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基于流固耦合作用的富水断层区隧道初期支护优化分析

李远远, 李春鹏, 和大钊, 康鑫

李远远,李春鹏,和大钊,等. 基于流固耦合作用的富水断层区隧道初期支护优化分析[J]. 水文地质工程地质,2025,52(3): 144-152. DOI: 10.16030/j.cnki.issn.1000-3665.202402013
引用本文: 李远远,李春鹏,和大钊,等. 基于流固耦合作用的富水断层区隧道初期支护优化分析[J]. 水文地质工程地质,2025,52(3): 144-152. DOI: 10.16030/j.cnki.issn.1000-3665.202402013
LI Yuanyuan, LI Chunpeng, HE Dazhao, et al. Optimization analysis of initial support for tunnels in water-rich fault zone based on fluid-solid interaction[J]. Hydrogeology & Engineering Geology, 2025, 52(3): 144-152. DOI: 10.16030/j.cnki.issn.1000-3665.202402013
Citation: LI Yuanyuan, LI Chunpeng, HE Dazhao, et al. Optimization analysis of initial support for tunnels in water-rich fault zone based on fluid-solid interaction[J]. Hydrogeology & Engineering Geology, 2025, 52(3): 144-152. DOI: 10.16030/j.cnki.issn.1000-3665.202402013

基于流固耦合作用的富水断层区隧道初期支护优化分析

详细信息
    作者简介:

    李远远(1993—),男,硕士,工程师,主要从事地质工程、地下建筑与隧道工程的研究。E-mail:1366671377@qq.com

    通讯作者:

    李春鹏(1980—),男,硕士,高级工程师,主要从事岩土勘察、工程地质灾害工程的研究。E-mail:42810437@qq.com

  • 中图分类号: U459.1;P642

Optimization analysis of initial support for tunnels in water-rich fault zone based on fluid-solid interaction

  • 摘要:

    穿越富水断层区隧道初期支护的研究主要集中在隧道断面破碎带突水、突泥机制以及隧道富水段支护结构的受力特征,但对穿越富水断层区隧道初期支护参数的选择研究较少。以赣州—深圳(赣深)铁路客运专线的龙南隧道为工程背景,基于流固耦合理论,采用FLAC3D对穿越F8富水断层区隧道开挖和支护全过程进行数值模拟;结合断层区的工程与水文地质条件以及六部CD法的施工特点,选取断层区中间部位的中轴线、左拱顶区、右拱顶区3个监测点的沉降值建立偏差平方和函数ST,分析拱顶变形、塑性区体积及渗流场变化特征。模拟结果表明:(1)钢拱架的合理间距为1.0 m,喷射混凝土的合理厚度为26~30 cm,并通过三次曲线拟合得出该典型断面喷射混凝土的最优厚度为28 cm;(2)钢拱架间距为1.0 m时,塑性区体积随初支混凝土厚度增大而减小,当初支喷射混凝土厚度大于28 cm时,塑性区体积减小幅度很小,通过增加喷射混凝土厚度来提高初支结构的安全性是不经济的,验证了初支钢拱架间距和喷射混凝土厚度优化的合理性;(3)在最优初支条件下,隧道渗流量较为明显部位是拱脚>边墙>拱底>拱顶;(4)将模拟结果与监测结果对比,两者虽然有所差异,但变化规律相近,量级一致,模拟结果能够反映实际情况。研究结果可为类似地层条件下的隧道施工与支护提供参考价值和理论依据。

    Abstract:

    The design of tunnel support structures in water-rich fault zones often relies on empirical and analogy-based methods, lacking rigorous and rational optimization methods. To ensure the stability of tunnel, designers frequently overestimate support parameters, resulting in excessive safety margins, construction challenges, and unnecessary economic costs. Based on the fluid-structure coupling theory, this study simulated the whole process of tunnel excavation and support across F8 water-rich fault zone by FLAC3D in the background of Longnan tunnel of Ganzhou−Shenzhen railway. Combined with the engineering and hydrogeological conditions of the fault zone and the construction characteristics of the six CD methods, the center axis, left vault area, and right vault area of the middle part of the fault zone were selected to establish the deviation square sum function (ST). The results show that the reasonable space of steel arch frame is 1.0 m, and the recommended shotcrete thickness ranges from 26 to 30 cm, with 28 cm being optimal based on cubic curve fitting. When the space between steel arch frames is 1.0 m, the volume of the plastic zone decreases with the increase of the thickness of the initial branch of shotcrete. However, beyond 28 cm, the marginal benefit diminishes significantly, making further increases uneconomical. To improve the safety of the initial-support structure, and the rationality of the optimization of the spacing of the initial-support steel arch frame and the thickness of shotcrete is verified. Under the optimal initial support condition, the primary seepage pathways are ordered as follows: arch foot > side wall > arch bottom > Arch crown. Comparison between simulated and field-monitored results reveals consistent trends and similar magnitudes, indicating that the simulation accurately reflects actual field behavior. This study provides the theoretical basis for tunnel construction and support design in similar water-rich fault zones.

