網(wǎng)格自適應有限元極限分析在邊坡穩(wěn)定分析中的應用
發(fā)布時間：2019-06-08 07:06
【摘要】：基于有限元極限分析理論,不需要像傳統(tǒng)極限分析方法在計算之前對破壞形式進行假設,結(jié)構(gòu)的破壞形式通過計算自動尋找出。為了避免Mohr-Coulomb屈服準則屈服面導數(shù)存在奇異點,通用的非線性規(guī)劃算法無法直接應用的問題,對Mohr-Coulomb屈服準則進行二次圓錐優(yōu)化,改寫為一個等式約束和一個二階錐約束,并寫入到極限分析公式推導中。對材料的理想彈塑性假設,將研究區(qū)域劃分為兩種:塑性滑動區(qū)域和彈性區(qū)域;強度折減過程中安全系數(shù)最終是由滑動帶的抵抗力決定的,材料的內(nèi)摩擦角φ和粘聚力c直接影響了抵抗力的大小,滑動帶為邊坡失穩(wěn)的塑性流動區(qū)域�；谟邢拊獦O限分析數(shù)值解的精度在很大程度上依賴網(wǎng)格布局,而安全系數(shù)的求解誤差主要來源于塑性滑動區(qū),對于塑性區(qū)網(wǎng)格進行局部加密優(yōu)化成為提高有限元計算精度的重要途徑。(1)在對初始粗劃分網(wǎng)格的模型計算分析的基礎上,將離散后單元的應力應變數(shù)據(jù)導出,依據(jù)預先設定的應力/應變閥值,通過優(yōu)化后的屈服準則對導出的單元衡量其屈服準則殘余或等效變形,標記出塑性區(qū)域網(wǎng)格單元,對標記網(wǎng)格單元即整個塑性滑動區(qū)域進行網(wǎng)格局部優(yōu)化處理,在一次優(yōu)化過程中指定區(qū)域的單元數(shù)量增加一倍,區(qū)域重新規(guī)劃后網(wǎng)格單元在數(shù)量和質(zhì)量均有所提高,再一次對模型計算。以上過程為網(wǎng)格自適應有限元計算系統(tǒng)一次迭代,循環(huán)迭代直到達到預設計算精度。網(wǎng)格自適應有限元算法實現(xiàn)了網(wǎng)格劃分過程中局部區(qū)域有目的自動化加密,結(jié)合實際工程二維邊坡例證了自適應算法使有限元計算在效率和精度上得到很大提升。(2)基于網(wǎng)格自適應有限元算法,從數(shù)值的角度揭示出邊坡失穩(wěn)的動態(tài)機理,邊坡失穩(wěn)進程中,塑性變形區(qū)域由坡角處不斷沿滑動帶方向向坡頂發(fā)展,當塑性區(qū)域發(fā)展到一定位置時,剩余尚處于彈性變形的區(qū)域應力與塑性區(qū)殘余應力之和不足以抵抗下滑力時,坡頂區(qū)域土體開始受拉,提供拉應力抵抗下滑力,直到拉應力達到土的最大抗拉強度,此時土體完全發(fā)生破壞,邊坡整體開始滑動。邊坡失穩(wěn)的外部監(jiān)測點的位移-時間曲線中,結(jié)構(gòu)變形有彈性階段過渡到彈塑性階段時會出現(xiàn)一個明顯的轉(zhuǎn)折點,此時處在滑塊上的監(jiān)測點和沒有處在滑塊上的監(jiān)測點位移-時間曲線會出現(xiàn)分化,線性發(fā)生變化,可以作為預測預報信息點。在應力/應變-時間曲線中坡頂出現(xiàn)拉應力時,外部擾動已達到邊坡失穩(wěn)的極限狀態(tài),坡頂拉裂縫的出現(xiàn)可以作為判斷邊坡破壞的最后階段。(3)邊坡穩(wěn)定對土材料參數(shù)敏感性分析,不同的彈性模量和泊松比值下,計算安全系數(shù)和應力/應變云圖以及塑性區(qū)的大小、位置等各方面均無差異,模型計算中彈性模量和泊松比僅作為中間變量引入計算,對結(jié)果無實質(zhì)性影響。重度的變化直接影響著邊坡的安全系數(shù),對滑動帶的位置和大小無影響,塑性區(qū)殘余應力大小未發(fā)生變化。粘聚力和內(nèi)摩擦角對塑性區(qū)位置的影響是相反的,隨著兩者值的增大,滑動帶以其最下端位置為軸心分別向下和向上轉(zhuǎn)動,粘聚力越大發(fā)生深層滑坡的可能性越大,內(nèi)摩擦角越大發(fā)生淺層滑坡的可能性越大,兩者相反的特點也正好解釋了在有限元極限分析計算中強度折減為什么要使兩者同步折減。另外內(nèi)摩擦角和粘聚力的大小還影響著塑性區(qū)殘余應力的大小,粘聚力越大塑性區(qū)殘余應力越小,假如無限大,那么接近脆性,殘余應力幾乎為0,這和事實相符,而內(nèi)摩擦角越大,塑性區(qū)殘余應力越大。
[Abstract]:Based on the finite element limit analysis theory, it is not necessary to assume the damage form before the calculation of the traditional limit analysis method, and the damage form of the structure is automatically searched through calculation. In order to avoid the singular point of the yield surface derivative of the Mohr-Coulomb yield criterion, the general nonlinear programming algorithm can't be applied directly, and the Mohr-Coulomb yield criterion is optimized by the quadratic cone, which is rewritten into an equality constraint and a second order cone constraint, and is written into the limit analysis formula derivation. The study area is divided into two types: plastic sliding area and elastic area. The safety factor in strength reduction is determined by the resistance of the sliding band, and the internal friction angle and the cohesive force c of the material directly influence the resistance. The sliding band is the plastic flow area of the slope instability. The precision of the numerical solution based on the finite element limit is dependent on the grid layout to a large extent, and the solution error of the safety factor is mainly from the plastic sliding area, and the local encryption optimization for the plastic area grid is an important way to improve the calculation accuracy of the finite element. (1) the stress-strain data of the discrete back unit is derived on the basis of the model calculation analysis of the initial rough dividing grid, the yield criterion residual or equivalent deformation of the derived unit is measured by the optimized yield criterion according to the pre-set stress/ strain threshold value, a plastic area grid unit is marked, the whole plastic sliding area of the marked grid unit, i.e. the whole plastic sliding area is subjected to a grid local optimization process, the number of units in the specified area is doubled in the one-time optimization process, and the number