Tresca材料椭球形孔扩张问题研究
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摘要
岩土工程中诸多问题可以用小孔扩张理论来解释,本课题“Tresca材料椭球形孔扩张问题研究”针对小孔扩张理论中的椭球形孔扩张问题,分别采用复变函数保角变换及改变平衡系数法进行理论分析、采用电敏低强度弹塑性材料进行室内物理模拟试验、采用ABAQUS进行数值模拟等方法,对Tresca材料中椭球形孔扩张过程的受力及位移特性进行了系统的计算和分析。
论文采用复变函数中保角变换等方法对无限均质岩土体中单连通孔洞扩张问题的弹性状态应力和位移进行了求解和分析,在假设材料服从Tresca准则基础上分析了无限均质体中的单连通孔洞,特别是对受均布内压荷载的椭球形孔洞的弹塑性力学性状进行了求解和分析,给出了弹塑性界线的影响因素、形状函数和求解方法,分析了材料进入塑性状态后,塑性区域的扩展特点,同时采用滑移线理论分析了椭圆孔周围塑性状态应力及位移的分布。
论文针对不同长短轴比值的椭球形孔扩张问题,首次采用改变平衡方程中k值的方法,推导给出了弹性阶段的应力及位移公式、弹塑性阶段的弹性应力和塑性应力计算公式,给出了无限体中椭球形扩张下的孔壁位移表达式,在探讨k值物理含义和取值原则的基础上给出了不同k值情况下问题的理论闭合解算例,同时指出,柱形孔扩张解和球形孔扩张解是椭球形孔扩张解的上下限值。
论文首次通过电敏弹塑性材料的模型试验研究了不同长短轴比值的椭球形孔扩张问题,研究了椭球形孔扩张过程中周围介质的力学特性特别是塑性区范围随荷载的变化规律,通过在材料内部径向方向布置不同测点、轴向方向布置不同测层来实测逐渐增大压力作用下周围介质中的电阻比变化,通过电阻比的演变规律来研究其力学特性的演变规律,实测规律和理论分析规律一致,验证了理论分析的正确性。
论文通过数值模拟研究了不同长短轴比值下椭球形孔扩张问题,分析了在内压力逐渐增大过程中孔壁的变形形状和孔周围介质的弹塑性性状及位移场演变规律与特点,数值模拟结果规律和数值与理论分析结果一致,验证了理论分析的正确性。
Analysis of the expansion of cylindrical and spherical cavities in soil and rock provides a surprisingly versatile and accurate geomechanics approach for study of important problems in geotechnical engineering. It is necessary to extend the cavity expansion methods. The primary objective of this study is to perform ellipsoidal cavity expansion analysis in geotechnical engineering area for implementing and improving the cavity expansion methods.
Adopted theoretical analysis, numerical simulation and physical simulation test, Oval cavity(which shape is different from circle and cylinder ) expansion problem is studied.
Through complex variable methods of conformal transformation, elastic properties and displacement of ellipsoidal cavity in infinite homogeneity soil are studied. And the plastic properties which includs elastio-plastic boundary’s figure, influecing factor and solving methods also have been reasearched by supposing for Tresca matria. At the same time the slip line field around the ellipse are given by using difference methods.
By analogying the hollow sphere expansion and thick-walled cylider expansion, through changing the figure factor k value in equilibrium equation, the stress and displacement formula both in elastic state and in plastic state are given for the ellipsoidal expansion. And using the model test parameter, the theoretical result of test’s stress and displacement are sloved.
The paper has also studied the similar cylindrical expansion from the perspective of indoor physical model test. By changing the test materials, it is the first innovation to performance the measurable materials in studying the cavity expansion problems. And it has acheieved the resistance ratio around the cavity, by compare to the resistance ratio versus strain in material testing, the strain field around similar-cylindrical cavity has gain. The resistance ratio versus strain is different in the elastic state and in the plastic state, so it can deduce the material’s elastic or plastic state under different uniform internal pressure at the cell.