  • 近年来我国铁路建设迅速发展,大量铁路客货运专线全面投入运营,铁路建设必然伴随着大量的铁路隧道出现,这些隧道面临的工程地质条件较为复杂,其中以富水断层破碎带较为常见[12]。隧道在穿越富水断层破碎带时,一方面,地下水的处理是极其复杂的,施工中的隧道涌突水以及地下水对隧道衬砌的作用都将直接影响隧道施工的安全性、结构的耐久性以及后期运营的安全性[35];另一方面,断层破碎带中岩体破碎,为地下水的渗流提供通道,稳定性较差,易发生塌方、突水、涌泥等事故[67]。在施工中,隧道围岩的初始应力与渗流应力相互耦合引起应力重新分布,同时地下水渗流作用弱化了洞周围岩的自承能力,因此进一步开展穿越富水断层区隧道初期支护优化的研究尤为重要[810]

    Shi等[11]、Zhu等[12]研究了断层所处采空区位置以及断层要素与突水的关系,结果表明底板岩层应力分布的峰值应力线与工作面前方垂直方向呈20°~25°的倾斜,且只有峰值应力线后方的底板岩层才能被地压破坏[13];矿井底板突水途径是从含水层通过断层至底板上的破碎地层进入工作面;Wolkersdoorfer等[14]、Valkó等[15]研究了隧道穿越破碎岩体后围岩渗透性变化规律,通过损伤积累定律推导出断裂扩展率的表达式,解释了断裂过程如何延迟断裂扩展率,从而导致处理压力比“流体流动受限”边界条件预测的压力高很多;李鹏飞等[16]、李地元等[1]基于达西定律,推导出复合衬砌结构外水压力的解析公式,为海底隧道或富水区隧道复合衬砌加固圈参数的确定提供依据;钱忠运[17]、王涛等[18]研究了隧道浅埋富水段的围岩压力和支护体系的受力特征,通过现场监测分析得出富水段隧道边墙底部压力较大与钢拱架受力不均的受力特点;何本国等[19]对膏溶角砾岩隧道支护体系进行了现场试验,并对比分析了无水段和富水量段的复合式衬砌的受力特征,得出富水段隧道围岩竖向压力为双峰型或均匀分布,水平压力为折线型分布的特征;仇文革等[20]、谢壁婷等[21 ]、何乐平等[22]通过对初期支护中喷射混凝土、型钢钢架、锚杆的应力进行监测,提出了隧道三度空间分布理论D -E-D ,并通过该理论验证了数值计算和现场监测结果的合理性;张湉[23]、Calvellom等[24]、陈秋雨等[25]、张杰达等[26]结合自主设计的模型试验箱和量测系统建立相似模型,进行了隧道支护优化设计的研究,得出锚杆的优化对控制围岩变形作用小,喷层厚度、钢拱架间距和二衬厚度的优化效果较为显著。综上,当前研究主要集中在隧道断层破碎带突水、突泥机制以及隧道富水段支护结构的受力特征,但对穿越富水断层区隧道初期支护参数的选择研究较少。

    江西赣州—深圳(赣深)高铁全线最长双线隧道——龙南隧道长10 244.27 m,最大埋深约580 m,沿线共穿越11条断层,其中F8断层附近地表有溪水发育,是下方水库的主要水源。钻探和水文勘察结果表明:F8断层带呈砂加块石状,断层以下揭示灰岩夹层,断层富含承压水,钻探孔口涌水,隧道洞身水压为0.5 MPa。隧道与地表溪水有紧密的水力联系,施工中极易发生突水、涌泥等突发灾害[27]。本文以龙南隧道为工程背景,选择典型F8断层破碎带,结合现场变形监测数据和水文地质调查,采用FLAC3D对流固耦合作用下隧道开挖和支护全过程进行数值模拟,分析拱顶变形特征、塑性区体积大小和渗流区变化,提出钢拱架的合理间距以及合理的喷射混凝土厚度。