and the quality of the grid units are improved after the area re-planning, And then calculating the model again. The above process is a one-time iteration of the grid self-adaptive finite element calculation system, and the loop iteration is repeated until the preset calculation accuracy is reached. In this paper, the mesh self-adaptive finite element algorithm is used to realize the automatic encryption of the local area in the process of grid division, and the two-dimensional slope of the project is used to illustrate the adaptive algorithm to make the calculation of the finite element greatly improved in efficiency and precision. (2) Based on the mesh self-adaptive finite element method, the dynamic mechanism of the slope instability is revealed from the angle of the numerical value, and the plastic deformation area is continuously developed in the direction of the sliding belt in the direction of the sliding belt from the angle of the slope, and when the plastic region is developed to a certain position, when the sum of the residual stress of the residual stress in the elastic deformation and the residual stress of the plastic region is insufficient to resist the sliding force, the soil body in the top region of the slope is in tension, and the tensile stress is provided to resist the sliding force until the tensile stress reaches the maximum tensile strength of the soil, The whole slope of the side slope is started to slide. in the displacement-time curve of the external monitoring point of the slope instability, a significant turning point appears when the structural deformation is in the elastic phase transition to the elastic-plastic phase, the monitoring point on the slide block and the displacement-time curve of the monitoring point which are not on the slide block can be differentiated, The linear change can be used as the prediction information point. In the case of tensile stress in the top of the slope in the stress/ strain-time curve, the external disturbance has reached the limit state of the slope instability, and the occurrence of the slope-top-pull crack can be used as the final stage to judge the slope failure. (3) The stability of the slope has no difference in the sensitivity analysis of soil material parameters, different elastic modulus and Poisson's ratio value, the calculation safety factor and the stress/ strain cloud picture and the size and position of the plastic zone, In the model calculation, the elastic modulus and the Poisson's ratio are calculated only as the intermediate variable, and there is no material effect on the results. The severe change directly affects the safety factor of the slope, and has no effect on the position and size of the sliding belt, and the residual stress in the plastic zone is not changed. the influence of the cohesion and the internal friction angle on the position of the plastic region is the opposite, with the increase of the value of the two, the sliding belt is rotated downwards and upwards at the most lower end position of the sliding belt, the greater the cohesion is, the greater the possibility of the deep landslide, The larger the internal friction angle, the greater the probability of the shallow landslide, and the opposite characteristics of the two also explain the reason why the strength is reduced in the finite element limit analysis calculation. In addition, the size of the residual stress in the plastic region is also affected by the size of the internal friction angle and the cohesive force, and the smaller the residual stress in the plastic region, the smaller the residual stress in the plastic region, if it is infinite, the residual stress is almost zero, which is in line with the fact, and the larger the internal friction angle, the greater the residual stress in the plastic region.
