土木建筑与环境工程
土木建築與環境工程
토목건축여배경공정
JOURNAL OF CIVIL, ARCHITECTURAL & ENVIRONMENTAL ENGINEERING
2010年
1期
4-11
,共8页
理想弹塑性%广义Hoek-Brown破坏准则%平面应变问题%滑移线场%圆形硐室%极坐标曲线方程%岩体%剪应力
理想彈塑性%廣義Hoek-Brown破壞準則%平麵應變問題%滑移線場%圓形硐室%極坐標麯線方程%巖體%剪應力
이상탄소성%엄의Hoek-Brown파배준칙%평면응변문제%활이선장%원형동실%겁좌표곡선방정%암체%전응력
perfectly elasto-plasticity%the generalized Hoek-Brown failure criterion%plane strain problem%slip line field%circular opening%curve equation of polar coordinate%rock%shear stress
根据弹塑性力学平面应变问题的特点,推导广义Hoek-Brown破坏准则平面应变问题应力分量的双参数表达式.代入静力平衡微分方程,得到双曲型一阶拟线性偏微分方程组.运用行列式方法,在适当的变量代换后,获得应力偏微分方程组的特征方向和特征上的微分关系.特征方向表明塑性区中的共轭斜交剪切滑移面形成两族非正交滑移线,其共轭角随极限应力状态和Hoek-Brown岩体材料物性参数而变化.由于对称初始应力场条件下圆形硐室理想弹塑性围岩塑性区内最大主应力方向为环向,而滑移线切线方向与最大主应力方向的夹角是最小主应力(径向应力)的函数,结合圆形硐室理想弹塑性围岩的应力分布的分析解,获得滑移线的极坐标曲线所满足的微分方程,进而得到其极坐标曲线方程.
根據彈塑性力學平麵應變問題的特點,推導廣義Hoek-Brown破壞準則平麵應變問題應力分量的雙參數錶達式.代入靜力平衡微分方程,得到雙麯型一階擬線性偏微分方程組.運用行列式方法,在適噹的變量代換後,穫得應力偏微分方程組的特徵方嚮和特徵上的微分關繫.特徵方嚮錶明塑性區中的共軛斜交剪切滑移麵形成兩族非正交滑移線,其共軛角隨極限應力狀態和Hoek-Brown巖體材料物性參數而變化.由于對稱初始應力場條件下圓形硐室理想彈塑性圍巖塑性區內最大主應力方嚮為環嚮,而滑移線切線方嚮與最大主應力方嚮的夾角是最小主應力(徑嚮應力)的函數,結閤圓形硐室理想彈塑性圍巖的應力分佈的分析解,穫得滑移線的極坐標麯線所滿足的微分方程,進而得到其極坐標麯線方程.
근거탄소성역학평면응변문제적특점,추도엄의Hoek-Brown파배준칙평면응변문제응력분량적쌍삼수표체식.대입정력평형미분방정,득도쌍곡형일계의선성편미분방정조.운용행렬식방법,재괄당적변량대환후,획득응력편미분방정조적특정방향화특정상적미분관계.특정방향표명소성구중적공액사교전절활이면형성량족비정교활이선,기공액각수겁한응력상태화Hoek-Brown암체재료물성삼수이변화.유우대칭초시응력장조건하원형동실이상탄소성위암소성구내최대주응력방향위배향,이활이선절선방향여최대주응력방향적협각시최소주응력(경향응력)적함수,결합원형동실이상탄소성위암적응력분포적분석해,획득활이선적겁좌표곡선소만족적미분방정,진이득도기겁좌표곡선방정.
According to the characteristics of plane strain problem of elastic and plastic mechanics, the bi-parametric expressions were derived for stress components satisfying the generalized Hoek-Brown failure criterion. Being substituted into the static equilibrium partial differential equations, a group of first-order hyperbolic pseudo-linear differential equation partial differential equations was obtained. Utilizing the determinant method and proper variable transformation, the characteristic direction and the differential relation equation for the stress partial differential equations were acquired. The characteristic direction indicted that in plastic zone obliquely-intersecting conjugate shear slip surfaces formed two families of non-orthogonal slip lines, in which conjugate angle varied with the limit stress state and the material physical properties of Hoek-Brown rock mass. Since the principal direction of the maximum principal stress was circumferential in perfectly elasto-plastic surrounding rock of the plastic zone around a circular opening suffering the symmetric initial stress field, the angle between the tangential direction of slip line with the principal direction of the maximum principal stress was the function of the minimum principal stress(i. e. the radial stress). Combined with the analytical solution, the polar coordinate differential equation was derived and furthermore, the polar coordinate curve equation for the slip line was obtained.