CALCULATION METHOD FOR SURROUNDING ROCK PRESSURE OF DEEPLY BURIED TRIPLE-ARCH TUNNEL
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摘要: 基于普氏压力拱理论和过程载荷设计方法, 考虑连拱隧道组合成拱作用, 以及施工工序和中隔墙支撑作用, 量化相邻简化导洞间的施工扰动, 提出深埋三连拱隧道不同施工断面及工序下的载荷分布模型, 进而改进了深埋三连拱隧道围岩压力的计算方法, 结合八达岭长城站三连拱隧道工程, 将理论结果与实测数据对比, 验证计算方法的合理性. 最后系统分析施工工序、中隔墙宽度和开挖跨度等因素对围岩压力的影响规律. 结果表明: 深埋三连拱隧道相互间的施工扰动影响无法忽视, 次行洞、后行洞的开挖都会扩大先行洞上方松散破碎围岩区域, 造成较为明显的偏压现象; 当中隔墙岩体抗压强度较小时, 增加中隔墙宽度难以改善围岩压力分布状态, 当中隔墙岩体抗压强度较大时, 增大宽度能够显著减小围岩压力; 围岩条件越差, 三连拱隧道各洞室所受围岩压力越大, 同时偏压现象也更加明显. 文章基于普氏压力拱理论和过程载荷设计方法所得出的计算方法, 增加考虑了连拱隧道相邻洞室间的施工影响, 揭示了三连拱隧道的偏压效应, 填补了有关三连拱隧道围岩压力计算方法的研究空缺, 为相关工程设计提供了重要参考.Abstract: Based on the Platts pressure arch theory and process load design method, considering the combined arch effect of the continuous arch tunnel, considering the construction process and the supporting role of the middle partition wall, quantifying the construction disturbance between the adjacent simplified guide holes, and proposing the load distribution model under different construction sections and processes of the deep buried three-arch tunnel, and then improving the calculation method of the surrounding rock pressure of the deep-buried three-arch tunnel, combined with the three-arch tunnel project of Badaling Great Wall station, the theoretical results are compared with the measured data to verify the rationality of the calculation method. Finally, the systematic analysis of the construction process, the width of the diaphragm wall, the span of excavation and other factors on the influence of the surrounding rock pressure law. The results show that: the influence of construction disturbance among deeply buried triple-arch tunnels cannot be ignored, and the excavation of secondary and posterior caverns will expand the loose and broken surrounding rock area above the first cavern causing a more obvious bias pressure phenomenon; when the compressive strength of the rock body of the diaphragm wall is small, it is difficult to improve the surrounding rock pressure distribution by increasing the width of the diaphragm wall. While the compressive strength of the rock body of the diaphragm wall is large, increasing the width can significantly reduce the surrounding rock pressure; the poorer the rock condition, the greater the rock pressure in each chamber of the triple-arch tunnel, and the more obvious the bias pressure phenomenon. Based on the calculation method obtained by Platts pressure arch theory and process load design method, this paper adds the construction influence between adjacent caverns of the continuous arch tunnel, reveals the bias effect of the three-arch tunnel, fills the research gap on the calculation method of surrounding rock pressure of the three-arch tunnel, and provides important reference and guiding significance for the related engineering design.
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引 言
随着国家经济社会的快速发展, 我国在隧道建设与研究方面已取得长足的进步, 对围岩稳定性、支护与围岩的关系以及支护结构体系的动力响应有了新的认识[1-5]. 由于特殊地形和展线困难, 导致越来越多的双连拱隧道出现在工程建设中. 但日益增长的交通流量及特定的建设需求, 使双连拱隧道受其车道数量所限, 已难以满足实际需求, 因此工程界也逐渐涌现出一些三连拱公路隧道, 如香港岛北岸三连拱公路隧道干道[6]、台湾新北市新店地区三连拱公路隧道[7]等. 大跨度三连拱隧道洞室相继开挖对围岩叠加扰动更为严重, 使得施工风险和建造难度远大于双连拱隧道.
不少学者对于深埋道双洞隧道载荷分布模式进行研究. 申玉生[8]提出利用《公路隧道设计规范》统计公式时, 应按照净跨度来计算围岩压力; 丁文其等[9]改进了双塌落拱理论, 认为围岩载荷应依据隧道宽度线性取值; 朱正国等[10]指出现行《公路隧道设计规范》公式的不合理, 给出了新的隧道深浅埋划分依据, 并建议采用修正比尔鲍曼公式来计算连拱隧道载荷; 李鸿博等[11]根据普氏压力拱理论, 推导了连拱隧道深、浅埋情况下的围岩载荷计算公式, 确定了中隔墙是结构稳定的关键; 李亮等[12]给出了连拱隧道破碎围岩的定义和类别, 并在此基础上推导了载荷理论解; 黎敬俊等[13]提出了附加修正系数并优化了求解方法, 可用于改进既有规范方法和塌落拱方法, 工程应用效果良好; 李鹏飞等[14-15]结合普氏理论建立了深埋双洞隧道的3种载荷模型, 进而提出了相应的围岩压力计算方法, 理论值与实测值较为接近. 但是上述研究均未考虑连拱隧道相邻洞室间的施工影响, 在力学模型中直接采取对称载荷形式.
