DE), then an intelligent back analysis program is developed. The computational efficiency and correctness of the relevant procedure is verification. It is applied in the practical engineering.
(3) Softening and damage characteristics of rock have important influence on seepage field and chemical field. While researching the coupling problem of rock elastoplastic damage and MHC, rock softening and damage characteristics are studied firstly. Establish corresponding constitutive model and develop the solution program for it. Strain softening problem in geotechnical engineering and the difficult solution problem of the finite element numerical calculation due to the negative tangent stiffness of strain softening model are studied in this article. First of all, the elastoplastic strain softening constitutive model of rock is established based on the Drucker-Prager strength criteria. Then, consider the shortcomings of low efficiency of the arc-length method in judging stiffness matrix, Newton-Raphson scheme and arc-length method are combined to use in the iterative calculation of elastoplastic incremental finite element equations. Namely Newton-Raphson scheme is used before the structure reaches the limit load, and when the structure is close to the limit load turn to the arc-length method, so that the structure over the peak point ino the softening region until destruction. NR-AL method has the advantages of both in the iterative solution. Finally, a program of the built strain softening model and elastoplastic incremental finite element to solve the constitutive equation for the iterative process is compiled using C++language. The program is applied in numerical calculation, and the stress-strain curves of the idealied elastoplastic model, strain softening and strain hardening model based on the Drucker-Prager strength criteria are comparative analyzed. The research results show that the strain softening constitutive model can simulate the characteristics after the post-peak softening of rock material well, and it can reveal the features of the post-peak strain softening and failure mechanism. NR-AL method can solve the negative stiffness problem caused by strain softening and also overcome the shortcomings of low efficiency in judging stiffness matrix using the arc-length only.
(4) In practical tunnel construction, the stress redistribution of underground rock is caused by tunnel excavation, which is usually made of microcrack of surrounding rock extension damage and accompanied the plastic flow deformation. In order to study the coupling effect of two kinds of failure mechanism which are the stiffness degradation caused by the damage and the flow caused by the plastic, from the perspective of elastoplastic mechanics and damage theory, the correction formula of effective stress is introduced to consider the role of the pore water pressure.The elastoplastic damage constitutive model is established based on the Drucker-Prager yield criterion.The most elastoplastic damage model involve in the problems of much parameters and not easy to determine. The damage parameters are given by back analysis method to solve the problem of damage model parameters are difficult to determine; The elastoplastic damage constitutive solver is compiled by adopting the method of object-oriented programming using C++language, and the experiment and numerical verification have carried on for two aspects of the established elastoplastic damage model and the program; Finally its application in Jilin FuSong tunnel project, the development and change of the plastic zone and the damage zone are simulated. The results show that the established elastoplastic damage constitutive model can describe the mechanical properties, plasticity and damage change trend of the rock well, and the practical engineering problems can be simulate by the program to give certain guidance to the site construction. The research of numerical computing problem involving coupled elastoplastic damage of the complex material not only need to select the appropriate constitutive model to forecast damage, but also need to be a robust and effective constitutive integration algorithm. The basic steps of seting up the elastoplastic damage constitutive model are expounded in the framework of thermodynamics and continuum mechanics. The finite element solving program of the constitutive is compiled using C++language in Visual6.0environment, which is based on Lemaitre's isotropic hardening coupled elastoplastic damage constitutive model, the corresponding constitutive integration algorithm-fully implicit return mapping algorithm and the consistent tangent modulus. The constitutive equation is needed to solve a nonlinear scalar equation, and the form of the constitutive equation improving computational efficiency is simple relatively. The validity of the application program is demonstrated through a numerical example of a cylindrical notched bar. Enrich the constitutive model of dominant mechanical program in the elastoplastic damage and MHC coupling program of rock, provide ways and means for the study of damage and other problems of rock material.
