本文選題：巖石　切入點(diǎn)：統(tǒng)計(jì)損傷本構(gòu)模型　出處：《清華大學(xué)》2013年碩士論文

【摘要】：巖石等準(zhǔn)脆性材料的本構(gòu)關(guān)系一直是工程界十分關(guān)注的問題。本文結(jié)合統(tǒng)計(jì)強(qiáng)度理論和連續(xù)損傷理論建立了一種巖石統(tǒng)計(jì)損傷本構(gòu)模型。與常規(guī)的損傷本構(gòu)方程不同，本文分別基于統(tǒng)計(jì)強(qiáng)度理論和連續(xù)損傷理論導(dǎo)出了統(tǒng)計(jì)損傷演化方程和連續(xù)損傷演化方程，并在兩種損傷演化方程中消去損傷變量后結(jié)合成為統(tǒng)計(jì)損傷本構(gòu)方程，本構(gòu)方程本身并不含有損傷變量。 在統(tǒng)計(jì)損傷演化方程的建立過程中，需要引入微元強(qiáng)度滿足的概率分布，以及微元應(yīng)力水平的表達(dá)式。對于微元強(qiáng)度分布，本文引入了抗力常用的對數(shù)正態(tài)分布和Weibull分布。對于微元應(yīng)力表達(dá)式，文本借鑒了巖土材料常用的M-C準(zhǔn)則和D-P準(zhǔn)則中的應(yīng)力組合形式。在連續(xù)損傷演化方程的建立過程中，本文引入了線彈性Hooke定律。 基于巖石三軸壓縮試驗(yàn)，考慮到試驗(yàn)中實(shí)測的應(yīng)力值和應(yīng)變值并非真實(shí)值，本文建議將統(tǒng)計(jì)損傷本構(gòu)方程中的真實(shí)應(yīng)力、真實(shí)應(yīng)變進(jìn)行修正，建立了基于實(shí)測應(yīng)力、實(shí)測應(yīng)變的巖石統(tǒng)計(jì)損傷本構(gòu)方程。對于單軸壓縮情況，統(tǒng)計(jì)損傷本構(gòu)方程是顯式的，而對于三軸壓縮情況，統(tǒng)計(jì)損傷本構(gòu)方程是隱式的。 本文建立的巖石統(tǒng)計(jì)損傷本構(gòu)方程中含有兩個(gè)統(tǒng)計(jì)參數(shù)，需要與巖石單軸、三軸壓縮試驗(yàn)曲線匹配后擬合得出。本文主要介紹了統(tǒng)計(jì)參數(shù)確定的線性回歸法和峰值點(diǎn)法，并通過優(yōu)缺點(diǎn)對比后建議使用峰值點(diǎn)法。 通過對建立的巖石統(tǒng)計(jì)損傷本構(gòu)模型的數(shù)學(xué)意義和物理意義及其適用性進(jìn)行討論分析，可知該本構(gòu)方程能較好地描述巖石材料的非線性力學(xué)行為，也能逼近材料的線彈性本構(gòu)關(guān)系。對于巖石單軸壓縮試驗(yàn)曲線的壓密階段，本文給出了巖石初始損傷的估計(jì)方法。通過基于不同分布類型、不同強(qiáng)度準(zhǔn)則的統(tǒng)計(jì)損傷本構(gòu)方程理論曲線與若干巖石單軸、三軸壓縮試驗(yàn)曲線的對比分析，驗(yàn)證了本文建立的巖石統(tǒng)計(jì)損傷本構(gòu)模型的合理性，，肯定了本文建議的統(tǒng)計(jì)參數(shù)確定方法以及本構(gòu)方程的修正方法。比對結(jié)果顯示，微元強(qiáng)度分布類型對統(tǒng)計(jì)損傷本構(gòu)方程理論曲線的形態(tài)影響不大。對于單軸壓縮或低圍壓三軸壓縮情況，強(qiáng)度準(zhǔn)則對統(tǒng)計(jì)損傷本構(gòu)方程理論曲線的形態(tài)影響也不大。而對于高圍壓三軸壓縮情況，D-P準(zhǔn)則的表現(xiàn)要優(yōu)于M-C準(zhǔn)則。
[Abstract]:The constitutive relation of quasi brittle materials has been the focus problem in engineering field. Based on the statistical strength theory and continuum damage theory to establish a statistical damage constitutive model of rock. With the conventional damage constitutive equation, based on the statistical strength theory and continuum damage theory of damage evolution equation and continuous the damage evolution equation of statistics, and in two in the damage evolution equation of damage variable elimination combined with a statistical damage constitutive equation, the constitutive equation itself does not contain the damage variable.
In the process of establishing a statistical damage evolution equation, the probability distribution of the micro unit strength meet the need to introduce, and differential expression of stress level. The micro unit strength distribution, this paper introduces the commonly used resistance lognormal distribution and Weibull distribution. The differential stress expression, the text from the stress of combination of M-C and D-P criteria the geotechnical materials in common. In the continuous process of establishing damage evolution equation, this paper introduces the linear elastic Hooke law.
Three axial compression test of rock based on considering the measured value of stress and strain values are not real values, this thesis suggests the damage constitutive equation of the true stress true strain statistics, revised, established based on the measured stress, the damage constitutive equation of rock strain. For the uniaxial compression and the statistical damage constitutive equation is explicit, and for the three axial compression, the damage constitutive equation is implicit in the statistics.
Damage constitutive equation containing two statistical parameters of rock is established in this paper, with uniaxial and triaxial compression tests of the three curve fitting after matching. This paper mainly introduces the method of linear regression and peak point method to determine statistical parameters, and through comparing the advantages and disadvantages after the recommended peak point method.
The mathematical and physical meaning of damage constitutive model was analyzed and its applicability to rock establishment, the constitutive equation can describe the nonlinear mechanical behavior of rock material, also can approximate linear elastic material constitutive relationship for the uniaxial compression test curve of the compression phase, is given in this paper the estimation of initial damage of rock. Through different distribution types based on damage constitutive equation of the theoretical curve and some uniaxial strength criterion of different statistics, comparison and analysis of three axis compression test curve, verify the established rock damage constitutive model of rationality, affirmed the method to determine the statistical parameters proposed in this paper and the correction method of constitutive equations. Comparison results show that the intensity distribution of element types had little effect on morphology statistical damage constitutive equation theory for single axis curve. Compression or low confining pressure three axis compression, strength criterion has little effect on the shape of statistical damage constitutive equation, while for high confining pressure three axis compression, the performance of D-P criterion is better than M-C criterion.

【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：TU45

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