    渗流过程中的质量平衡方程:

    1Mpt+nsst=1sζtαεt (1)

    式中:M——Biot模量/(N·m−2);

    p——孔隙水压力/Pa;

    n——孔隙率/%;

    s——饱和度/%;

    α——Biot系数;

    ε——固体体积应变;

    ζ——流体体积应变。

    动量平衡方程:

    σij+ρgi=ρdvidt (2)
    ρ=(1n)ρs+nsρω (3)

    式中:σij——应力分量/Pa;

    gi——重力加速度/(m·s−2);

    vi——i方向的速度/(m·s−1);

    ρ——容积密度/(kg·m−3);

    ρs——固相密度/(kg·m−3);

    ρω——液相密度/(kg·m−3)。

    常密度流体在均匀、各向同性固体中流动时,符合Darcy定律:

    qi=kijˆk(s)[pρfxjgj] (4)

    式中:qi——渗流速度分量/(m·s−1);

    kij——渗透系数分量/(m2·Pa−1·s−1);

    ˆk(s)——相对渗透系数;

    ρf——流体密度/(kg·m−3);

    xj——渗流在j方向的投影。

    孔隙介质本构方程增量:

    Δσij+αΔpδij=Hij(σij,Δξij) (5)

    式中:Δσij——应力增量/Pa;

    Δp——孔隙水压力增量/Pa;

    δij——Kronecher因子;

    Hij——给定函数;

    Δξij——总应变增量。

    应变率与速度梯度应满足:

    ξij=12(νi,j+νj,i) (6)

    式中:νi,jνj,i——ij方向的速度梯度/s−1

    共有4种渗流计算的边界类型:①给定孔隙水压力;②给定边界外法线方向流速分量;③不透水边界,本程序默认;④透水边界,表达式如下:

    qn=h(ppe) (7)

    式中:qn——边界外法线方向流速分量/(m·s−1);

    h——渗漏系数/(m3·N−1·s−1);

    pe——渗流出口处的孔隙水压力/Pa。

    龙南隧道工程位于江西省赣州市全南县和龙南县境内,隧道起讫里程为DK91+531.00—DK101+775.27,沿线以侵蚀构造低山为主,地面标高210~860 m,地形起伏,局部陡峭,沟谷狭长,多呈“V”字型,隧道穿越变质砂岩、花岗岩、砂岩、石英砂岩等地层,地质构造及水文地质条件较复杂,局部发育多处断层,破碎带附近围岩一般IV~V级,施工难度大,属控制性重点隧道工程。其中F8断层破碎带围岩分级为VI级,断层带富含承压水,施工中极易发生突水、突泥等突发灾害。隧道穿越F8断层带纵断面如图1所示。

    图  1  F8断层带纵断面
    Figure  1.  F8 fault zone profile

    该研究区域采用钻爆法施工,当隧道穿越F8断层破碎带时,采用六部CD法(图2),其余部分采用三台阶临时仰拱法。计算范围为:x向垂直隧道边墙方向,左右各取45 m;y向为隧道开挖方向(150 m),即DK99+480— DK99+630,其中断层破碎带为80 m;z向为岩体自重方向,上部取至地表,拱顶最低埋深为36 m,最高埋深为94 m。应力边界条件:上表面为自然表面,其余四周均施加法向位移约束。渗流边界条件为:断层洞身水压为0.5 MPa,在地下水位线最低点(拱顶上方26.63 m)施加相应高度孔隙水压力0.19 MPa,模型四周为不透水边界,开挖后的隧道周边为透水边界。建立的数值模型如图3所示。

    图  2  六部CD法施工设计图(单位:cm)
    注:g1—g3为位移监测点位移;SL1—SL4为洞身收敛监测点;①—⑥为六部CD法各部。
    Figure  2.  Constriction design of Six CD method (Unit: cm)
    图  3  三维数值模型
    Figure  3.  3D numerical model

    结合现场实际施工情况(图2),用FLAC3D模拟现场施工工序:

    第1步,初始自重应力场平衡;第2步,在地下水位线最低点(拱顶上方26.63 m)施加相应高度孔隙水压力0.19 MPa,至洞身水压为0.5 MPa;第3步,对隧道轮廓线外8 m径向围岩改变参数进行加固,同时对掌子面前方围岩进行加固,分台阶开挖左①②③部,同时逐步施作导坑周边的主体结构的初期支护和中隔壁临时支护;第4步,初支和临时支护稳定后的应力场模拟;第5步,分台阶开挖④⑤⑥部,同时逐步施作导坑周边的主体结构的初期支护和临时支护;第6步,初支和临时支护稳定后的应力场模拟;第7步,中隔墙拆除;第8步,施作仰拱。

