【摘要】：隨著巖土工程的發(fā)展,圍巖的失穩(wěn)得到了各界的關(guān)注。圍巖的失穩(wěn)破壞問題是非常復(fù)雜的,具有非線性、突變性、離散性以及不確定性。目前針對(duì)圍巖失穩(wěn)破壞的研究大都停留在概念上或者精度較低的判據(jù)和理論上,因此需要尋找量化的、精度較高的判據(jù)來解決此問題。隨著復(fù)變函數(shù)解法和突變理論在巖土工程中的研究逐步深入,發(fā)現(xiàn)突變理論可提供一個(gè)量化的圍巖失穩(wěn)判據(jù)來判定,同時(shí)考慮到復(fù)變函數(shù)解法提供的圍巖彈性應(yīng)力應(yīng)變解析解可用于建立較高精度突變理論判據(jù)所需的勢能方程。因此,本文考慮結(jié)合突變理論分析和復(fù)變函數(shù)解法,編輯相關(guān)計(jì)算程序探索性的研究隧道圍巖穩(wěn)定性問題,主要從以下幾個(gè)方面開展研究： (1)利用復(fù)變函數(shù)解法求解隧洞圍巖的應(yīng)力應(yīng)變,并給出隧洞內(nèi)任意點(diǎn)應(yīng)力應(yīng)變解析解的計(jì)算程序； (2)建立突變理論能量勢能標(biāo)準(zhǔn)化方程和面積勢能標(biāo)準(zhǔn)化方程,并給出計(jì)算標(biāo)準(zhǔn)勢能方程的計(jì)算程序； (3)利用突變理論依據(jù)能量判據(jù)和面積判據(jù)研究隧洞圍巖的整體和局部穩(wěn)定性,并給出穩(wěn)定性判據(jù)的計(jì)算程序,然后通過計(jì)算和分析相關(guān)圍巖參數(shù)對(duì)隧洞圍巖穩(wěn)定性的影響規(guī)律。 本研究創(chuàng)新點(diǎn)如下： (1)在巖土工程穩(wěn)定性分析時(shí),采用了突變理論,給該領(lǐng)域研究提供了一大研究思路,具有很強(qiáng)的科研價(jià)值。對(duì)尖點(diǎn)突變模型進(jìn)行的較為深入的研究,初步獲得尖點(diǎn)突變模型的適用性,并進(jìn)一步闡述了擬合方法的操作； (2)在復(fù)變函數(shù)解法研究模型應(yīng)力應(yīng)變的基礎(chǔ)上,利用突變理論進(jìn)行穩(wěn)定性分析,使得研究結(jié)果更加精確、穩(wěn)定。根據(jù)復(fù)變函數(shù)解法,借助Fortran語言編輯程序成功的獲得圍巖的彈性應(yīng)力應(yīng)變解析解,使得結(jié)果更加準(zhǔn)確合理,給予后續(xù)的研究結(jié)果給予強(qiáng)大的精度支持。給現(xiàn)代化施工與設(shè)計(jì)提供了更加精確合理理論依據(jù),擺脫以往對(duì)安全系數(shù)的依賴,具有相當(dāng)?shù)慕?jīng)濟(jì)價(jià)值； (3)通過研究,將突變理論和復(fù)變函數(shù)解法結(jié)合,對(duì)以往研究思路的重大突破,提高了這兩個(gè)理論的工程應(yīng)用價(jià)值和科研價(jià)值。借鑒復(fù)變函數(shù)解法得到準(zhǔn)確彈性解析解的優(yōu)勢,將其引入以塑性區(qū)面積勢和彈性應(yīng)變能作為突變勢的突變理論模型中,結(jié)合突變理論來研究使得結(jié)果更加準(zhǔn)確合理。
[Abstract]:With the development of geotechnical engineering, the instability of surrounding rock has been paid more and more attention. The problem of instability and failure of surrounding rock is very complex, which is nonlinear, abrupt, discrete and uncertain. At present, the research on instability failure of surrounding rock mostly stays on the concept or the criterion and theory of low precision, so it is necessary to find a quantitative and high precision criterion to solve this problem. With the further study of complex function method and catastrophe theory in geotechnical engineering, it is found that the catastrophe theory can provide a quantitative criterion to judge the instability of surrounding rock. At the same time, the analytical solution of elastic stress and strain of surrounding rock provided by the method of complex variable function can be used to establish the potential energy equation required for the criterion of catastrophe theory with higher accuracy. Therefore, considering the combination of catastrophe theory analysis and complex variable function solution, this paper compiles the relevant calculation program to explore the stability of tunnel surrounding rock. The research is mainly carried out from the following aspects: (1) the complex variable function method is used to solve the stress and strain of the surrounding rock of the tunnel, and the calculation program of the analytical solution of stress and strain at any point in the tunnel is given; (2) the energy potential standardization equation and area potential energy standardization equation of catastrophe theory are established, and the calculation program of the standard potential energy equation is given. (3) on the basis of energy criterion and area criterion, the global and local stability of surrounding rock of tunnel is studied by catastrophe theory, and the calculation program of stability criterion is given. Then, the influence of the surrounding rock parameters on the stability of tunnel surrounding rock is calculated and analyzed. The innovations of this study are as follows: (1) in the stability analysis of geotechnical engineering, the catastrophe theory is adopted, which provides a great idea for the research in this field and has a strong scientific research value. Based on the in-depth study of the cusp mutation model, the applicability of the cusp mutation model is preliminarily obtained, and the operation of the fitting method is further expounded. (2) based on the study of the stress and strain of the model by the method of complex variable function, the stability analysis of the model is carried out by using the catastrophe theory, which makes the research results more accurate and stable. According to the method of complex variable function, the analytical solution of elastic stress and strain of surrounding rock is obtained successfully by means of Fortran language editing program, which makes the result more accurate and reasonable, and gives strong precision support to the follow-up research results. It provides a more accurate and reasonable theoretical basis for modern construction and design, and it has considerable economic value to get rid of the dependence on safety factor in the past. (3) through the research, the combination of catastrophe theory and complex function method can improve the engineering application value and scientific research value of the two theories. The advantage of accurate elastic analytical solution is obtained by using complex variable function method for reference. It is introduced into the catastrophe theoretical model in which the plastic area product potential and elastic strain energy are used as abrupt potentials. The results are more accurate and reasonable with the study of catastrophe theory.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TU457

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