(5) It is more likely to cause the collapse of tunnel surrounding rock and water disasters under the action of the coupling effect of the groundwater seepage field, the stress field and the damage field. First of all, surrounding rock is regarded as the isotropic continuum material, and the elastoplastic damage constitutive model of rock is established based on the criterion of Drucker Prager. The fully implicit return mapping algorithm is adopted to achieve the numerical solution of elastoplastic damage constitutive equations. Secondly, according to the dynamic evolution formula of permeability coefficient in elastoplastic state based on the above research, the elasoplastic damage and MHC model of rock is established, and the coupling solving iterative method of many fields is presented. Back analysis program is compiled on the basis of the principle of differential evolution algorithm in order to solve the problem that elastoplastic damage model involves many parameters and not easy to determine, and the damage parameters are inversion; Finally, compile the corresponding coupling program of the elastoplastic damage and MHC and parameters inversion program using C++language respectively, the following calculations are conducted by using the program:①The calculation results of the displacement field and the stress field by the elastic model and the elastoplastic model are compared.②The pore water pressure and the seepage flow are calculated without considering the effect of mechanics.③The interaction rules of stress field, seepage field and damage field of tunnel surrounding rock are calculated using the coupling model. Results show that the macro failure of rock material can be more realistically reflect through the interaction of the stress, the seepage and the damage of the built coupling model. The calculation program which provides a method for the engineering construction affected by groundwater severely can simulate the coupling characteristics of groundwater seepage field, stress field and damage field. The stability of surrounding rock of the Dalian Maritime University subway test line over the river in the process of tunnel construction is calculated by the numerical program.
(6) Research on MHC coupling proplem of rock is relatively small, it mostly revolves around test, and involving MHC coupling model of rock and relevant numerical program are relatively small. How to build a quantitative relationship and mathematical model considering the coupling effect of MHC of rock is still a urgently settled problem. Considering the coupling effect of stress field, seepage field and chemical field, MHC coupling damage variable is deduced according to the mechanical damage variable and the water chemical damage variable.