    右部导洞开挖,应滞后于左部导洞,距离15 m左右,台阶长度为3 m,每次循环进尺为0.5 m,开挖后应力释放系数为30%时,施加初期支护。

    围岩材料采用弹塑性Mohr-coulomb模型,模型中隧道施工里程方向前、后10 m的V级砂岩采用三台阶临时仰拱法,3 m径向超前预注浆;中间130 m(80 m断层破碎带)采用六部CD法,8 m径向超前预注浆,开挖循环进尺为0.5 m,左部①②③比右部④⑤⑥超前15 m。初期支护中喷射混凝土采用shell结构单元,钢拱架运用刚度等效原则折算成混凝土强度,锚杆采用cable结构单元;施工中超前小导管、超前大管棚和围岩加固注浆措施采用提高围岩加固区的参数来实现。根据龙南隧道工程地质勘察报告与《铁路隧道设计规范》(TB 10003—2016)[28]确定隧道围岩与支护材料的物理力学参数,具体计算参数见表1表2

    表  1  初期支护参数
    Table  1.  Initial support parameters
    项目 重度
    /(kN·m−3
    弹性模量
    /GPa
    泊松比 抗压强度
    /MPa
    抗拉强度
    /MPa
    C25混凝土 22 22.1 0.24 12.5 1.3
    C25+HW175型钢 23 40.0 0.20 20.8 1.5
    锚杆 210.0 0.20
    下载: 导出CSV 
    | 显示表格
    表  2  物理力学参数
    Table  2.  Physical and mechanical parameters
    项目 重度
    /(kN·m−3
    弹性模量
    /GPa
    泊松比 内摩擦角
    /(°)
    黏聚力
    /kPa
    渗透系数
    /(cm·s−1
    Ⅴ级围岩 20 1.2 0.38 24 140 1.74×10−4
    断层破碎带 17 0.9 0.40 14 90 1.96×10−2
    注浆加固圈 20 6.0 0.30 30 400 1.00×10−4
    下载: 导出CSV 
    | 显示表格

    隧道穿越F8断层破碎带时,隧道围岩处于应力场与渗流场耦合作用下,单一的应力和孔隙水压力并不能反映隧道的稳定性。所以,隧道在开挖和支护过程中,要重视应力场和渗流场的耦合作用,才能保证隧道安全、高效地通过F8断层破碎带。

    在无任何支护作用下,模拟隧道在有渗流场和无渗流场时的开挖,结果表明:无渗流场时,在隧道DK99+546.6处右拱顶部位位移沉降最大,最大为1.22 m,隧道有发生塌方和冒顶的可能;在隧道DK99+535.65处左仰拱部位隆起最大,最大为0.18 m。有渗流场时,计算出现负体积,隧道发生破坏,此时,隧道拱部沉降0.69 m,底部隆起0.61 m。在流固耦合作用下,隧道底部隆起较大,施作支护时,隧道支护要及时封闭成环,仰拱要尽快填充,做好排水和堵水的工作。

    由上述分析可知,在流固耦合作用下,隧道穿越F8断层破碎带时,拱顶沉降较大且不均匀,隧道底部出现大幅度隆起。隧道初期支护和超前注浆预加固能够有效控制隧道大幅度变形和减小孔隙水压力对隧道的破坏。在初期支护中,控制隧道大变形的主要是钢拱架和喷射混凝土,取钢拱架间距0.4,0.6,0.8,1.0,1.2 m和喷射混凝土厚度24,26,28 ,30,32 cm进行组合,分别对这25种工况进行数值模拟,通过分析位移场、应力场和渗流场的特征,寻找合理的钢拱架间距和喷射混凝土厚度。

    根据隧道的开挖方式和工程地质条件,分别取F8断层破碎带中间部位的中轴线、左拱顶区、右拱顶区3个监测点进行研究(位移分别记为g1g2g3)。采用数学中的偏差平方和函数ST=(g1g2)2+(g2g3)2+(g3g1)2,计算3个监测点位移差的平方和,ST值越大,说明隧道拱部围岩变形越不均匀。