针对既有围岩压力计算方法难以考虑邻近开挖扰动影响, 相关学者开展了一些研究. Xu等[16]考虑隧道双侧导坑分步开挖过程和临时支护对隧道围岩压力的影响, 推导了同施工顺序下松散载荷分布模式和计算方法; 刘灼[17]基于普氏压力拱理论, 提出施工影响系数, 解析出双侧壁导坑法下的连拱隧道围岩压力表达式; 姜成业等[18]基于普氏理论, 提出深埋条件下无中导洞连拱隧道围岩压力计算方法; 高红杰等[19]基于过程载荷计算方法推导了深埋非对称连拱隧道过程载荷计算公式; 还有不少学者采用数值模拟和现场监测的方法, 对双连拱隧道施工引起的地层变形、围岩力学特征等内容进行研究[20-26]. 双连拱隧道围岩压力理论研究已经相对成熟, 但能否直接应用于三连拱隧道还存在疑问.
目前, 对于三洞隧道围岩压力的研究相对较少. 课题组前期针对八达岭长城站三孔小净距隧道工程和三连拱隧道, 通过数值模拟和现场实测对隧道围岩变形特征、支护力学响应等进行了研究, 并提出了相应的控制措施[27-32].
为进一步研究深埋三连拱隧道的载荷分布规律, 本文基于普氏理论[33-34], 考虑过程载荷影响, 推导出深埋三连拱隧道围岩压力计算公式, 并通过现场实测验证理论公式的合理性, 最后对围岩压力影响因素进行参数分析.
1. 三连拱隧道组合成拱过程
三连拱隧道典型施工工序主要分为3种, 即工序1先行左洞、次行右洞和后行中洞; 工序2先行左洞、次行中洞和后行右洞; 工序3先行中洞、次行左洞和后行右洞, 各工序示意图如图1所示.
根据施工顺序的不同, 可以将三连拱隧道施工划分为小净距模式(图2)和连拱模式(图3).
小净距模式: 按照工序1顺序施工, 当左右洞分别开挖完成, 中洞尚未开挖时, 左右洞的围岩压力模式与双孔小净距隧道类似, 中间尚未开挖土体起到与中岩柱类似的支撑作用.
连拱模式按照工序2或3顺序施工, 当边洞、中洞开挖完成时, 其围岩压力模式即为一般双连拱隧道模式.
单一洞室的分步开挖会呈现出压力拱渐进组合成型的特点[35]. 各洞室间的组合成拱过程更为复杂, 但其内在规律实际与单一洞室的分步开挖过程较为类似.
1.1 组合成拱作用基本假定
由于施工的复杂性, 难以准确完整地使隧道压力拱的组合成型, 因此引入如下基本假定.
(1)由于深埋情况下不论单独拱或复合拱, 均具有一定承载能力, 竖向支撑力会和阴影内的承载岩土体自重形成平衡, 所以假定除考虑各洞单独拱载荷外, 还需要考虑复合压力拱附加载荷.
(2)由于现有三连拱隧道大部分皆为左右洞室断面尺寸相同, 且本文中所选用的工程实例也是左右洞室断面尺寸相同的情况, 为了简便计算, 所以假设整个三连拱隧道关于中线对称, 即左右洞室断面尺寸相同.
(3)由于三连拱隧道各洞室相互紧邻, 次行洞和后行洞的开挖均会进一步加剧对先行洞上方的围岩扰动程度, 削弱围岩承载能力. 所以假定先施作洞室上方最终围岩压力要考虑后施作洞室的开挖影响, 并进行一定的载荷修正.
(4)三连拱隧道各个洞室在纵向掘进过程中, 由于支护时机和掌子面间距的不同, 掌子面下围岩-支护作用的强弱会略有区别. 为方便计算, 假定隧道压力拱效应在距离掌子面前方0.5倍洞径和后方2.5倍洞径间呈线性变化.
(5)若三连拱隧道采用超前中导洞法施工, 一般情况下中导洞断面较小, 且支护较为及时, 形成的压力拱范围较为局限. 为了简化分析过程, 本文不考虑中导洞上方压力拱对整个三连拱隧道组合成拱的影响.
1.2 横向组合成拱过程与围岩压力表征
三连拱隧道在施工过程中会出现单一洞室、双洞室以及三洞室情况, 其中双洞室又分为小净距模式和双连拱模式.
1.2.1 单洞室断面
仅一个洞室开挖完成时, 其压力拱形态在深埋情况下为常见单洞隧道普氏拱(图4). 可按普氏理论围岩压力计算公式[36]进行计算
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图 4 普氏理论围岩压力示意图Figure 4. Calculation diagram of surrounding rock pressure based on Protodyakonov's theory$$ q = \gamma {H_q} $$ (1) 其中
$$ {H_q} = \frac{B}{{2f}} = \frac{{b + 2H\tan \left( {{{45}^\circ } - \varphi /2} \right)}}{{2f}} $$ $$ f = \frac{{{R_{{c}}}}}{{10}} $$ 式中, q为垂直围岩压力; $\gamma $为围岩重度; Hq为普氏压力拱等效高度; B为压力拱水平跨度; b为隧道开挖跨度; $\varphi $为岩石的计算摩擦角; f为普氏围岩坚固系数; Rc为岩石单轴饱和抗压强度; H为隧道开挖高度.
