高地应力软岩隧道预留变形量设计方法.pdf

引用格式:韩常领,徐晨,夏才初,等.高地应力软岩隧道预留变形量设计方法J.隧道建设(中英文),2023,43(11):1916.HAN Changling,XU Chen,XIA Caichu,et al.Design of reserved deformation for soft rock tunnels with high geostressJ.Tunnel Construction,2023,43(11):1916.收稿日期:2022-09-23;修回日期:2023-10-23基金项目:国家自然科学基金项目(42207176);宁波市自然科学基金项目(2022J116)第一作者简介:韩常领(1966),男,陕西西安人,1987 年毕业于长安大学(原西安公路学院),桥梁与隧道专业,本科,教授级高级工程师,主要从事隧道和地下工程领域的科研工作。E-mail:hanchangl 。通信作者:徐晨,E-mail:tjxuchen 。高地应力软岩隧道预留变形量设计方法韩常领1,徐 晨2,3,夏才初2,3,郑卜豪2,应轶微2(1.中交第一公路勘察设计研究院有限公司,陕西 西安 710075;2.宁波大学 岩石力学研究所,浙江 宁波 315211;3.宁波市能源地下结构重点实验室,浙江 宁波 315211)摘要:在弹塑性岩体中开挖隧道,若围岩无明显的流变性,支护施作太早将承受非常大的荷载,但支护结构并非越晚施作越好。如果支护结构刚度和强度设计不足,即使预留了变形空间,隧道仍可能因支护反力不足而发生大变形破坏。为确定合理的支护刚度和支护时机,基于 GZZ 强度准则采用大应变分析理论,考虑隧道扩挖影响,修正高地应力软岩隧道的围岩特征曲线。修正后的特征曲线与原始曲线有共同的起点,但随着变形增大逐渐偏离原始曲线;增大开挖半径会使特征曲线更高,这意味着支护结构需要提供更大的反力。因此,在工程设计时需要根据修正后的围岩特征曲线进行支护结构设计,避免因为支护刚度不足而发生大变形破坏。其次,基于初始地应力、围岩强度等参数对修正围岩特征曲线形态的影响,提出高地应力软岩隧道围岩最佳预留变形量的设计方法。当地应力较低时,特征曲线有明显的“最低点”,该点对应的支护反力最小,为最佳支护时机;在高地应力条件下,即使变形很大,围岩特征曲线也仍然未达到最低点,这是因为形变压力占主导,松散压力远小于形变压力。因此,在高地应力条件下,采用应力释放措施是有必要的,可通过特征曲线的曲率寻找最佳预留变形量。关键词:高地应力;软岩隧道;大变形;预留变形量;修正围岩特征曲线DOI:10.3973/j.issn.2096-4498.2023.11.011文章编号:2096-4498(2023)11-1916-08中图分类号:U 45 文献标志码:A开放科学(资源服务)标识码(OSID):D De es si ig gn n o of f R Re es se er rv ve ed d D De ef fo or rm ma at ti io on n f fo or r S So of ft t R Ro oc ck k T Tu un nn ne el ls s WWi it th h H Hi ig gh h G Ge eo os st tr re es ss sHAN Changling1,XU Chen2,3,*,XIA Caichu2,3,ZHENG Buhao2,YING Yiwei2(1.CCCC First Highway Consultants Co.,Ltd.,Xian 710075,Shaanxi,China;2.Institute of Rock Mechanics,Ningbo University,Ningbo 315211,Zhejiang,China;3.Ningbo Key Laboratory of Energy Underground Structure,Ningbo 315211,Zhejiang,China)A Ab bs st tr ra ac ct t:Early support implementation can lead to an excessive load-bearing burden if the surrounding rock lacks apparent rheology during the construction of a tunnel in elastic-plastic rocks.This underscores the importance of timely support.In instances where the stiffness and strength of the support structure are inadequate,large deformation failure induced by insufficient support reaction force becomes a distinct possibility,even with reserved deformation in place.To ascertain optimal support stiffness and determine the appropriate supporting duration,the ground reaction curve(GRC)for soft rock tunnels experiencing high geostress is modified.The modification is based on the generalized Zhang-Zhu strength criterion and large strain analysis theory,accounting for the effects of tunnel expansion.The modified and original GRCs share a common