【學位授予單位】：西北農(nóng)林科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TU43
本文編號：2495096
[Abstract]:Based on the finite element limit analysis theory, it is not necessary to assume the damage form before the calculation of the traditional limit analysis method, and the damage form of the structure is automatically searched through calculation. In order to avoid the singular point of the yield surface derivative of the Mohr-Coulomb yield criterion, the general nonlinear programming algorithm can't be applied directly, and the Mohr-Coulomb yield criterion is optimized by the quadratic cone, which is rewritten into an equality constraint and a second order cone constraint, and is written into the limit analysis formula derivation. The study area is divided into two types: plastic sliding area and elastic area. The safety factor in strength reduction is determined by the resistance of the sliding band, and the internal friction angle and the cohesive force c of the material directly influence the resistance. The sliding band is the plastic flow area of the slope instability. The precision of the numerical solution based on the finite element limit is dependent on the grid layout to a large extent, and the solution error of the safety factor is mainly from the plastic sliding area, and the local encryption optimization for the plastic area grid is an important way to improve the calculation accuracy of the finite element. (1) the stress-strain data of the discrete back unit is derived on the basis of the model calculation analysis of the initial rough dividing grid, the yield criterion residual or equivalent deformation of the derived unit is measured by the optimized yield criterion according to the pre-set stress/ strain threshold value, a plastic area grid unit is marked, the whole plastic sliding area of the marked grid unit, i.e. the whole plastic sliding area is subjected to a grid local optimization process, the number of units in the specified area is doubled in the one-time optimization process, and the number and the quality of the grid units are improved after the area re-planning, And then calculating the model again. The above process is a one-time iteration of the grid self-adaptive finite element calculation system, and the loop iteration is repeated until the preset calculation accuracy is reached. In this paper, the mesh self-adaptive finite element algorithm is used to realize the automatic encryption of the local area in the process of grid division, and the two-dimensional slope of the project is used to illustrate the adaptive algorithm to make the calculation of the finite element greatly improved in efficiency and precision. (2) Based on the mesh self-adaptive finite element method, the dynamic mechanism of the slope instability is revealed from the angle of the numerical value, and the plastic deformation area is continuously developed in the direction of the sliding belt in the direction of the sliding belt from the angle of the slope, and when the plastic region is developed to a certain position, when the sum of the residual stress of the residual stress in the elastic deformation and the residual stress of the plastic region is insufficient to resist the sliding force, the soil body in the top region of the slope is in tension, and the tensile stress is provided to resist the sliding force until the tensile stress reaches the maximum tensile strength of the soil, The whole slope of the side slope is started to slide. in the displacement-time curve of the external monitoring point of the slope instability, a significant turning point appears when the structural deformation is in the elastic phase transition to the elastic-plastic phase, the monitoring point on the slide block and the displacement-time curve of the monitoring point which are not on the slide block can be differentiated, The linear change can be used as the prediction information point. In the case of tensile stress in the top of the slope in the stress/ strain-time curve, the external disturbance has reached the limit state of the slope instability, and the occurrence of the slope-top-pull crack can be used as the final stage to judge the slope failure. (3) The stability of the slope has no difference in the sensitivity analysis of soil material parameters, different elastic modulus and Poisson's ratio value, the calculation safety factor and the stress/ strain cloud picture and the size and position of the plastic zone, In the model calculation, the elastic modulus and the Poisson's ratio are calculated only as the intermediate variable, and there is no material effect on the results. The severe change directly affects the safety factor of the slope, and has no effect on the position and size of the sliding belt, and the residual stress in the plastic zone is not changed. the influence of the cohesion and the internal friction angle on the position of the plastic region is the opposite, with the increase of the value of the two, the sliding belt is rotated downwards and upwards at the most lower end position of the sliding belt, the greater the cohesion is, the greater the possibility of the deep landslide, The larger the internal friction angle, the greater the probability of the shallow landslide, and the opposite characteristics of the two also explain the reason why the strength is reduced in the finite element limit analysis calculation. In addition, the size of the residual stress in the plastic region is also affected by the size of the internal friction angle and the cohesive force, and the smaller the residual stress in the plastic region, the smaller the residual stress in the plastic region, if it is infinite, the residual stress is almost zero, which is in line with the fact, and the larger the internal friction angle, the greater the residual stress in the plastic region.
【學位授予單位】：西北農(nóng)林科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TU43
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