Though numerci analysis, it has been found that, at low internal pressure the cell has a relative large deformed, and at higher internal pressure level the cell’s plastic deformed has a feature of tenting for circle figure. This is consistent with theoretical analysis.
论文采用复变函数中保角变换等方法对无限均质岩土体中单连通孔洞扩张问题的弹性状态应力和位移进行了求解和分析,在假设材料服从Tresca准则基础上分析了无限均质体中的单连通孔洞,特别是对受均布内压荷载的椭球形孔洞的弹塑性力学性状进行了求解和分析,给出了弹塑性界线的影响因素、形状函数和求解方法,分析了材料进入塑性状态后,塑性区域的扩展特点,同时采用滑移线理论分析了椭圆孔周围塑性状态应力及位移的分布。
论文针对不同长短轴比值的椭球形孔扩张问题,首次采用改变平衡方程中k值的方法,推导给出了弹性阶段的应力及位移公式、弹塑性阶段的弹性应力和塑性应力计算公式,给出了无限体中椭球形扩张下的孔壁位移表达式,在探讨k值物理含义和取值原则的基础上给出了不同k值情况下问题的理论闭合解算例,同时指出,柱形孔扩张解和球形孔扩张解是椭球形孔扩张解的上下限值。
论文首次通过电敏弹塑性材料的模型试验研究了不同长短轴比值的椭球形孔扩张问题,研究了椭球形孔扩张过程中周围介质的力学特性特别是塑性区范围随荷载的变化规律,通过在材料内部径向方向布置不同测点、轴向方向布置不同测层来实测逐渐增大压力作用下周围介质中的电阻比变化,通过电阻比的演变规律来研究其力学特性的演变规律,实测规律和理论分析规律一致,验证了理论分析的正确性。
论文通过数值模拟研究了不同长短轴比值下椭球形孔扩张问题,分析了在内压力逐渐增大过程中孔壁的变形形状和孔周围介质的弹塑性性状及位移场演变规律与特点,数值模拟结果规律和数值与理论分析结果一致,验证了理论分析的正确性。
Analysis of the expansion of cylindrical and spherical cavities in soil and rock provides a surprisingly versatile and accurate geomechanics approach for study of important problems in geotechnical engineering. It is necessary to extend the cavity expansion methods. The primary objective of this study is to perform ellipsoidal cavity expansion analysis in geotechnical engineering area for implementing and improving the cavity expansion methods.
Adopted theoretical analysis, numerical simulation and physical simulation test, Oval cavity(which shape is different from circle and cylinder ) expansion problem is studied.
Through complex variable methods of conformal transformation, elastic properties and displacement of ellipsoidal cavity in infinite homogeneity soil are studied. And the plastic properties which includs elastio-plastic boundary’s figure, influecing factor and solving methods also have been reasearched by supposing for Tresca matria. At the same time the slip line field around the ellipse are given by using difference methods.
By analogying the hollow sphere expansion and thick-walled cylider expansion, through changing the figure factor k value in equilibrium equation, the stress and displacement formula both in elastic state and in plastic state are given for the ellipsoidal expansion. And using the model test parameter, the theoretical result of test’s stress and displacement are sloved.
The paper has also studied the similar cylindrical expansion from the perspective of indoor physical model test. By changing the test materials, it is the first innovation to performance the measurable materials in studying the cavity expansion problems. And it has acheieved the resistance ratio around the cavity, by compare to the resistance ratio versus strain in material testing, the strain field around similar-cylindrical cavity has gain. The resistance ratio versus strain is different in the elastic state and in the plastic state, so it can deduce the material’s elastic or plastic state under different uniform internal pressure at the cell.
Though numerci analysis, it has been found that, at low internal pressure the cell has a relative large deformed, and at higher internal pressure level the cell’s plastic deformed has a feature of tenting for circle figure. This is consistent with theoretical analysis.
引文
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