    图4可知,在不同喷射混凝土厚度下,ST值随钢拱架间距的变化规律基本一致,当钢拱架间距较小时,钢拱架间距的变化对ST值影响较大,而当钢拱架间距大于1.0 m时,ST值基本不再变化,故选择钢拱架间距为1.0 m,而且隧道循环进尺为0.5 m,便于钢拱架的架立。

    图  4  ST与钢拱架间距关系曲线
    Figure  4.  Relationship between ST and steel arch spacing

    图5可知,在钢拱架间距为1.0 m时,随着喷射混凝土厚度的增加,拱顶沉降量得到抑制;右拱顶区由于受到左导洞开挖的影响,导致右拱顶区的沉降量大于左拱顶区;在喷射混凝土厚度为26~30 cm时,拱顶沉降变化较缓,故在此类工程地质条件下,采用六部CD法施工工序时,喷射混凝土厚度的合理取值为26~30 cm。对钢拱架间距为1.0 m,不同喷射混凝土厚度时的ST值进行三次曲线拟合(图6),得出此断面喷射混凝土最优厚度为28 cm。

    图  5  拱顶沉降量与初支喷射混凝土厚度关系曲线
    Figure  5.  Relationship between settlement of arch crown and the thickness of primary support shotcrete
    图  6  ST与喷射混凝土厚度关系曲线
    Figure  6.  Relationship between ST and shotcrete thickness

    在FLAC3D软件中输入计算塑性区大小的FISH语言命令能够计算模型剪切塑性区和拉伸塑性区的体积,两者之和为塑性区体积。计算钢拱架间距为1.0 m时不同喷射混凝土厚度塑性区的体积(图7),当初支喷射混凝土厚度小于28 cm时,塑性区体积随混凝土厚度增大而减小,两者近乎成反比关系,增加混凝土厚度在初支作用中较为明显;当初支喷射混凝土厚度大于28 cm时,初支起到一定强支护作用,但塑性区体积减小幅度很小,所以通过增加初支喷射混凝土厚度来提高初支结构的安全性是不经济的。从斜率看,喷射混凝土厚度不能太薄,故在钢拱架间距为1.0 m时,初支喷射混凝土厚度取28 cm对本断面是较为经济合理的。

    图  7  塑性区体积与初支喷射混凝土厚度关系曲线
    Figure  7.  Relationship between the volume of the plastic zone and the thickness of primary support shotcrete

    模拟钢拱架间距为1.0 m,喷射混凝土厚度为28 cm时围岩地下水渗流情况,超前径向预加固后,隧道洞口周围8 m范围内岩石参数发生变化,渗透系数降为1×10−4 cm/s。为便于分析,对断层中间断面渗流情况进行研究。

    图89所示,隧道开挖后,隧道周边围岩孔隙水压力不断消散,在水头压差作用下,地下水渗进隧道内,造成渗流场的改变,形成一个以隧道开挖区域为中心的类似漏斗的渗流场[29]。渗流场的变化主要在8 m预浆加固圈内,说明注浆加固效果对孔隙水压力分布影响很大,被加固的岩体起到隔渗效果,阻止了大量地下水向隧道内涌进。在此工况下,隧道渗流量较为明显部位是拱脚>边墙>拱底>拱顶,渗流量较明显部位是地下水重要的排泄通道,故在施工中要重视相应部位的加固工作。

    图  8  孔隙压力及渗流矢量图(单位:Pa)
    Figure  8.  Vector diagram of pore pressure and seepage (Unit: Pa)
    图  9  孔隙压力等值线(单位:Pa)
    Figure  9.  Contour map of pore pressure (Unit: Pa)

    图1011可知,采用六部CD法施工时,围岩变形相对均匀,在超前预加固与初期支护联合作用下,围岩变形得到控制。图10数据对比表明,前期计算值比现场监测值大,可能由于现场监测点布置较晚,开始量测时围岩已经发生较大变形,监测值偏小;后期现场监测值比计算值大,是由于实际施工时爆破振动、机械扰动和中隔墙拆除等各种扰动因素的影响,以及计算采用的弹塑性模型没有考虑其长期效应,导致监测值偏大。图11洞身收敛数据对比情况与拱顶沉降量数据对比情况相近,隧道左侧收敛值明显比右侧小,这与开挖方式和临时支撑等因素有关;收敛监测数据在5 d左右出现收敛减缓的趋势,是由于隧道施加临时支撑,导致收敛减缓。但是由于两者变化规律相近,量级一致,故该数值计算能够反映实际情况。