1.2.2 双洞室断面
(1) 小净距模式
左右洞室开挖完成后, 除在各自拱顶上方形成独立压力拱外, 在整个跨度范围内还会形成复合压力拱. 独立压力拱提供的载荷定义为基本围岩压力, 形式为均布载荷; 复合压力拱提供的载荷为附加围岩压力, 假定为线性分布载荷. 根据以上分析, 小净距模式下隧道竖向围岩压力叠加如图5所示. 图中, q11和q13分别为左洞和右洞的基本围岩压力, q2r和q2l为隧道内、外侧边缘处的附加围岩压力, 二者叠加后可得到q2R和q2L.
定义中间未开挖土体支撑宽度为Lz, 根据其是否发挥作用, 竖向围岩压力分为两种情况讨论, 如图6和图7所示.
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图 6 小净距模式载荷模型1附加围岩压力(Lz > 0)Figure 6. Load distribution 1 additional surrounding rock pressure of closely spaced mode (Lz > 0)![]()
图 7 小净距模式载荷模型2附加围岩压力(Lz = 0)Figure 7. Load distribution 2 additional surrounding rock pressure of closely spaced mode (Lz = 0)① 当Lz > 0时, 中间未开挖土体参与承受阴影内的岩土体压力, 并起到抑制围岩变形的作用, 可得
$$ {L_z} = {B_L} - {B_{p1}} - {B_{p3}} $$ (2) 其中
$$ {B_L} = {B_S} - 2{B_1},\quad {B_{p1}} = {H_{q1}}\tan \theta ,\quad {B_{q3}}{\text{ = }}{H_{q{\text{3}}}}\tan \theta $$ 式中, BL为中间未开挖土体宽度, Bp1和Bp3为左右边洞两侧破裂面的水平投影长度, B1为左洞和右洞的开挖跨度, BS为整个三连拱隧道的开挖跨度.
图中阴影部分的岩土体重力Gm1可由下式求得
$$ {G_{m1}} = \frac{2}{3}\gamma \left( {{B_{m1}}{H_{m1}} - {B_{t1}}{H_{q1}} - {B_{t3}}{H_{q3}}} \right) $$ (3) 其中, Bm1为双洞复合压力拱跨度, Bt1和Bt3为左右边洞单独压力拱跨度, Hm为双洞复合压力拱高度, Hq1和Hq3为左洞和右洞通过考虑施工过程影响而形成的综合压力拱.
该部分岩土重力将在附加压力和未开挖土体支撑力的作用下保持受力平衡, 可得
$$ {G_{m1}} = {P_{vir}} + \frac{1}{2}\left( {{B_{t1}}{q_{21}} + {B_{t3}}{q_{22}}} \right) $$ (4) 式中, Pvir = qvirLz, qvir为中间未开挖岩土体的抗压强度, 其值为qvir = Rs/K, Rs指岩土体抗压强度设计值; K为安全系数, 一般取2[30]. q21和q22存在如下关系
$$ \frac{{{q_{21}}}}{{{q_{22}}}} = \frac{{{B_{t1}}}}{{{B_{t3}}}} $$ (5) 联立式(4)和式(5), 可求得
$$ {q_{21}} = \frac{{{B_{t1}}}}{{{B_{t3}}}} \cdot {q_{22}} $$ (6) $$ {q_{22}} = \frac{{2{B_{t3}}\left( {{G_{m1}} - {P_{vir}}} \right)}}{{{B_{t1}}^2 + {B_{t3}}^2}} $$ (7) 附加围岩压力假定为线性分布载荷, 根据比例关系, 可得左右边洞的竖向围岩压力
$$ \left. \begin{aligned} & {q_{2R}^1 = {q_{11}} + \frac{{{B_{p1}}}}{{{B_{t1}}}} \cdot {q_{21}}} \\ & {q_{2L}^1 = {q_{11}} + \frac{{{B_{p1}} + {B_1}}}{{{B_{t1}}}} \cdot {q_{21}}} \\ & {q_{2R}^3 = {q_{13}} + \frac{{{B_{p3}}}}{{{B_{t3}}}} \cdot {q_{22}}} \\ & {q_{2L}^3 = {q_{13}} + \frac{{{B_{p3}} + {B_1}}}{{{B_{t3}}}} \cdot {q_{22}}} \end{aligned} \right\}$$ (8) 以左洞为例, 作用在左洞拱部和拱脚的水平压力为
$$ \left. \begin{aligned} & {e_1} = \lambda \left( {{q_{11}} + {q_{2r - 1}}} \right) \\ & {e_2} = \lambda \left( {{q_{11}} + {q_{2r - 1}} + \gamma {H}} \right) \end{aligned} \right\} $$ (9) ② 当Lz = 0时, 中间未开挖土体不参与承受阴影内的岩土体压力, 仅起到抑制围岩变形的作用, 此时左洞和右洞的间距为BL = Bp1−Bp3.