①Given the dynamic evolution of the damage variable water chemistry empirical formula based on water chemistry damage between ultrasonic velocity from the results of experimental studies. The coupling damage variable is instead by the mechanical damage variable, and the numerical calculation is conducted by elastoplastic damage and MH coupling program. This coupling mode belongs to the unidirectional coupling mode, it can reflect the chemical field corresponds to the force field, seepage field only.②The water chemical damage variable is given in the form of porosity based on the calculation of chemical kinetics, and the elastoplastic damage and MHC coupling program of rock is developed combination the elastoplastic damage and MH coupling program and the water chemical dynamics software phreeqc. The coupling mode belongs to the relaxation coupling mode. The simulated calculation of the chemical corrosion problems is conducted. The results show that the deformation and the stress characteristics under the multi-field coupling condition can be analysis with this method to provide reference and basis for engineering. Finally, the tunnel of Guiyang Metro Line1under the Nanming river is simulated.
本文在国家自然科学基金资助项目(No.51079010：渗流-应力耦合海床基岩开挖损伤机理和模型研究)和大连海事大学全国优秀博士学位论文培育基金资助项目(No.2013YB03：海水作用下隧道围岩MHC损伤耦合机理试验及模型研究)下围绕“岩石弹塑性损伤MHC耦合问题”开展研究,具体将其细化为5个子问题进行研究,岩石超声损伤、冻胀力及渗透性试验,岩石弹塑性软化、损伤模型建立及数值算法,岩石弹塑性损伤MH耦合模型及程序实施,岩石弹塑性损伤MHC耦合模型及程序实施,同时为了准确的进行计算,解决复杂模型中参数无法确定的瓶颈,进行参数反演研究。具体开展以下研究工作：
(1)岩石压缩过程伴随着岩石微裂纹闭合、萌生、扩展和贯通等,宏观表现为岩石变形、破坏过程。在此过程中声波波速随着损伤、破坏表现出一定的变化规律,运用这种变化规律预测岩体工程结构稳定性有着重要的意义。从声波波速的角度出发,测试无受力和受力状态下干燥、饱水裂隙片岩的纵波波速,研究饱水天然裂隙片岩的波速特性及压缩全过程中波速随应变的变化规律,波速变化与岩石损伤、破裂之间的内在关系。同时进行受压饱水裂隙片岩断裂与损伤分析,基于张开型裂纹推导Drucker-Prager准则的尖端塑性区半径,以此反应压缩过程中产生的水压力对尖端塑性区的影响。关于岩石饱水冻胀力试验装置、环向渗流-应力耦合岩石渗透性试验装置还鲜见报道,为了研究岩石冻胀损伤及环向渗流-应力耦合下渗透性的变化规律问题,自主研制相应试验装置。采用饱水岩石冻胀力试验装置进行不同冻融温度、不同岩石含水率、不同冻融循环次数条件下岩石冻胀力测试试验。采用环向渗流-应力耦合岩石渗透性试验装置进行不同渗透压、不同轴压条件下岩石渗透性试验。
(2)搭建岩石弹塑性损伤MHC耦合程序框架,采用模块化的思想,分别针对各部分程序进行开发,然后按照一定的规则相互调用,以这种方式构成一个有机整体,为开展岩石多场耦合问题提供数值计算手段。基于von Mises本构模型、Drucker-Prager本构模型的完全隐式返回映射算法(Fully implicit return mapping algorithm)以及相对应的一致切线模量(Consistent tangent modulus),采用面向对象的编程方法,利用C++语言编制相应求解程序,作为主控力学程序基本部分。返回映射算法可避免预测应力漂移屈服面的现象,对于准静态变形条件下的本构方程可以获得准确的解,在迭代中使用Newton-Raphson法可获得近似平方的收敛速度,具有较高的精确性和稳定性。结果表明算法的优越性、程序的正确性和工程中的实用性,具有一定的理论价值和实际意义。将岩石弹塑性损伤MHC耦合程序嵌入到差异进化算法(Differential evolution algorithm,DE)中,开发智能反分析程序,对相关程序的计算效率、正确性等进行验证,并在实际工程中应用。
(3)岩石的软化、损伤特性对渗流场、化学场有重要影响,在展开岩石弹塑性损伤MHC耦合问题研究时,针对岩石软化、损伤特性进行研究,建立相应本构模型并开发求解程序。关于岩土工程材料应变软化问题及有限元对其数值计算时切线刚度矩阵负定造成求解困难的问题进行研究。首先,建立基于Drucker-Prager强度准则的岩石弹塑性应变软化本构模型。其次,考虑弧长法在判断切线刚度矩阵正定性导致效率低的缺点,在弹塑性增量有限元方程的迭代计算中尝试采用Newton-Raphson法和Arc-Length法(NR-AL法)联合迭代求解的思路,即在结构未达到极限荷载前采用Newton-Raphson迭代法,而当结构接近极限荷载时转换为Arc-Length法控制迭代,从而使结构越过峰值点进入软化区直至破坏,NR-AL法汲取了2者迭代求解中具有的优势。最后,利用C++语言对所建应变软化模型的本构求解和弹塑性增量有限元方程迭代求解过程给予程序实现,应用所编程序进行数值计算,分析Drucker-Prager理想弹塑性模型、应变软化模型、应变硬化模型计算的应力-应变曲线的区别,同时将应变软化模型计算结果与试验数据进行对比。研究结果表明所建应变软化本构模型可以较好地模拟岩石材料的峰后软化特性,能够揭示峰后应变软化特性和破坏机制,NR-AL法能够求解由于应变软化造成的负刚度问题,也克服了单独使用弧长法时判断切线刚度矩阵正定性效率低的缺点。
