【摘要】：剪切帶是巖土工程災(zāi)變的常見形式,精確再現(xiàn)剪切帶產(chǎn)生和擴(kuò)展過程對揭示巖土工程災(zāi)變機(jī)理、制定災(zāi)害防控措施具有十分重要的意義。剪切帶問題實(shí)質(zhì)上是一類粘聚裂紋動(dòng)態(tài)擴(kuò)展問題,其模擬涉及非連續(xù)變形分析,是目前的熱點(diǎn)研究課題之一。論文針對非連續(xù)變形及其擴(kuò)展模擬中存在的若干關(guān)鍵問題開展研究,提出了一種基于網(wǎng)格分離的位移插值技術(shù)及增強(qiáng)有限元法,及基于增強(qiáng)有限元法、適合任意剪切帶擴(kuò)展模擬的非連續(xù)變形描述及網(wǎng)格自適應(yīng)方法,并應(yīng)用于斷層錯(cuò)動(dòng)導(dǎo)致上覆土層破裂問題的分析。主要研究成果如下： (1)將常規(guī)有限元網(wǎng)格分離為幾何上相互獨(dú)立的用于構(gòu)造位移插值的數(shù)學(xué)網(wǎng)格和離散分析域的物理網(wǎng)格,提出了以網(wǎng)格分離和位移映射法則為核心的有限元位移插值技術(shù),形成了基于常規(guī)有限元法的增強(qiáng)有限元法理論框架。數(shù)學(xué)網(wǎng)格和物理網(wǎng)格的幾何分離與位移映射法則的引入使得網(wǎng)格剖分、良好性態(tài)的位移插值函數(shù)的構(gòu)造更易實(shí)現(xiàn),極大地增強(qiáng)了有限元法的靈活性和適用性。常規(guī)有限元法是增強(qiáng)有限元法的特殊形式,增強(qiáng)有限元法是常規(guī)有限元法的增強(qiáng)形式。 (2)引入過渡單元,提出了由關(guān)聯(lián)數(shù)學(xué)單元與過渡單元位移的重構(gòu)規(guī)則Rr和關(guān)聯(lián)過渡單元與物理單元位移的覆蓋規(guī)則Rc構(gòu)成的統(tǒng)一映射法則。導(dǎo)出了增強(qiáng)有限元法的基本列式、光滑應(yīng)力計(jì)算方法和單元元素矩陣的積分技術(shù),給出了基于常規(guī)有限元軟件的增強(qiáng)有限元實(shí)現(xiàn)方法。 (3)基于統(tǒng)一映射法則,借鑒無網(wǎng)格法、半解析有限元法等的近似位移場構(gòu)造思想,提出了與之相應(yīng)的重構(gòu)規(guī)則,從而使得增強(qiáng)有限元法兼具無網(wǎng)格法、半解析有限元法和光滑有限元法的優(yōu)點(diǎn)。此外,論文還基于增強(qiáng)有限元法提出了一種適用于移動(dòng)邊界問題的固定網(wǎng)格求解方法。 (4)保持位移映射法則不變,通過富集數(shù)學(xué)節(jié)點(diǎn)和過渡節(jié)點(diǎn)分別為裂紋穿越后形成的兩個(gè)物理單元構(gòu)造相應(yīng)的過渡單元和數(shù)學(xué)單元,提出了適于描述穿越單元內(nèi)部的非連續(xù)變形和模擬任意多裂紋擴(kuò)展的方法,突破了常規(guī)有限元法必須將裂紋設(shè)置為單元邊界的局限性,克服了擴(kuò)展有限元法和Hansbo＆Hansbo法在處理幾何關(guān)系復(fù)雜的多裂紋擴(kuò)展問題時(shí)近似位移場構(gòu)造上的困難。 (5)提出了在單元級(jí)別上處理任意階非規(guī)則節(jié)點(diǎn)的統(tǒng)一方法,建立了以裂尖單元尺度和裂尖影響范圍為控制參數(shù)、基于單元細(xì)劃的裂紋動(dòng)態(tài)擴(kuò)展模擬網(wǎng)格自適應(yīng)策略。分析結(jié)果表明,網(wǎng)格自適應(yīng)技術(shù)提高了粘聚裂紋尖端附近應(yīng)力場的計(jì)算精度和裂紋擴(kuò)展過程的分析精度；裂尖附近的網(wǎng)格密度對荷載-位移曲線影響較大,但是對裂紋擴(kuò)展路徑的影響不大。 (6)提出了利用摩擦型粘聚區(qū)域模型表征剪切帶粘聚力-剪切位移間的軟化特性和剪切帶能量耗散機(jī)制、利用增強(qiáng)有限元法描述非連續(xù)變形的土體剪切帶擴(kuò)展過程模擬方法。通過數(shù)值直剪試驗(yàn)確定粘聚區(qū)域模型本構(gòu)參數(shù),數(shù)值再現(xiàn)了斷層錯(cuò)動(dòng)導(dǎo)致上覆土層破裂的離心機(jī)試驗(yàn)結(jié)果,對比研究了流動(dòng)法則和剪切帶軟化特性對上覆土層破裂的影響規(guī)律,分析結(jié)果表明基于關(guān)聯(lián)流動(dòng)法則確定的剪切帶傾角更接近試驗(yàn)結(jié)果。
[Abstract]:The shear zone is a common form of rock - soil engineering disaster . It is of great significance to reveal the mechanism of shear band generation and expansion to reveal the catastrophe mechanism of geotechnical engineering and to establish disaster prevention and control measures . The simulation involves discontinuous deformation analysis , it is one of the hot research topics .

