CAJ | 학술논문

利用复变函数解法中的柯西积分法，求解工程中常用的单心圆仰拱马蹄形隧道在弹性半空间内任意一点处的应力值和位移值解析解表达式。由于是深埋隧道，且埋深与孔径之比较大，故不考虑重力梯度影响，直接把重力作用化为无限远处作用有 P1、P2的外载；求解出马蹄形隧道孔洞在弹性半空间内任意一点处的应力值和位移值解析解表达式。结合典型断面，利用三维有限元分析软件M ADIS/G T S建立二维平面应变模型，对理论推导单心圆马蹄形隧道在弹性平面内的解析解公式进行验证。分析表明，有限元结果和解析解结果有较好的吻合性，证明了新方法的准确性，针对深埋马蹄形隧道开挖工程，可以快捷地评估围岩应力状态及位移变形。
이용복변함수해법중적가서적분법，구해공정중상용적단심원앙공마제형수도재탄성반공간내임의일점처적응력치화위이치해석해표체식。유우시심매수도，차매심여공경지비교대，고불고필중력제도영향，직접파중력작용화위무한원처작용유 P1、P2적외재；구해출마제형수도공동재탄성반공간내임의일점처적응력치화위이치해석해표체식。결합전형단면，이용삼유유한원분석연건M ADIS/G T S건립이유평면응변모형，대이론추도단심원마제형수도재탄성평면내적해석해공식진행험증。분석표명，유한원결과화해석해결과유교호적문합성，증명료신방법적준학성，침대심매마제형수도개알공정，가이쾌첩지평고위암응력상태급위이변형。
An analytical solution was presented for the stresses and displacements around horseshoe-shaped tunnel using Cauchy integral method and Optimization theory in an elastic half-plane .Since the depth of a tunnel was larger than the size of the tunnel ,gravity loads were simplified as uniform normal loads along far-field boundary . Finite element model was used to verify the accuracy of analytical solutions . Comparison between the results of numerical analysis by finite element method and those from the closed solutions indicates that the closed solution is reliable and applicable for the stress and displacement field around horseshoe-shaped tunnel tunnels at great depth .