收敛−约束法(特性曲线法)是将理论解析、现场实测、工程经验相结合的一种地下工程结构设计方法，是目前分析围岩−支护相互作用关系及开展支护优化设计的常用方法。基于收敛−约束法的基本原理，总结给出了经典的支护特征与支护结构变形方程，理论计算获得了喷射混凝土、锚杆(索)、U型钢支架等支护结构的支护特征曲线，分析了支护结构的几何尺寸(直径、长度)、间排距、材料强度等参数对支护压力的影响特征；随着喷射混凝土厚度及强度等级的增加，喷射混凝土提供的支护刚度和支护压力逐渐增大；随着锚杆(索)直径、长度、杆体材料强度的增加及间排距的减小，锚杆的支护压力显著增加；U型钢支架的排距越小及材料强度越大，其提供的支护压力越大。采用FLAC^3D内嵌的莫尔库伦应变软化本构模型，建立了考虑岩石峰后应变软化与扩容特性的深部软岩巷道数值分析模型，计算获得了不同应力状态下巷道纵剖面变形曲线、围岩特征曲线，分析了锚喷、锚杆(索)喷、锚喷U型钢等3种联合支护技术对深部巷道围岩大变形控制的适用性，验证了锚喷U型钢联合支护技术应用于深部巷道支护工程的可行性。考虑岩石峰后应变软化与扩容特性的应变软化本构模型和经典的莫尔库伦本构模型的数值模拟结果相差较大，采用莫尔库伦本构模型的数值模拟结果保守，支护结构提供的支护压力无法满足深部巷道稳定性控制要求，支护后巷道围岩变形较大甚至会发生冒顶、片帮等安全事故。

Convergence-constraint method is a design approach for underground engineering structures that combines theoretical analysis, field measurements, and engineering experience. It is a commonly used method for analyzing the interaction between surrounding rock and support system, as well as for conducting optimized support design. Based on the basic principle of convergence-constraint method, the classical supporting characteristics and supporting structure deformation equations were summarized. The supporting characteristic curves of supporting structures such as shotcrete, bolt (cable) and U-shaped steel were obtained by theoretical calculation. The effects of the geometric size (diameter, length), row spacing and material strength of supporting structure on the support pressure were analyzed. As the thickness and strength grade of shotcrete increase, the support stiffness and support pressure provided by shotcrete gradually escalate. Simultaneously, the support pressure of bolts experiences a significant increase with the augmentation of bolt (cable) diameter, length, material strength, and reduction in row-spacing between them. Furthermore, the support pressure delivered by U-shaped supports intensifies as the row-spacing decreases and the material strength increases. By using the Mohr-Coulomb strain softening constitutive model embedded in FLAC^3D, the numerical analysis model of deep soft rock roadway considering the post-peak strain softening and dilatancy characteristics of rock was established. The deformation curves of roadway longitudinal section and the characteristic curves of surrounding rock under different stress states were calculated. The applicability of three kinds of combined support technologies such as bolting shotcrete, bolt (cable) shotcrete and bolting-shotcrete U-shaped steel to the large deformation control of surrounding rock in deep roadway were analyzed. The feasibility of applying the combined support technique of bolting-shotcrete U-shaped steel in deep roadway support projects has been verified. The numerical simulation results of the strain-softening constitutive model considering the post-peak strain-softening and dilatancy characteristics of rocks are quite different from those based on the classical Mohr-Coulomb constitutive model. The numerical simulation results of the Mohr-Coulomb constitutive model are conservative, and the supporting pressure provided by the supporting structure cannot meet the stability control requirements of the deep roadway. After roadway support, the surrounding rock exhibits pronounced deformation, which may give rise to safety incidents such as roof collapse and wall instability.