本文選題：裂隙巖體 + 非平衡演化�。� 參考：《清華大學(xué)》2013年博士論文

【摘要】：天然巖石受不同尺度節(jié)理、裂隙切割，構(gòu)成裂隙巖體復(fù)合介質(zhì)。各種裂隙巖體進(jìn)一步構(gòu)成大規(guī)模巖體工程結(jié)構(gòu)。我國巖石工程規(guī)模與復(fù)雜度迅速增長，巖體工程結(jié)構(gòu)穩(wěn)定性問題突出。本文采用動態(tài)演化觀點研究巖體結(jié)構(gòu)穩(wěn)定與控制問題，提出相對完整的巖體結(jié)構(gòu)非平衡演化研究體系，重點研究該體系數(shù)學(xué)與力學(xué)相關(guān)理論基礎(chǔ)。主要工作與創(chuàng)新性成果如下： (1)非平衡態(tài)熱力學(xué)基礎(chǔ)研究：證明齊次Onsager流必然全等次，從而證明基于齊次Onsager流的Rice正則結(jié)構(gòu)等價于Ziegler最大耗散率原理；該結(jié)論表明巖土類材料本構(gòu)關(guān)系熱力學(xué)基礎(chǔ)需要建立在有旋熱力學(xué)流范圍。 (2)方向分布函數(shù)與組構(gòu)張量：提出最一般形式的方向分布函數(shù)——張量型方向分布函數(shù)，建立其相對完備的組構(gòu)張量代數(shù)，，包括非對稱與全對稱組構(gòu)張量解析解、收斂性與擬合精度、不同階組構(gòu)張量關(guān)系等。 (3) Kachanov-Rabotnov (K-R)損傷有效應(yīng)力：基于矢量型方向分布函數(shù)建立K-R損傷有效應(yīng)力三維各向異性微平面模型，實現(xiàn)嚴(yán)格宏—細(xì)觀幾何等效原理；該模型澄清連續(xù)體損傷力學(xué)若干基本問題，包括常用各向異性與各向同性有效應(yīng)力模型適用條件、損傷效應(yīng)張量正定性與Voigt對稱性等。 (4)廣義Hamilton原理：建立內(nèi)變量熱力學(xué)耗散材料體系廣義Hamilton原理，相比經(jīng)典彈性體Hamilton原理，只需將結(jié)構(gòu)彈性應(yīng)變能替換為特定內(nèi)能與非彈性內(nèi)耗散功之和，適用于非保守外力與內(nèi)力以及有限變形情況；廣義Hamilton原理是以下Lyapunov穩(wěn)定與控制理論的連續(xù)介質(zhì)力學(xué)基礎(chǔ)。 (5) Rice非彈性體Lyapunov穩(wěn)定與控制理論：基于Lyapunov第二類穩(wěn)定性方法，證明理想Rice非彈性體在恒定外部作用條件與擬靜力條件下的最小流動勢原理，結(jié)合材料損傷效應(yīng)闡明結(jié)構(gòu)非平衡演化的一般規(guī)律；在此基礎(chǔ)上提出結(jié)構(gòu)穩(wěn)定評價與失穩(wěn)控制的有效方法，同時闡明新奧法原理、潘家錚最大最小原理等巖土工程實用穩(wěn)定性原理的理論依據(jù)。 (6)變形加固理論：基于Rice非彈性體Lyapunov穩(wěn)定與控制理論證明變形加固理論，并依托變形加固理論這一特例將前者應(yīng)用于工程結(jié)構(gòu)穩(wěn)定評價與加固設(shè)計。結(jié)合有限元算例初步研究結(jié)構(gòu)整體穩(wěn)定性、加固措施效果與效率、結(jié)構(gòu)長期穩(wěn)定性監(jiān)測與預(yù)測等巖土工程重要問題。
[Abstract]:Natural rock is cut by joints and fissures of different scales, forming composite medium of fractured rock mass. All kinds of fractured rock mass further constitute large-scale rock mass engineering structure. The scale and complexity of rock engineering in China are increasing rapidly, and the stability of rock mass engineering structure is prominent. In this paper, the problem of stability and control of rock mass structure is studied from the viewpoint of dynamic evolution, and a relatively complete research system of non-equilibrium evolution of rock mass structure is proposed, with emphasis on the theoretical basis of mathematics and mechanics of the system. The main work and innovative results are as follows: 1) the fundamental study of nonequilibrium thermodynamics: it is proved that the homogeneous Onsager flow must be all equal, and that the Rice canonical structure based on the homogeneous Onsager flow is equivalent to the Ziegler principle of maximum dissipation rate; The conclusion shows that the thermodynamic basis of constitutive relations of geotechnical materials needs to be based on the direction distribution function and fabric Zhang Liang distribution function in the range of rotational thermodynamic flow. The most general form of directional distribution function-Zhang Liang directional distribution function is proposed. Its relatively complete fabric Zhang Liang algebras are established, including asymmetric and fully symmetric Zhang Liang analytic solutions, convergence and fitting accuracy. (3) Kachanov-Rabotnov) damage effective stress: based on vector direction distribution function, a three-dimensional anisotropic micro-plane model of K-R damage effective stress is established to realize the strict macro-meso-geometric equivalent principle; The model clarifies some basic problems of continuum damage mechanics, including the applicable conditions of anisotropic and isotropic effective stress models. Damage effect Zhang Liang positive definite and Voigt Symmetry etc. Generalized Hamiltonian principle: the generalized Hamiltonian principle of internal variable thermodynamic dissipative material system is established, compared with the classical elastic body Hamiltonian principle. It is only necessary to replace the elastic strain energy of the structure with the sum of specific internal energy and inelastic internal dissipative work, which is suitable for non-conservative external force and internal force and finite deformation. The generalized Hamilton principle is the continuous medium mechanics foundation of the following Lyapunov stability and control theory. 5) Rice nonelastic Lyapunov stability and control theory: based on Lyapunov second stability method, The principle of minimum flow potential of ideal Rice non-elastic body under constant external and quasi-static conditions is proved, and the general law of non-equilibrium evolution of structure is explained by combining material damage effect. On this basis, an effective method for structural stability evaluation and instability control is proposed, and the principle of the new Austrian method is expounded. The theoretical basis of the practical stability principle of geotechnical engineering, such as the Pan Jiazheng maximum and minimum principle, and the deformation reinforcement theory: based on the Lyapunov stability and control theory of Rice non-elastic body, the deformation strengthening theory is proved. Based on the theory of deformation reinforcement, the former is applied to the stability evaluation and reinforcement design of engineering structures. Combined with finite element examples, the main problems of geotechnical engineering, such as overall stability of structure, effect and efficiency of reinforcement measures, monitoring and prediction of long-term stability of structures, are studied.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：TU45

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