数值流形方法研究及其在岩土工程中的应用
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摘要
数值流形方法是一种具有一般化意义的数值方法,能对连续变形与非连续变形问题进行统一求解,对问题具有较高的求解精度。同时,数值流形方法以覆盖技术为基础,为工程问题提供了一种更自然和简便的解决方法。数值流形方法是目前岩土工程数值分析方法的一个研究热点。
本文针对流形方法及其在岩土工程中的应用,并结合西部交通建设科技项目“红层软岩填石路堤不均匀沉降机理研究” 开展了对流形方法的研究工作,开展的工作及取得的研究成果主要有以下几个方面:。
(1)研究了材料裂隙及分层界线对流形元覆盖系统形成的影响,指出流形元数学网格必须与材料物理网格(裂隙及分层界线)相协调来构造流形元的覆盖系统,并建议了按此原理形成流形元覆盖系统的基本过程;
(2)基于流形单元上位移函数的组成,提出了流形方法中固定约束处理的新方法,在流形单元上构造能反映边界位移条件的位移函数使边界的固定约束条件得到自动满足,推导了相应的流形单元刚度矩阵及荷载矩阵的数值计算格式;
(3)基于有限覆盖技术,建立了全长粘结杆件的数值流形方法模型。该模型是一种新的杆件数值模型,它采用局部解析的位移模式,有较高的计算精度。该模型中,规则的网格可以适应杆件的复杂布局,没有数值模拟中杆件布置与单元划分相互制约的矛盾,且可以考虑杆件中施加预应力的情况。该模型可用于岩土锚杆和钢筋混凝土问题的模拟计算;
(4)系统的提出了数值流形方法对开挖卸荷问题的模拟方法。提出了流形元模拟开挖时覆盖系统的处理方法、不平衡力计算方法、使用高阶覆盖函数时对开挖的模拟方法及流形元对开挖模拟的一般过程,提出了开挖作用的直接分析法和间接分析法的概念。流形方法对岩土工程开挖卸荷问题的模拟比传统数值方法有更多的优点:①覆盖技术的使用,使简单的数学覆盖可以适应任意的开挖过程;②开挖作用的直接分析法使流形方法对开挖的模拟可以放弃开挖释放荷载的概念,使计算变得更自然、简便和可靠;③高阶的流形方法对开挖问题的模拟具更好的求解精度;
(5)针对“红层软岩填石路堤不均匀沉降机理研究”,推导了流形元与DDA的耦合计算方程,并提出了填石路堤工后变形的简化计算方法,首次使用完全非连续散体系统模型对填石路堤问题进行数值模拟分析,在模拟方法的研究上取得了一些有意义的成果,在一定程度上揭示了填石路堤变形的细观机理及规律。数值模拟的结果显示,填石路堤的不连续变形与不均匀变形明显,这与将填石体视
The numerical manifold method is a generalization numerical method, it is capable of uniformly dealing with the problem of continuous deformation and discontinuous deformation, and it has higher calculation precision for problem. At the same time, The numerical manifold method is based on finite cover, it is a simple and convenient resolvent for engineering problem. The numerical manifold method is pop method of research for the numerical method in geotechnical engineering.
Aim at the theory and application of numerical manifold method, and combine the west traffic construction scientific and technical project “study on non-uniformed settlement mechanism of rock-fill embankment of red-bed”, have researched the theory and application of numerical manifold method, works and research findings mainly has following aspects mainly:
(1) Have research the effects of crack and boundary line in rock mass to the generation of cover system for numerical manifold method, put forward that mathematical cover must suit with crack and boundary line in rock mass, and put forward corresponding method that form the cover system for numerical manifold method;
(2) Base on the composition of displacement function on manifold element, a new method of constraints treatment of fixed boundary is proposed, fixation constraint terms is strictly met by using corresponding cover function on the physical cover made up of the manifold element, deduce the corresponding numerical calculation format of manifold element’s stiffness matrix and load matrix with fixation constraint terms;
(3) Created numerical manifold model of fully bonded bar based on the limited cover technology of manifold method, this model is a new numerical model of bolt which use partially analytic displacement pattern. When use high-order cover function, it have feature of partial analytic solution and better calculation accuracy. At the same time, bolt and mathematics cover relatively independent, general grid can meet complex arrange of bolt, have eliminated the contradiction of mutual restriction between bolt disposal and grid partition in numerical simulation of bolt, and this model can consider to the case that exert prestressing force in anchor rod. This model can be used in simulating geotechnics bolt and analyzing the interaction of reinforcing bar and concrete;
(4) Have research the simulation of excavation with numerical manifold method.