( 1 ) The traditional finite element mesh is separated into a physical grid which is geometrically independent and used to construct displacement interpolation , and a finite element displacement interpolation technique based on the conventional finite element method is proposed . The geometric separation and displacement mapping rules of the mathematical grid and the physical grid are introduced so that the structure of the displacement interpolation function is easier to realize , and the flexibility and applicability of the finite element method are greatly enhanced . The conventional finite element method is a special form of the reinforcement finite element method , and the reinforcement finite element method is the reinforcement form of the conventional finite element method .

( 2 ) Introducing the transition unit , this paper proposes a unified mapping rule consisting of the reconstruction rule Rr of the displacement of the associated mathematical unit and the transition unit and the covering rule Rc of the displacement of the associated transition unit and the physical unit . The basic determinant , the smooth stress calculation method and the integral technique of the element matrix are derived . A method for enhancing the finite element method based on the conventional finite element software is presented .

( 3 ) Based on the unified mapping rule , this paper presents the corresponding reconstruction rules by using the approximate displacement field structure idea of non - grid method , semi - analytic finite element method and so on , so that the enhanced finite element method has the advantages of no grid method , semi - analytic finite element method and smooth finite element method .

( 4 ) Maintaining the rule of displacement mapping is not the same . Through enriching the mathematical node and the transition node , the corresponding transition unit and the mathematical unit are constructed for the two physical units formed after the crack crossing , and the method suitable for describing the non - continuous deformation and the simulation of any multi - crack propagation inside the crossing unit is proposed . The limitation of the conventional finite element method that the crack is set to the boundary of the unit is broken , and the difficulty of the extended finite element method and the Hansbo & Hansbo method in dealing with the complicated multi - crack propagation problem is overcome .

( 5 ) The unified method of dealing with arbitrary order non - rule nodes at the unit level is put forward , and the simulation grid adaptation strategy based on the crack tip cell scale and the crack tip influence range is established . The results show that the grid adaptive technique improves the calculation precision of the stress field near the tip of the crack tip and the analysis accuracy of the crack propagation process .
The grid density near the crack tip has great influence on the load - displacement curve , but the influence on the crack propagation path is not large .

( 6 ) The softening characteristic and the shear band energy dissipation mechanism of shear band cohesion - shear displacement are characterized by using friction - type cohesive zone model , and the simulation method of shear zone expansion process is described by means of the enhanced finite element method . The influence of the flow law and the softening characteristics of shear zone on the rupture of overlying soil layer is studied . The results show that the shear band inclination determined based on the correlation flow rule is closer to the experimental results .
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TU433

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