(4)在实际隧道施工过程中,隧道开挖引起地下岩体应力重分布使得围岩的微裂纹扩展损伤,并伴随有塑性流动变形。为研究损伤引起的刚度退化和塑性导致的流动两种破坏机制的耦合作用,从弹塑性力学和损伤理论的角度出发,同时引入修正有效应力原理来考虑孔隙水压力的作用,建立基于Drucker-Prager屈服准则的弹塑性损伤本构模型。针对该本构模型推导了孔隙水压力作用下弹塑性损伤本构模型的数值积分算法-隐式返回映射算法。大多数弹塑性损伤模型中涉及参数多且不易确定的问题,采用反分析方法获得损伤参数,解决损伤模型参数不易确定的难题。采用面向对象的编程方法使用C++语言编制了弹塑性损伤本构求解程序,并对所建弹塑性损伤模型和所编程序进行试验和数值两方面的验证；最后将其在吉林抚松隧道工程中进行应用,模拟了塑性区和损伤区的发展变化。研究结果表明所建立弹塑性伤损本构模型能够较好地描述岩石的力学性能、塑性和损伤变化趋势,所编程序能够进行实际工程问题的模拟,对现场施工给予一定的指导。同时基于Lemaitre等向硬化弹塑性损伤耦合本构模型,采用C++语言在Visual6.0环境下编制有限元本构求解程序,在塑性损伤修正步中求解返回映射方程时,选取一种简单的形式,只需迭代求解一个标量非线性方程,计算效率较高。通过缺口圆棒数值算例初步验证了程序的正确性。同时丰富了岩石弹塑性损伤MHC耦合程序中主控力学程序的本构模型,为研究岩石等材料损伤问题提供方法和途径。
(5)在地下水渗流场、应力场、损伤场的耦合作用下,更易造成隧道围岩坍塌或涌水等灾害。首先,将围岩材料视作各向同性连续介质,采用基于前文Drucker-Prager准则建立岩石弹塑性损伤本构模型进行数值求解。其次,根据岩石处于弹塑性状态时渗透系数动态演化公式,建立岩石弹塑性损伤MH耦合模型,并给出三场耦合情况下的数值求解迭代方法。同时针对耦合模型中涉及参数较多且不易测定的问题,基于前文差异进化算法原理建立的智能反分析方法,对耦合模型中的损伤参数进行反演。最后,利用C++语言编制相应的岩石弹塑性损伤MH耦合程序,利用所编程序进行以下计算：①分别采用弹性模型和弹塑性损伤模型进行隧道围岩位移场、应力场的计算。②不考虑力学作用的情况下进行孔隙水压力、渗流量的计算。③采用所建耦合模型计算得到隧道围岩应力场、渗流场以及损伤场的相互影响规律。研究结果表明所建立的耦合模型通过应力、渗流和损伤的相互作用更能够真实地反映出岩石材料的宏观破坏现象,所编计算程序能够模拟地下水渗流场、应力场、损伤场之间的耦合特性,为受地下水影响严重的工程建设提供了方法。采用上述所建模型及程序对大连地铁海事大学试验线路过河段隧道施工过程中的围岩稳定性进行计算。
(6)关于岩石MHC耦合的研究相对较少,这其中大多数是围绕试验展开的,涉及岩石MHC耦合模型及相关数值程序方面的研究相对较少,如何建立岩石应力-渗流-化学耦合作用的定量关系和数学模型,仍是一个亟待解决的问题和难题。考虑应力场、渗流场、化学场三者的耦合作用,根据力学损伤变量和水化学损伤变量推导岩石弹塑性MHC耦合损伤变量。①基于已有试验研究得出的水化学损伤与超声波速之间的经验公式给出水化学损伤变量的动态演化规律。以耦合损伤变量代替力学损伤变量,采用所编制的弹塑性损伤MH耦合程序进行数值计算,此耦合属于单向耦合方式,只能够反映出水化学场对应力场、渗流场的作用。②基于水化学动力学的计算,采用孔隙度的形式给出水化学损伤变量,将岩石弹塑性损伤MH耦合程序与水化学动力学软件phreeqc结合,开发岩石弹塑性损伤MHC耦合程序,此耦合方式属于松弛耦合方式,通过耦合损伤变量将化学场与应力场、渗流场联系起来,能够反映三场之间的相互作用及影响,采用该程序对受水化学溶液作用影响的问题进行模拟计算。最后对贵阳地铁1号线下穿南明河段隧道进行数值模拟。
Most rock engineerings are not occur in a single geological environment, but in a more complex environment, such as:mechanical field (Mechanical, M), hydrological field (Hydrological, H), thermal field (Thermal, T) and chemical field (Chemical, C). The interaction between them constitutes the hot issues of international society for rock mechanics, namely "multi-field coupling problems of rock". The mechanical-hydrolo-gical-chemical (MHC) coupling problem of rock engineering under the action of load and water-rock has become important increasingly with the large-scale construction of rock engineering in China. In this paper, the numerical calculation method as the priority, the test means as the auxiliary, the elastoplastic damage and MHC coupling problem as the main research content, the program development as clue to research of implementation issues layer of progressive, the interaction between multi-field coupling, failure mechanism as the research target, Dalian subway tunnel engineering, Jilin FuSong tunnel engineering, Guiyang subway tunnel engineering as the background in order to reflect the significance and the value of research work.