starting point but gradually diverge due to increasing deformation.The modified GRC exhibits an upward trend as the excavation radius expands,resulting in a higher reaction force.Consequently,the modified GRC serves as a valuable guide for designing support structures that minimize the substantial deformations arising from inadequate support stiffness.Following the analysis of the impact of initial geostress and rock strength on the modified GRC,a method for designing optimal reserved deformation in the surrounding rock for soft rock tunnels subject to high geostress is proposed.In cases of low geostress,the optimal support timing aligns with the lowest point 第 11 期韩常领,等:高地应力软岩隧道预留变形量设计方法on the GRC,corresponding to the smallest support reaction force.Conversely,under high geostress conditions,the GRC fails to reach the lowest point,even with significant deformation,attributed to predominantly small loose pressure than deformation pressure.Therefore,stress release becomes imperative under high geostress conditions,and the optimal reserved deformation can be determined from the curvature of the GRC.K Ke ey yw wo or rd ds s:high geostress;soft rock tunnel;large deformation;reserved deformation;modified ground reaction curve0 引言 在高地应力软岩环境下进行隧道开挖时,如果岩石应力超过峰值强度,则围岩会发生应变软化1,这是引起软岩隧道发生大变形破坏的根本原因2。为了表达围岩的峰后行为,人们基于各种应变软化本构关系和强度准则进行了大量研究3-11。对于隧道围岩应变软化问题,其求解思路3是:首先,通过有限差分的思想将塑性区围岩分割成 n 个圆环,通过联立强度准则、平衡方程和边界条件求解塑性区围岩的应力分布;然后,结合本构方程、相容方程以及塑性流动法则求得塑性区围岩的应变;最后,基于几何方程,通过迭代的方法求解塑性区围岩的位移和塑性区半径。在理论推导和数值模拟时,较多研究者仍采用基于小变形的弹塑性理论去计算围岩的大变形,然而围岩变形较大时已经不能满足经典弹塑性理论的小变形假设。既有研究也表明,基于小变形的弹塑性理论计算得到的围岩变形和塑性区均偏大12-16。因此,在分析高地应力软岩隧道的大变形问题时,有必要采用大应变理论。为了适应大变形以避免支护结构破坏,隧道施工期间常采用各种应力释放措施,如超挖、设置超前导洞和让压支护等17-20。然而,如果支护结构刚度和强度设计不足,即使预留了变形空间,隧道仍可能因支护反力不足而发生大变形破坏。收敛约束法是分析支护与围岩相互作用的常规方法。围岩特征曲线(GRC)和支护特征曲线(SRC)通常结合在一起,以指导工程设计21-22。传统的 GRC 通过假设隧道开挖半径为计算中的某个设计值 R0来描述支护反力和围岩变形之间的关系。但对于大变形情况,尤其是超挖,隧道实际开挖的断面通常远大于设计断面,有时甚至远大于设计半径,而断面的大小对围岩的受力变形影响较大。因此,在进行隧道预留变形量设计时有必要考虑超挖的影响23。围岩强度准则是描述围岩力学特性的关键力学指标,Mohr-Coulomb 准则和 Hoek-Brown 准则是最常用的模型。前者表达式简单,计算方便,而后者可以反映岩体的力学性质。近年来,国际岩石力学学会(ISRM)推荐的广义 Zhang-Zhu 强度准则(GZZ 准则)24-26在岩体工程中得到了广泛的应用27-29。该准则是在传统的广义 Hoek-Brown 准则基础上发展的三维强度准则,它继承了 Hoek-Brown 强度准则的优点,同时考虑了中间主应力的影响。既有研究已经证明,采用 GZZ准则分析岩体三维力学问题是可靠的,且由于该准则考虑了中间主应力的贡献,其可以充分反映围岩的自承载能力。本文基于 GZZ 强度准则采用大应变分析理论,考虑隧道扩挖影响,在修正高地应力软岩隧道围岩特征曲线23的基础上,提出高地应力软岩隧道围岩最佳预留变形量的设计方法。1 考虑超挖的修正围岩特征曲线1.1 大变形计算方法 在高地应力条件下,采用传统的方式来支护软岩隧道往往会发生围岩大变形,且隧道洞壁变形可达10%甚至 20%以上30,如图 1 所示。各种“让”的措施实际上是通过扩挖使围岩发生部分变形后再施作强支护。由于隧道实际开挖的断面通常远大于设计断面的大小,而断面的大小对围岩的受力变形影响较大,因此有必要对围岩特征曲线进行修正。