附加力Gm1的表达式与式(3)相同. 依据竖向受力平衡, 可得
$$ {G_{m1}} = \frac{1}{2}\left( {{B_{t1}}{q_{21}} + {B_{t3}}{q_{22}}} \right) = \frac{1}{2}{B_{m1}}{q_{21}} $$ (10) 联立式(3)和式(10), 可求得
$$ {q_{21}} = {q_{22}} = \frac{{2{G_{m1}}}}{{{B_{m1}}}} $$ (11) 根据比例关系求得左右边洞的竖向与水平围岩压力, 具体过程与Lz > 0工况相同, 此处不再赘述.
(2) 连拱模式
在连拱模式下会施作中隔墙, 中隔墙的稳定性和其对上部土体的支撑能力强弱直接影响连拱隧道的载荷作用模式. 隧道拱顶水平线上方载荷与小净距模式类似, 同样为基本围岩压力和附加围岩压力(图8)的叠加. 此外, 连拱模式下中隔墙顶和左洞、中洞拱顶之间还存在部分松散土体载荷q3, 同样假定其为线性分布形式(图9). 因此, 连拱模式下隧道围岩压力可看作由隧道拱顶水平线上方围岩压力和中隔墙顶部松散围岩压力组合形成.
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图 8 连拱模式载荷模型附加围岩压力Figure 8. Additional surrounding rock pressure of multi-arch load model阴影部分的岩土体重力Gm2, 由下式求得
$$ {G_{m2}} = \frac{2}{3}\gamma \left( {{B_{m2}}{H_{m2}} - {B_{t1}}{H_{q1}} - {B_{t2}}{H_{q2}}} \right) $$ (12) 中隔墙支撑力Pz表达式如下
$$ {P_z} = {q_z}{B_z} $$ (13) 式中, qz取值实际与前文未开挖土体支撑力qvir计算表达式相同, Bz为隧道中隔墙设计宽度.
根据竖向受力平衡, 可得
$$ {G_{m2}} = \frac{1}{2}\left( {{B_{t1}}{q_{2l}} + {B_{t2}}{q_{2l}}} \right) + {P_z} = \frac{1}{2}{B_{m2}}{q_{2l}} + {P_z} $$ (14) 有
$$ {q_{2l}} = \frac{{2\left( {{G_{m2}} - {P_z}} \right)}}{{{B_{m2}}}} $$ (15) 可得左、中洞的竖向围岩压力
$$ \left. \begin{aligned} & {q_{2R}^1 = {q_{11}} + \frac{{{B_{p1}}}}{{{B_{t1}}}} \cdot {q_{2l}}} \\ & {q_{2L}^1 = {q_{11}} + {q_{2l}} + {q_3} + {q_z}} \\ & {q_{2R}^2 = {q_{12}} + \frac{{{B_{p2}}}}{{{B_{t2}}}} \cdot {q_{2l}}} \\ & {q_{2L}^2 = {q_{12}} + {q_{2l}} + {q_3} + {q_z}} \end{aligned}\right\} $$ (16) 水平侧压力, 以左洞为例, 与式(9)相似, 此处不再赘述.
1.2.3 全断面
全断面载荷模型如图10所示, 阴影部分的岩土体重力Gm由复合拱内部土体载荷减去三洞单独拱载荷求得
$$ {G_m} = \frac{2}{3}\gamma \left( {{B_{m1}}{H_{m1}} - {B_{t1}}{H_{q1}} - {B_{t2}}{H_{q2}} - {B_{t3}}{H_{q3}}} \right) $$ (17) 该部分岩土体受力平衡, 可得
$$ {G_m} = 2{P_z} + \frac{1}{2}{B_m}{q_2} $$ (18) 由式(18)可解得
$$ {q_2} = \frac{{2{G_m} - 4{P_z}}}{{{B_m}}} $$ (19) 同样根据对应比例关系, 可得各洞的竖向围岩压力
$$ \left. \begin{aligned} & {q_{2R}^1 = {q_{11}} + \frac{{2{B_{p1}}}}{{{B_m}}} \cdot {q_2}} \\ & {q_{2L}^1 = {q_{11}} + \frac{{2\left( {{B_{p1}} + {B_1}} \right)}}{{{B_m}}} \cdot {q_2} + {q_3} + {q_z}} \\ & {q_{2R}^2 = {q_{12}} + \frac{{2\left( {{B_{t1}} + {B_z}/2} \right)}}{{{B_m}}} \cdot {q_2} + {q_3} + {q_z}} \\ & {q_{2L}^2 = {q_{12}} + \frac{{2\left( {{B_{t3}} + {B_z}/2} \right)}}{{{B_m}}} \cdot {q_2} + {q_3} + {q_z}} \\ & {q_{2R}^3 = {q_{13}} + \frac{{2{B_{p3}}}}{{{B_m}}} \cdot {q_2}} \\ & {q_{2L}^3 = {q_{13}} + \frac{{2\left( {{B_{t3}} + {B_z}/2} \right)}}{{{B_m}}} \cdot {q_2} + {q_3} + {q_z}} \end{aligned}\right\} $$ (20) 水平侧压力, 以左洞为例, 与式(9)相似, 此处不再赘述.