Based on the national natural science fund project (No.51079010:Research of Damage Mechanism and Model of Seabed Rock Excavation with the Mechanical-Hydrological Coupling) and the excellent doctor dissertation fund project of Dalian Maritime University (No.2013YB03:MHC and Damage Coupling Mechanism Test and the Model Research of Tunnel Surrounding Rock under the Action of Seawater), to carry out the research around "the rock elastoplastic damage and MHC coupling problem." Specific to divide it into5subproblems, rock ultrasonic damage, frost heaving force and permeability test, rock elastoplastic softening, damage model establishment and numerical algorithm, rock elastoplastic damage and MH coupling model and program implementation, rock elastoplastic damage and MHC coupling model and program implementation. At the same time, the parameter inversion problem is studied in order to accurately calculate and solve the bottleneck of parameters uncertain in complex model. Mainly in the following research work:
(1) Compression process of rock with micro crack closure, initiation, extension and penetration, the macro performance deformation and failure process of rock. Acoustic wave velocity as the change law of damage, destruction in the process, using the change law to predict the stability of rock engineering structural has important significance. Testing acoustic wave velocity without stress state and stress state under the dry and saturated fractured schist and wave velocity vary with compressional strain response from the perspective of acoustic wave velocity. Full water wave characteristics of rock and the relationship between the change of wave speed and rock damage, fracture are analyzed. At the same time, fracture and damage of the full water schist are analyed, the tip of the radius of plastic zone of Drucker-Prager criterion is deduced. About fill water rock frost heaving force test device, the report of the ring seepage-stress coupling of rock permeability testing device is also rare. In order to study the frost heaving damage and the change rule of permeability of rock under the ring seepage-stress coupling, the corresponding test apparatus are developed. Different freezing and thawing temperature, moisture content of rock, frost heaving force under the conditions of different freeze-thaw cycles test are conducted using the saturated rock frost heaving force test device. Permeability tests are conducted under the conditions of different osmotic pressure and axial compression using the ring seepage-stress coupling device.
(2) Set up elastoplastic damage and MHC coupling application framework of rock, each part of the program is developed separately adopting the idea of modularization, and then call each other according to certain rules, constitute an organic whole in this way which provide the numerical calculation method for multi-field coupling problems of rock. The corresponding solving program is compiled using C++language and using object-oriented programming method, based on fully implicit return mapping algorithm (Fully implicit return mapping algorithm) of von Mises constitutive model and Drucker Prager constitutive model as well as the corresponding to the Consistent tangent modulus (Consistent tangent modulus). It is the dominant mechanical basic parts program. Return mapping algorithm can avoid the drift phenomenon of the trial stress, and achieve the accurate solution of the constitutive equation on the condition of the quasi-static deformation, a quadratic convergence rate when using the Newton-Raphson iteration scheme, higher accuracy and stability. The results show that the superiority of the algorithm, and the correctness and the practicality of the program. The coupling procedure of the rock elastoplastic damage and MHC is embedded in differential evolution algorithm (Differential evolution algorithm, DE), then an intelligent back analysis program is developed. The computational efficiency and correctness of the relevant procedure is verification. It is applied in the practical engineering.
(3) Softening and damage characteristics of rock have important influence on seepage field and chemical field. While researching the coupling problem of rock elastoplastic damage and MHC, rock softening and damage characteristics are studied firstly. Establish corresponding constitutive model and develop the solution program for it. Strain softening problem in geotechnical engineering and the difficult solution problem of the finite element numerical calculation due to the negative tangent stiffness of strain softening model are studied in this article. First of all, the elastoplastic strain softening constitutive model of rock is established based on the Drucker-Prager strength criteria. Then, consider the shortcomings of low efficiency of the arc-length method in judging stiffness matrix, Newton-Raphson scheme and arc-length method are combined to use in the iterative calculation of elastoplastic incremental finite element equations. Namely Newton-Raphson scheme is used before the structure reaches the limit load, and when the structure is close to the limit load turn to the arc-length method, so that the structure over the peak point ino the softening region until destruction. NR-AL method has the advantages of both in the iterative solution. Finally, a program of the built strain softening model and elastoplastic incremental finite element to solve the constitutive equation for the iterative process is compiled using C++language. The program is applied in numerical calculation, and the stress-strain curves of the idealied elastoplastic model, strain softening and strain hardening model based on the Drucker-Prager strength criteria are comparative analyzed. The research results show that the strain softening constitutive model can simulate the characteristics after the post-peak softening of rock material well, and it can reveal the features of the post-peak strain softening and failure mechanism. NR-AL method can solve the negative stiffness problem caused by strain softening and also overcome the shortcomings of low efficiency in judging stiffness matrix using the arc-length only.