Have research the treatment method of cover system and calculation method of unbalance force while simulate excavation with manifold method, and have research the simulation method for excavation while use high-order cover function, finally have made general course of simulation of excavation with manifold method. Have made the direct analysis and indirect analysis of excavation action, and have discussed their relation in detail. The manifold method have more merits than FEM while apply in excavation: ①based on cover technology, simple grid can meet the arbitrary course of excavation; ②the direct analysis of excavation can give up the concept of released load, the simulation course is simpler and more natural and more reliable; ③high-order manifold have better precision for excavation; (5) Aim at “study on non-uniformed settlement mechanism of rock-fill embankment of red-bed”, research the coupling problem of numerical manifold method and DDA, put forward the simplified calculation method of the settlement after construction of full-rock embankment, used this completely discontinuous system study for rock fill problem for the first time, have disclosure microscopic the mechanism and law of displacement of fill-rock embankment in some degree. The simulation result display that the uneven and discontinuity of embankment displacement is obvious, it have greatly difference from condition considered rock fill as equivalent continuum. Have carried out numerical simulated analysis for the sensitivity of various factors that affects deformation of embankment, the reduction of friction coefficient between rock block and reduction of deformation parameter of rock have greater influence for deformation of embankment after construction, but the deformation form and law caused by them is different, the influence of reduction of rock block is very little. (6) Programmed the Object-Oriented program with C++ language in VC++ platform, it is capable of calculating the common problem of manifold method, fully bonded bar and excavation etc. The program have better preprocess and postprocess function. And the program have been proved correct by example. At the same time, programmed calculation program EDAnalysis according to “study on non-uniformed settlement mechanism of rock-fill embankment of red-bed”, EDAnalysis have better preprocess and postprocess and the function of dynamic simulation.
本文针对流形方法及其在岩土工程中的应用,并结合西部交通建设科技项目“红层软岩填石路堤不均匀沉降机理研究” 开展了对流形方法的研究工作,开展的工作及取得的研究成果主要有以下几个方面:。
(1)研究了材料裂隙及分层界线对流形元覆盖系统形成的影响,指出流形元数学网格必须与材料物理网格(裂隙及分层界线)相协调来构造流形元的覆盖系统,并建议了按此原理形成流形元覆盖系统的基本过程;
(2)基于流形单元上位移函数的组成,提出了流形方法中固定约束处理的新方法,在流形单元上构造能反映边界位移条件的位移函数使边界的固定约束条件得到自动满足,推导了相应的流形单元刚度矩阵及荷载矩阵的数值计算格式;
(3)基于有限覆盖技术,建立了全长粘结杆件的数值流形方法模型。该模型是一种新的杆件数值模型,它采用局部解析的位移模式,有较高的计算精度。该模型中,规则的网格可以适应杆件的复杂布局,没有数值模拟中杆件布置与单元划分相互制约的矛盾,且可以考虑杆件中施加预应力的情况。该模型可用于岩土锚杆和钢筋混凝土问题的模拟计算;
(4)系统的提出了数值流形方法对开挖卸荷问题的模拟方法。提出了流形元模拟开挖时覆盖系统的处理方法、不平衡力计算方法、使用高阶覆盖函数时对开挖的模拟方法及流形元对开挖模拟的一般过程,提出了开挖作用的直接分析法和间接分析法的概念。流形方法对岩土工程开挖卸荷问题的模拟比传统数值方法有更多的优点:①覆盖技术的使用,使简单的数学覆盖可以适应任意的开挖过程;②开挖作用的直接分析法使流形方法对开挖的模拟可以放弃开挖释放荷载的概念,使计算变得更自然、简便和可靠;③高阶的流形方法对开挖问题的模拟具更好的求解精度;
(5)针对“红层软岩填石路堤不均匀沉降机理研究”,推导了流形元与DDA的耦合计算方程,并提出了填石路堤工后变形的简化计算方法,首次使用完全非连续散体系统模型对填石路堤问题进行数值模拟分析,在模拟方法的研究上取得了一些有意义的成果,在一定程度上揭示了填石路堤变形的细观机理及规律。数值模拟的结果显示,填石路堤的不连续变形与不均匀变形明显,这与将填石体视
The numerical manifold method is a generalization numerical method, it is capable of uniformly dealing with the problem of continuous deformation and discontinuous deformation, and it has higher calculation precision for problem. At the same time, The numerical manifold method is based on finite cover, it is a simple and convenient resolvent for engineering problem. The numerical manifold method is pop method of research for the numerical method in geotechnical engineering.