图 1 木寨岭铁路隧道大变形状况Fig.1 Large deformation of Muzhailing railway tunnel经典弹塑性力学中的小变形假设认为,材料在经历小变形后其位置的变化与其自身的尺寸相比可以忽略。如图 2(a)所示,采用小变形假设建立几何方程时认为变形后的尺寸等于变形前的尺寸,因此是在变形前的状态下建立几何方程。然而,当材料变形较大时,由于小变形分析方法产生的误差较大,需要考虑变形前后材料尺寸的变化,所以应在变形后的状态下建立几何方程,如图 2(b)所示。7191隧道建设(中英文)第 43 卷(a)小变形分析方法(b)大变形分析方法图 2 基于小变形分析方法和大变形分析方法的隧道开挖计算模型对比Fig.2 Comparison of tunnel excavation calculation models based on small strain method and large strain methodXu 等30基于 GZZ 强度准则给出了通过大应变理论计算围岩变形的方法。GZZ 强度准则中围岩各主应力满足ca-1a32oct()1a+mb232oct()-mbm,2=sc。(1)式中:c为岩石单轴抗压强度;mb、s、a 为 Hoek-Brown强度准则力学参数,取值与地质强度指标 GSI 有关,见式(2)(4);oct为八面体的剪应力表达式见式(5);m,2为最大和最小主应力的均值表达式见式(6)。mb=miexp(GSI-100)/28;(2)s=exp(GSI-100)/9(GSI25),0(GSI25);(3)a=0.5(GSI25),0.65-GSI/200(GSI25)。(4)oct=13(1-2)2+(2-3)2+(3-1)2;(5)m,2=1+32。(6)式(2)中 mi为经验参数,取值为 025;式(5)(6)中 1、2、3分别为第一、二、三主应力。考虑软岩的应变软化特性,需要对强度参数进行折减。假定 GZZ 准则中的地质强度指标 GSI 在塑性软化阶段的软化规律与 p相关,其关系式为GSI(p)=GSIp-GSIp-GSIrpp(0p2.5 m 后,围岩特征曲线几乎为水平直线,这意味着即使再增加预留变形量也无法继续降低围岩压力。3.3 围岩强度参数的影响 不同地质条件下的修正围岩特征曲线如图 9 所示。图 9(a)中隧道设计半径为 8 m,初始地应力为10 MPa,围岩的强度参数 GSIp和 GSIr分别取不同的值。图 9(b)中计算参数为:p0=10 MPa,R0=8 m,GSIp=40,GSIr=25,mi=6,c=5 MPa,p=0.005,E=2 GPa,v=0.35。可以看出,图 9(b)中特征曲线有明显的最低点,该点应为最佳支护时机。图 9(a)中特征曲线没有明显的最低点,在洞壁处围岩径向位移 u0达到 2 m 以后,围岩压力并没有得到很大程度的降低,也没有得到较大程度的增加。此时,即使再采用各种应力释放措施,作用在支护上的荷载也不会得到明显的改变,反而会增加工程量和施工工期,达不到预期效果。这说明,在这种情况下,不宜采用过度的应力释放,而应在适当地应力释放的基础上,增加支护体系的强度。0291第 11 期韩常领,等:高地应力软岩隧道预留变形量设计方法 (a)p0=30 MPa(b)p0=20 MPa (c)p0=10 MPa(d)p0=7 MPa图 7 不同地应力条件下的修正围岩特征曲线Fig.7 Modified GRCs under different geostress conditions(a)pc=0.005(b)pc=0.01(c)pc=0.02图 8 不同临界破裂应变条件下的修正围岩特征曲线Fig.8 Modified GRCs under different critical fracture strains(a)特征曲线没有明显的最低点(b)特征曲线有明显的最低点图 9 不同地质条件下的修正围岩特征曲线Fig.9 Modified GRCs under different geological conditions4 结论与建议 在高地应力软岩环境下开挖隧道,难免会遇到围岩大变形。当围岩变形较大时必须进行扩挖,计算时需考虑扩挖的影响。基于 GZZ 强度准则采用大变形计算理论,考虑隧道扩挖影响,在修正高地应力软岩隧道围岩特征曲线的基础上,提出高地应力软岩隧道围1291隧道建设(中英文)第 43 卷岩最佳预留变形量的设计方法。结果表明:1)支护若施作太早将承受非常大的荷载,需要通过让压的方式来延迟支护时机,但支护时机并非越晚越好。当围岩变形较大时必须进行扩挖,计算时需考虑扩挖的影响。2)在地应力相对较低时,考虑扩挖影响后,围岩特征曲线有一个最低点,该点对应的支护反力最小,为最佳支护时机。围岩的预留变形量和支护刚度应按照该点设计。最佳支护时机通常与初始地应力大小、围岩强度、临界塑性应变等参数相关。3)在高地应力条件下,即使在变形很大时围岩特征曲线仍没达到最低点,这是因为在高地应力条件下,形变压力占主导,松散压力远小于形变压力。因此在高地应力条件下采取应力释放措施是有必要的。4)若围岩特征曲线后半段较平缓,则很难找到最低点,说明这种情况下不宜过度地进行应力释放,因为即使采取各种应力释放措施,作用在支护上的荷载也不会得到明显改变,反而会增加工程量和施工工期,达不到预期的效果。建议通过特征曲线的曲率寻找最佳支护时机,在适当的地应力释放基础上,增加支护体系的强度。参考文献(R Re ef fe er re en nc ce es s):1 HOEK E,BROWN E T.Empirical strength criterion for rock massesJ.Journal of the Geotechnical and Engineering Division,1980,106:1013.2 LI Guang,MA Fengshan,LIU Gang,et al.A strain-softening constitutive model of 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