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图 10 全断面载荷模型附加围岩压力Figure 10. Additional surrounding rock pressure of full section load model1.3 纵向组合成拱过程与围岩压力表征
前文1.2节分析了横向断面(即二维平面)下的三连拱隧道组合成拱过程, 但实际三连拱隧道各个洞室在纵向掘进过程中, 由于支护时机和掌子面间距的不同, 掌子面下围岩-支护作用的强弱会略有区别, 这直接导致围岩压力呈现在距离掌子面前方0.5倍洞径和后方2.5倍洞径间动态变化的特点. 为方便计算和基于前文假定, 认为该变化呈线性. 不同施工工序下的三连拱隧道各洞室纵向开挖掘进示意图如图1所示.
单洞室、双洞室和全断面下的洞室围岩压力分别定义为Q1, Q2和Q3, 任取一断面位置P, 各洞室掌子面前方0.5倍洞径处距离断面P的纵向距离分别定义为L1, L2和L3, 则断面P处的各洞室围岩压力分别为
$$ {Q_{{{L}}}} = {m_1}{Q_{11}} + {m_2}\left( {{Q_{12}} - {Q_{11}}} \right) + {m_3}\left( {{Q_{13}} - {Q_{12}}} \right) $$ (21) $$ {Q_{{R}}} = {m_1}{Q_{21}} + {m_2}\left( {{Q_{22}} - {Q_{21}}} \right) + {m_3}\left( {{Q_{23}} - {Q_{22}}} \right) $$ (22) $$ {Q_{{M}}} = {m_1}{Q_{31}} + {m_2}\left( {{Q_{32}} - {Q_{31}}} \right) + {m_3}\left( {{Q_{33}} - {Q_{32}}} \right) $$ (23) 式中, QL, QR和QM分别为左洞、右洞和中洞的围岩压力, m1, m2和m3分别为关于L1, L2和L3的函数. 基于假设可得
$$ {m_1} = \left\{ \begin{aligned} & 0,\quad 0 \leqslant {L_1} < 0.5{B_1} \\ & \frac{{{L_1}}}{{3{B_1}}},\quad 0.5{B_1} \leqslant {L_1} < 3{B_1} \\ & 1,\quad 3{B_1} \leqslant {L_1} \end{aligned} \right. $$ (24) $$ {m_2} = \left\{\begin{aligned} & 0,\quad 0 \leqslant {L_2} < 0.5{B_1} \\ & \frac{{{L_2}}}{{3{B_1}}},\quad 0.5{B_1} \leqslant {L_2} < 3{B_1} \\ & 1,\quad 3{B_1} \leqslant {L_2} \end{aligned} \right. $$ (25) $$ {m_3} = \left\{\begin{aligned} & 0,\quad 0 \leqslant {L_3} < 0.5{B_2} \\ & \frac{{{L_3}}}{{3{B_2}}},\quad 0.5{B_2} \leqslant {L_3} < 3{B_2} \\ & 1,\quad 3{B_2} \leqslant {L_3}\end{aligned} \right. $$ (26) 2. 基于过程载荷的围岩压力计算
普氏公式、围岩分级体系公式和隧道设计规范推荐公式等均是基于终态载荷进行计算, 未考虑施工工法及工序对围岩载荷的影响. 过程载荷设计考虑了施工工法和施工过程的影响, 更加符合现场和实际情况. 本文将基于过程载荷设计理念, 建立深埋三连拱隧道过程载荷压力拱模型. 为构建载荷压力拱模型, 有以下假定:
(1)当各导洞间距大于2倍导洞宽度时, 不考虑二者间施工的相互影响;
(2)为便于计算, 隧道最终载荷是各导洞载荷在各自位置上的简单垂直叠加, 然后考虑各自权系数, 进行加权平均得到总载荷;
(3)各导洞的简化基于一定的规则, 保证宽度、高度等基本不变.
2.1 单一洞室过程载荷设计实现
2.1.1 模型简化
单洞隧道常用施工工法主要有全断面开挖法、台阶法、中隔壁法、双侧壁导坑法等. 简化时遵循以下原则: (1)保证简化后的导洞开挖高度与原开挖步的开挖高度基本相同; (2)导洞简化开挖宽度与原开挖宽度基本一致, 偏差不超过5%; (3)简化导洞底面要处于同一水平线上. 简化模型如图11所示.
2.1.2 影响系数
过程载荷设计为考虑和量化隧道施工时相邻开挖导洞间的影响, 引入了施工影响系数η来表征隧道先行洞开挖完成时, 后行洞开挖对先行洞围岩载荷的影响, 如图12所示. η取值如下
$$ \eta = \left\{\begin{aligned} & \frac{{{m_1}{m_2}{m_3}}}{{{m_4}{m_5}}},\quad \eta \geqslant {\text{1}} \\ & 1,\qquad\qquad \eta < 1 \end{aligned} \right. $$ (27) 式中, m1指导洞间距; m2指后行洞高跨比; m3指隧道所处地质条件; m4指有无支护及其参数; m5指围岩等级. 各参数的取值参考文献[37].
当η≥1时, 表明两开挖导洞相互影响, 后行洞施工时会加大先行洞围岩载荷. 当η < 1时, 则表明两导洞施工相互独立.