(4) In practical tunnel construction, the stress redistribution of underground rock is caused by tunnel excavation, which is usually made of microcrack of surrounding rock extension damage and accompanied the plastic flow deformation. In order to study the coupling effect of two kinds of failure mechanism which are the stiffness degradation caused by the damage and the flow caused by the plastic, from the perspective of elastoplastic mechanics and damage theory, the correction formula of effective stress is introduced to consider the role of the pore water pressure.The elastoplastic damage constitutive model is established based on the Drucker-Prager yield criterion.The most elastoplastic damage model involve in the problems of much parameters and not easy to determine. The damage parameters are given by back analysis method to solve the problem of damage model parameters are difficult to determine; The elastoplastic damage constitutive solver is compiled by adopting the method of object-oriented programming using C++language, and the experiment and numerical verification have carried on for two aspects of the established elastoplastic damage model and the program; Finally its application in Jilin FuSong tunnel project, the development and change of the plastic zone and the damage zone are simulated. The results show that the established elastoplastic damage constitutive model can describe the mechanical properties, plasticity and damage change trend of the rock well, and the practical engineering problems can be simulate by the program to give certain guidance to the site construction. The research of numerical computing problem involving coupled elastoplastic damage of the complex material not only need to select the appropriate constitutive model to forecast damage, but also need to be a robust and effective constitutive integration algorithm. The basic steps of seting up the elastoplastic damage constitutive model are expounded in the framework of thermodynamics and continuum mechanics. The finite element solving program of the constitutive is compiled using C++language in Visual6.0environment, which is based on Lemaitre's isotropic hardening coupled elastoplastic damage constitutive model, the corresponding constitutive integration algorithm-fully implicit return mapping algorithm and the consistent tangent modulus. The constitutive equation is needed to solve a nonlinear scalar equation, and the form of the constitutive equation improving computational efficiency is simple relatively. The validity of the application program is demonstrated through a numerical example of a cylindrical notched bar. Enrich the constitutive model of dominant mechanical program in the elastoplastic damage and MHC coupling program of rock, provide ways and means for the study of damage and other problems of rock material.
(5) It is more likely to cause the collapse of tunnel surrounding rock and water disasters under the action of the coupling effect of the groundwater seepage field, the stress field and the damage field. First of all, surrounding rock is regarded as the isotropic continuum material, and the elastoplastic damage constitutive model of rock is established based on the criterion of Drucker Prager. The fully implicit return mapping algorithm is adopted to achieve the numerical solution of elastoplastic damage constitutive equations. Secondly, according to the dynamic evolution formula of permeability coefficient in elastoplastic state based on the above research, the elasoplastic damage and MHC model of rock is established, and the coupling solving iterative method of many fields is presented. Back analysis program is compiled on the basis of the principle of differential evolution algorithm in order to solve the problem that elastoplastic damage model involves many parameters and not easy to determine, and the damage parameters are inversion; Finally, compile the corresponding coupling program of the elastoplastic damage and MHC and parameters inversion program using C++language respectively, the following calculations are conducted by using the program:①The calculation results of the displacement field and the stress field by the elastic model and the elastoplastic model are compared.②The pore water pressure and the seepage flow are calculated without considering the effect of mechanics.③The interaction rules of stress field, seepage field and damage field of tunnel surrounding rock are calculated using the coupling model. Results show that the macro failure of rock material can be more realistically reflect through the interaction of the stress, the seepage and the damage of the built coupling model. The calculation program which provides a method for the engineering construction affected by groundwater severely can simulate the coupling characteristics of groundwater seepage field, stress field and damage field. The stability of surrounding rock of the Dalian Maritime University subway test line over the river in the process of tunnel construction is calculated by the numerical program.
(6) Research on MHC coupling proplem of rock is relatively small, it mostly revolves around test, and involving MHC coupling model of rock and relevant numerical program are relatively small. How to build a quantitative relationship and mathematical model considering the coupling effect of MHC of rock is still a urgently settled problem. Considering the coupling effect of stress field, seepage field and chemical field, MHC coupling damage variable is deduced according to the mechanical damage variable and the water chemical damage variable.①Given the dynamic evolution of the damage variable water chemistry empirical formula based on water chemistry damage between ultrasonic velocity from the results of experimental studies. The coupling damage variable is instead by the mechanical damage variable, and the numerical calculation is conducted by elastoplastic damage and MH coupling program. This coupling mode belongs to the unidirectional coupling mode, it can reflect the chemical field corresponds to the force field, seepage field only.②The water chemical damage variable is given in the form of porosity based on the calculation of chemical kinetics, and the elastoplastic damage and MHC coupling program of rock is developed combination the elastoplastic damage and MH coupling program and the water chemical dynamics software phreeqc. The coupling mode belongs to the relaxation coupling mode. The simulated calculation of the chemical corrosion problems is conducted. The results show that the deformation and the stress characteristics under the multi-field coupling condition can be analysis with this method to provide reference and basis for engineering. Finally, the tunnel of Guiyang Metro Line1under the Nanming river is simulated.
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