Aim at the theory and application of numerical manifold method, and combine the west traffic construction scientific and technical project “study on non-uniformed settlement mechanism of rock-fill embankment of red-bed”, have researched the theory and application of numerical manifold method, works and research findings mainly has following aspects mainly:
(1) Have research the effects of crack and boundary line in rock mass to the generation of cover system for numerical manifold method, put forward that mathematical cover must suit with crack and boundary line in rock mass, and put forward corresponding method that form the cover system for numerical manifold method;
(2) Base on the composition of displacement function on manifold element, a new method of constraints treatment of fixed boundary is proposed, fixation constraint terms is strictly met by using corresponding cover function on the physical cover made up of the manifold element, deduce the corresponding numerical calculation format of manifold element’s stiffness matrix and load matrix with fixation constraint terms;
(3) Created numerical manifold model of fully bonded bar based on the limited cover technology of manifold method, this model is a new numerical model of bolt which use partially analytic displacement pattern. When use high-order cover function, it have feature of partial analytic solution and better calculation accuracy. At the same time, bolt and mathematics cover relatively independent, general grid can meet complex arrange of bolt, have eliminated the contradiction of mutual restriction between bolt disposal and grid partition in numerical simulation of bolt, and this model can consider to the case that exert prestressing force in anchor rod. This model can be used in simulating geotechnics bolt and analyzing the interaction of reinforcing bar and concrete;
(4) Have research the simulation of excavation with numerical manifold method.
Have research the treatment method of cover system and calculation method of unbalance force while simulate excavation with manifold method, and have research the simulation method for excavation while use high-order cover function, finally have made general course of simulation of excavation with manifold method. Have made the direct analysis and indirect analysis of excavation action, and have discussed their relation in detail. The manifold method have more merits than FEM while apply in excavation: ①based on cover technology, simple grid can meet the arbitrary course of excavation; ②the direct analysis of excavation can give up the concept of released load, the simulation course is simpler and more natural and more reliable; ③high-order manifold have better precision for excavation; (5) Aim at “study on non-uniformed settlement mechanism of rock-fill embankment of red-bed”, research the coupling problem of numerical manifold method and DDA, put forward the simplified calculation method of the settlement after construction of full-rock embankment, used this completely discontinuous system study for rock fill problem for the first time, have disclosure microscopic the mechanism and law of displacement of fill-rock embankment in some degree. The simulation result display that the uneven and discontinuity of embankment displacement is obvious, it have greatly difference from condition considered rock fill as equivalent continuum. Have carried out numerical simulated analysis for the sensitivity of various factors that affects deformation of embankment, the reduction of friction coefficient between rock block and reduction of deformation parameter of rock have greater influence for deformation of embankment after construction, but the deformation form and law caused by them is different, the influence of reduction of rock block is very little. (6) Programmed the Object-Oriented program with C++ language in VC++ platform, it is capable of calculating the common problem of manifold method, fully bonded bar and excavation etc. The program have better preprocess and postprocess function. And the program have been proved correct by example. At the same time, programmed calculation program EDAnalysis according to “study on non-uniformed settlement mechanism of rock-fill embankment of red-bed”, EDAnalysis have better preprocess and postprocess and the function of dynamic simulation.
引文
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