2.1.3 权系数
权系数$\alpha $是指每一开挖导洞计算得到的竖向围岩压力占整个隧道竖向围岩压力的比重, 其计算公式如下
$$ {\alpha _i} = \frac{{{Q_i}}}{{{Q_s}}} = \frac{{{q_i}{b_i}}}{{\displaystyle\sum\limits_{i = 1}^n {{q_i}{b_i}} }} $$ (28) 式中, Qi为单个开挖步简化导洞的竖向围岩压力, Qs为隧道总的竖向围岩压力, qi为单个简化导洞开挖引起的均布载荷, bi为导洞宽度, $n$为导洞个数.
2.2 围岩压力载荷计算
2.2.1 单洞室断面
单一洞室断面下无组合成拱效应, 按照过程载荷设计理念结合普氏理论求解.
2.2.2 双洞室断面
在双洞室断面工序2和3会呈现连拱模式, 工序1会呈现小净距模式(图13), 针对两种模式进行分析.
(1)小净距模式
当右洞施工时, 若左右洞间距小于2B, 会扰动左洞上方围岩, 加大围岩松散载荷, 此时需考虑影响系数.
① 先行洞、次行洞在各简化导洞开挖时产生的竖向均布载荷$q_{11}^i $和$q_{13}^i $
$$\left. \begin{aligned} & {q_{11}^i = \eta _1^i \cdot \gamma H_{q1}^i} \\ & {q_{13}^i = \eta _3^i \cdot \gamma H_{q3}^i} \end{aligned}\right\}$$ (29) 式中, $\eta _1^i $和$\eta _3^i $分别为三连拱隧道左洞和右洞分步开挖时的施工影响系数.
② 基本围岩压力q1
左洞开挖时, 与单洞隧道情况相同; 当右洞开挖时, 若左右洞间距较小, 需考虑施工影响系数η1
$$ \left.\begin{aligned} & {{\eta _1}{q_{11}} = {\eta _1}\sum\limits_{i = 1}^n {\alpha _1^i} q_{11}^i = {\eta _1}\frac{{\displaystyle\sum\limits_{i = 1}^n {q{{_{11}^i}^2}b_1^i} }}{{\displaystyle\sum\limits_{i = 1}^n {q_{11}^ib_1^i} }}} \\ & {{q_{13}} = \sum\limits_{i = 1}^n {\alpha _3^i} q_{13}^i = \frac{{\displaystyle\sum\limits_{i = 1}^n {q{{_{13}^i}^2}b_3^i} }}{{\displaystyle\sum\limits_{i = 1}^n {q_{13}^ib_3^i} }}} \end{aligned}\right\} $$ (30) 式中, α1和α3分别表示先行洞和次行洞在各导洞施工时引起的竖向均布载荷占整体载荷的比重.
③ 附加松散围岩压力q2
当考虑施工过程的影响, Gm1由下式确定
$$ {G_{m1}} = \frac{2}{3}\gamma \left( {{B_{m1}}{H_{m1}} - \sum\limits_{i = 1}^n {B_{q1}^iH_{q1}^i - \sum\limits_{i = 1}^n {B_{q3}^iH_{q3}^i} } } \right) $$ (31) 式中
$$ \mathit{B} _{ \mathit{q} \mathrm{1}}^{ \mathit{i} } \mathrm{ = } \mathit{b} _{ \mathrm{1}}^{ \mathit{i} } \mathrm{ + } \mathit{B} _{ \mathit{p} \mathrm{1}}^{ \mathit{i} } \mathrm{ + 1/2\cdot } \mathit{b} _{ \mathrm{1}}^{ \mathit{i} } \mathrm{/} \mathit{B} _{ \mathrm{1}} \mathrm{\cdot } \mathit{B} _{ \mathit{z} } $$ $$ \mathit{B} _{ \mathit{q} \mathrm{3}}^{ \mathit{i} } \mathrm{ = } \mathit{b} _{ \mathrm{3}}^{ \mathit{i} } \mathrm{ + } \mathit{B} _{ \mathit{p} \mathrm{3}}^{ \mathit{i} } \mathrm{ + 1/2\cdot } \mathit{b} _{ \mathrm{3}}^{ \mathit{i} } \mathrm{/} \mathit{B} _{ \mathrm{3}} \mathrm{\cdot } \mathit{B} _{ \mathit{z} } $$ 将Gm1代入式(7)和式(11), 可得到q22数值. 各洞围岩压力参照式(8)计算可得.
④ 衬砌两侧侧向围岩压力
以左洞为例, 作用在先行左洞拱部和拱脚的水平压力为
$$ \left.\begin{aligned} & {{e_1} = \lambda \left( {{\eta _1}{q_{11}} + {q_{2r - 1}}} \right)} \\ & {{e_2} = \lambda \left( {{\eta _1}{q_{11}} + {q_{2r - 1}} + \gamma H} \right)} \end{aligned}\right\} $$ (32) ![]()
图 13 工序1双洞室断面(小净距模式)载荷分布图Figure 13. Procedure 1 load distribution of double tunnels section (closely spaced mode)(2) 连拱模式
工序2和3会出现连拱模式(图14), 主要区别在于前者左洞受到开挖扰动, 后者是中洞受到开挖扰动. 以工序3为例进行分析.
