Hoek-Brown破坏准则求解圆形硐室塑性区半径与修正的芬纳公式比较  

Comparison between Plastic Radius around a Circular Opening Derived from Hoek-Brown Failure Criterion and Calculated through Modified Fenner Formula

作　　者：曾钱帮[1,2] 王恩志[1,2] 王思敬[2,3] 

机构地区：[1]清华大学水沙科学与水利水电工程国家重点实验室,北京100084 [2]清华大学水利水电工程系,北京100084 [3]中国科学院地质与地球物理研究所,北京100029

出　　处：《沈阳建筑大学学报（自然科学版）》2008年第6期933-938,共6页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家科技支撑计划重点项目(2006BAK30B02)

摘　　要：目的为定量确定围岩塑性区半径和给支护锚杆的深度设计提供科学依据.方法以Hoek-Brown破坏准则为极限平衡条件，推求侧压力系数为1.0时圆形硐室理想弹塑性围岩的弹塑性应力和塑性区半径，运用Mohr-Coulomb准则直线拟合Hoek-Brown准则曲线和面积差补方法，求取等效的岩体Mohr-Coulomb强度参数后，建立相对塑性区半径随支护力和地质强度指标变化的二元非线性回归数学模型，并与源自于Mohr-Coulomb强度准则为屈服条件的修正的芬纳公式进行比较研究.结果支护力每增加1.0 MPa，就可确保地质强度指标降低10-20的岩体中不会出现塑性区.在支护力较小和岩体质量较差情况下，采用Hoek-Brown破坏准则推导得出的塑性区半径和修正的芬纳公式计算得出的塑性区半径差别稍大.相对塑性区半径与地质强度指标都呈负乘幂函数关系，随着支护力的增大，塑性区半径随着岩体质量等级的升高而下降的趋势逐渐变缓.建立的相对塑性区半径随地质强度指标和支护力变化的二元非线性回归数学模型简明，使支护力连续变化，提高了工程实用性.结论在岩体质量较差情况下，锚杆深度取1.8-3.0倍硐半径为宜.In order to quantitatively determine and provide scientific basis for the support design of rockbolt depth in surrounding rock around underground tunnels, the closed-form analytical solutions for the elastoplastic stress field and plastic radius in an elastic-perfectly plastic surrounding rock around a circular opening were derived from the Hock-Brown failure criterion as the limit equilibrium condition, on condition that the lateral pressure coefficient equals to 1.0. By means of fitting the non-linear Hock-Brown failure criterion with the linear Mohr-Coulomb strength criterion and an area compensation method, after obtaining the e- quivalent Mohr-Coulomb strength parameters, a bi-variable non-linear regression mathematic model for the relative plastic radius varied with the support pressure and the Geologic Strength Index （GSI） was formulated to compare with the modified Fenner formula, which was originated from the Mohr-Coulomb yield criterion. An increment of the support pressure per 1.0 MPa could guarantee that no plastic zone exited in the rock with the GSI decrement of 10-20. The difference of plastic radius between compatible with the Hock- Brown failure criterion and calculated from the Mohr-Coulomb yield criterion was slightly greater only in poor-quality rock and low support pressure. Minus power function relationships between the relative plastic radius and the GSI value were indicated both for the two yield criterions and the descending trend of plastic radius with the increment of rock quality grade became gentler when the support pressure increased. The bivariable no-linear regression mathematic models for the relative plastic radius varied with support pressure and the GSI value was concise and, since the regression equations made the support pressure varied continuously, their engineer practicability was boosted. It was reasonable that 1.8-3.0 times of tunnel＇s radius was adopted as the rockbolt depth when the rock quality was poor.

关 键 词：Hoek-Brown破坏准则 地质强度指标 相对塑性区半径 Mohr-Coulomb强度准则 修正的芬纳公式 

分 类 号：TV554[水利工程—水利水电工程]