    图  10  拱顶沉降量计算值与监测值对比曲线
    Figure  10.  Comparison of calculated and monitored arch values
    图  11  洞身收敛计算值与监测值对比曲线
    注:以左侧监测点SL1、SL3的收敛值为正,则右侧监测点SL2、SL4的收敛值为负。
    Figure  11.  Comparison of calculated and monitored convergence values

    (1)在流固耦合作用下,隧道穿越F8断层破碎带时,拱顶沉降较大且不均匀,隧道底部出现大幅度隆起,隧道要做好超前注浆预加固措施,施作支护时,隧道支护要及时封闭成环,仰拱要尽快填充,做好排水和堵水的工作。

    (2)结合F8断层破碎带中间部位的典型断面,通过中轴线、左拱顶区、右拱顶区3个监测点的沉降量建立偏差平方和ST函数,对不同钢拱架间距和喷射混凝土厚度的各种工况进行计算,通过分析位移场、应力场和渗流场的特征,发现断层破碎带地段的初支钢拱架合理间距为1.0 m,喷射混凝土合理厚度为26~30 cm,研究断面的最优厚度为28 cm。

    (3)钢拱架间距为1.0 m,喷射混凝土厚度为28 cm时,模拟结果表明隧道渗流量较为明显部位是拱脚>边墙>拱底>拱顶,且渗流场的变化主要在8 m预浆加固圈内,在施工中要重视相应部位的加固工作。

    (4)现场实际施工工况监测结果与计算结果对比表明,现场拱顶沉降监测值比计算值大,洞身左侧收敛小于右侧收敛,但监测结果与计算结果的变化规律相近,量级一致,说明计算结果能够反映实际情况,可供类似工程参考。

  • 图  1   F8断层带纵断面

    Figure  1.   F8 fault zone profile

    图  2   六部CD法施工设计图(单位:cm)

    注:g1—g3为位移监测点位移;SL1—SL4为洞身收敛监测点;①—⑥为六部CD法各部。

    Figure  2.   Constriction design of Six CD method (Unit: cm)

    图  3   三维数值模型

    Figure  3.   3D numerical model

    图  4   ST与钢拱架间距关系曲线

    Figure  4.   Relationship between ST and steel arch spacing

    图  5   拱顶沉降量与初支喷射混凝土厚度关系曲线

    Figure  5.   Relationship between settlement of arch crown and the thickness of primary support shotcrete

    图  6   ST与喷射混凝土厚度关系曲线

    Figure  6.   Relationship between ST and shotcrete thickness

    图  7   塑性区体积与初支喷射混凝土厚度关系曲线

    Figure  7.   Relationship between the volume of the plastic zone and the thickness of primary support shotcrete

    图  8   孔隙压力及渗流矢量图(单位:Pa)

    Figure  8.   Vector diagram of pore pressure and seepage (Unit: Pa)

    图  9   孔隙压力等值线(单位:Pa)

    Figure  9.   Contour map of pore pressure (Unit: Pa)

    图  10   拱顶沉降量计算值与监测值对比曲线

    Figure  10.   Comparison of calculated and monitored arch values

    图  11   洞身收敛计算值与监测值对比曲线

    注:以左侧监测点SL1、SL3的收敛值为正,则右侧监测点SL2、SL4的收敛值为负。

    Figure  11.   Comparison of calculated and monitored convergence values

    表  1   初期支护参数

    Table  1   Initial support parameters

    项目 重度
    /(kN·m−3
    弹性模量
    /GPa
    泊松比 抗压强度
    /MPa
    抗拉强度
    /MPa
    C25混凝土 22 22.1 0.24 12.5 1.3
    C25+HW175型钢 23 40.0 0.20 20.8 1.5
    锚杆 210.0 0.20
    下载: 导出CSV

    表  2   物理力学参数

    Table  2   Physical and mechanical parameters

    项目 重度
    /(kN·m−3
    弹性模量
    /GPa
    泊松比 内摩擦角
    /(°)
    黏聚力
    /kPa
    渗透系数
    /(cm·s−1
    Ⅴ级围岩 20 1.2 0.38 24 140 1.74×10−4
    断层破碎带 17 0.9 0.40 14 90 1.96×10−2
    注浆加固圈 20 6.0 0.30 30 400 1.00×10−4
    下载: 导出CSV
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出版历程
  • 收稿日期:  2024-02-02
  • 修回日期:  2024-05-26
  • 网络出版日期:  2025-04-08
  • 刊出日期:  2025-05-14

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