① 先行洞、次行洞在各简化导洞开挖时产生竖向均布载荷$q_{11}^i $和$q_{12}^i $, 左洞竖向均布载荷表达式与式(29)相同, $q_{12}^i $计算公式如下
$$ q_{12}^i = \eta _2^i \cdot \gamma H_{q2}^i $$ (33) 式中, $\eta _2^i $为三连拱隧道中洞分步开挖时的施工影响系数.
② 基本围岩压力q1
左洞开挖时, 考虑施工影响系数η1
$$ \left.\begin{aligned} & {{\eta _1}{q_{12}} = {\eta _1}\sum\limits_{i = 1}^n {\alpha _2^i} q_{12}^i = {\eta _1}\frac{{\displaystyle\sum\limits_{i = 1}^n {q{{_{12}^i}^2}b_2^i} }}{{\displaystyle\sum\limits_{i = 1}^n {q_{12}^ib_2^i} }}} \\ & {{q_{11}} = \sum\limits_{i = 1}^n {\alpha _1^i} q_{11}^i = \frac{{\displaystyle\sum\limits_{i = 1}^n {q{{_{11}^i}^2}b_1^i} }}{{\displaystyle\sum\limits_{i = 1}^n {q_{11}^ib_1^i} }}} \end{aligned}\right\} $$ (34) 式中, α2为中洞在各导洞施工时引起的竖向均布载荷占整体载荷的比重.
③ 附加松散围岩压力q2
Gm2由下式计算得到
$$ {G_{m2}} = \frac{2}{3}\gamma \left( {{B_{m2}}{H_{m2}} - \sum\limits_{i = 1}^n {B_{q1}^iH_{q1}^i - \sum\limits_{i = 1}^n {B_{q2}^iH_{q2}^i} } } \right) $$ (35) 式中, $B_{q2}^i $ = $b_{2}^i $ + $B_{p2}^i $ + 1/2∙ $b_{2}^i $/B2∙Bz. 将Gm2代入式(15), 可得到q2l.
各洞围岩压力参照式(16)计算.
④ 中隔墙顶松散围岩压力q3
${q_3}$假定为三角形载荷, 按下式计算
$$ {q_3} = \gamma {H_3} $$ (36) 松散岩体高度H3近似取中隔墙顶至拱顶水平线的垂直距离.
⑤ 衬砌两侧侧向围岩压力
参照式(32)计算.
⑥ 中隔墙顶两侧侧向围岩压力
以先行左洞拱顶和衬砌内侧为例, 见下式
$$ \left.\begin{aligned} & {{e_{n1}} = \lambda \left( {{q_{11}} + {q_{2l}}} \right)} \\ & {{e_{n2}} = \lambda \left( {{q_{11}} + {q_{2l}} + {q_3}} \right)} \end{aligned}\right\} $$ (37) ![]()
图 14 工序3双洞室断面(连拱模式)载荷分布图Figure 14. Procedure 3 load distribution of double tunnels section (multi-arch mode)(3) 全断面
全断面情况以工序1为例(图15)进行分析.
① 基本围岩压力q1
当右洞开挖时, 若两洞室紧邻, 需考虑施工影响系数η1. 当中洞施工时, 又会再次加大左洞、右洞上方松散载荷, 需考虑施工影响系数η2
$$ \left.\begin{aligned} & {{\eta _1}{\eta _2}{q_{11}} = {\eta _1}{\eta _2}\sum\limits_{i = 1}^n {\alpha _1^i} q_{11}^i = {\eta _1}{\eta _2}\frac{{\displaystyle\sum\limits_{i = 1}^n {q{{_{11}^i}^2}b_1^i} }}{{\displaystyle\sum\limits_{i = 1}^n {q_{11}^ib_1^i} }}} \\[-3pt] & {{q_{12}} = \sum\limits_{i = 1}^n {\alpha _2^i} q_{12}^i = \frac{{\displaystyle\sum\limits_{i = 1}^n {q{{_{12}^i}^2}b_2^i} }}{{\displaystyle\sum\limits_{i = 1}^n {q_{12}^ib_2^i} }}} \\[-3pt] & {{\eta _2}{q_{13}} = {\eta _2}\sum\limits_{i = 1}^n {\alpha _3^i} q_{13}^i = {\eta _2}\frac{{\displaystyle\sum\limits_{i = 1}^n {q{{_{13}^i}^2}b_3^i} }}{{\displaystyle\sum\limits_{i = 1}^n {q_{13}^ib_3^i} }}} \end{aligned}\right\} $$ (38) ② 附加松散围岩压力q2
Gm由下式确定
$$ \begin{split} &{G_m} = \frac{2}{3}\gamma \left( {B_{m2}}{H_{m2}} - \sum\limits_{i = 1}^n B_{q1}^iH_{q1}^i -\right. \\[-3pt] &\qquad \left.\sum\limits_{i = 1}^n {B_{q2}^iH_{q2}^i - \sum\limits_{i = 1}^n {B_{q3}^iH_{q3}^i} } \right) \end{split}$$ (39) 式中, $B_{{q2}}^i = b_2^i + b_2^i/{B_2} \cdot {B_z}$.
各洞围岩压力参照式(20)计算.
③ 中隔墙顶松散围岩压力q3、衬砌两侧侧向围岩压力、隔墙顶两侧侧向围岩压力
参照式(32)、式(36)和式(37)计算.
3. 工程验证
3.1 八达岭三连拱隧道工程概况
八达岭长城站位于北京市境内八达岭滚天沟停车场下方新八达岭隧道内. 车站中心里程DK68 + 050.000, 到发线有效长650 m, 车站有效站台长450 m, 车站总长470 m, 地下部分建筑面积为
36143 m2, 地面部分建筑面积约为5000 m2, 总建筑面积约为41143 m2. 车站透视图如图16所示.三连拱区段位于车站两端, 总长72 m, 隧址区围岩条件为V级, 断面示意如图17所示.
3.2 理论值与实测值对比
3.2.1 实测结果
围岩压力的实测选择DK68 + 310 (V级围岩)作为施工力学响应的典型监测断面, 此外每隔5 m布设一组围岩压力测点, 监测断面的测点布置如图18和图19所示, 单个隧道布设3个测点, 从左往右依次为左拱肩、拱顶和右拱肩.
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图 18 双洞式断面监测点布置Figure 18. Layout of double-hole cross-section monitoring measurement points3.2.2 理论计算结果与实测结果对比
根据八达岭隧道实测地勘资料, 采用本文推导的过程载荷深埋三连拱隧道围岩压力计算方法, 计算V级围岩条件下的围岩压力值. 已知三连拱隧道中洞开挖净跨度13.2 m, 侧洞开挖净跨度14.5 m, 隧道开挖高度12.9 m, 中隔墙宽度1.0 m, 中隔墙高度9.0 m, 采用的施工工序为先施工左洞, 后施工右洞, 最后采用无导洞法施工中洞, 见表1.
表 1 围岩基本参数Table 1. Basic parameters of surrounding rockSurrounding rock grade γ/(kN·m−3) φ/(°) φg/(°) Rc/MPa V 20 20 40 15 通过代入各参数可以得到计算模型中各围岩压力的数值, 见表2.
表 2 各断面围岩压力数值Table 2. Surrounding rock pressure of each sectionPressure η1q11/kPa — q13/kPa q22/kPa q21/kPa — Double hole 128.3 — 111.6 236.6 236.6 — Pressure η1η2q11/kPa q12/kPa η2q13/kPa q22/kPa q21/kPa q3/kPa Full section 219.5 88.8 190.9 333.9 71.4 80.0 通过计算模型得到各基本和附加围岩压力后, 将其沿洞周按对应角度进行叠加, 得到围岩压力分布图, 并与实测数据进行对比, 如图20和图21所示.
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图 20 双洞室断面围岩压力理论值与实测值对比结果Figure 20. Comparison between theoretical value and the measured value of double tunnels section surrounding rock pressure![]()
图 21 全断面围岩压力理论值与实测值对比结果Figure 21. Comparison between theoretical value and the measured value of full section surrounding rock pressure结果表明: (1)随着八达岭三连拱隧道的开挖, 双洞室断面发展到三洞室全断面, 围岩压力呈现较为明显的增长, 尤其左右洞室内侧围岩压力分别由225和212 kPa增至376和301 kPa, 可见中洞的开挖对左右边洞上方围岩扰动较为明显, 且越靠近中洞一侧扰动越剧烈; (2)两种断面下采用本文推导的理论公式计算和现场实测的结果, 均表明采用左洞先行、右洞次行、中洞后行的施工工序时, 围岩压力的分布呈现较明显的偏压效应, 左洞围岩压力相对右洞较大, 同时中洞的施工也会增大左右洞的围岩压力; (3)围岩压力实测值呈现一定程度的离散分布性, 这主要是测点数量较少、现场实测时影响因素过多等因素引起的. 但采用本文推导的计算公式得到的围岩压力分布能够很好地包络实测值, 证明了本文公式的适用性.
4. 围岩压力影响因素分析
为便于对比分析, 取基础算例: 施工工法为无导洞台阶法, 施工工序选择工序1; 隧道尺寸取边洞跨度B1 = 15 m, 中洞跨度B1 = 13 m, 中隔墙宽度Bz = 1 m, 开挖高度H = 12 m, 中隔墙回填高度H3 = 12 m; 围岩基本参数取γ = 19 kN/m3, 计算摩擦角φ = 40°, 围岩饱和单轴抗压强度取20 MPa. 综合分析施工工序、开挖跨度、围岩等级等因素对三连拱隧道竖向和侧向围岩压力分布特征的影响.
4.1 施工工序对围岩压力的影响
使用传统的状态载荷计算方法, 三连拱隧道3种工序的围岩压力计算结果是相同的, 明显不合理. 采用本文计算模型对3种工序三连拱隧道围岩压力分布规律进行研究, 如图22和图23所示.
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图 22 竖向围岩压力与施工工序关系曲线Figure 22. Relationship curve between vertical surrounding rock pressure and construction procedure![]()
图 23 侧向围岩压力与施工工序关系曲线Figure 23. Relationship curve between lateral surrounding rock pressure and construction procedure结果表明施工工序的不同对三连拱隧道围岩压力的分布具有显著影响. 对于左洞, 3种工序下, 前两种工序计算所得围岩压力基本一致, 而工序3由于左洞受扰动次数较小, 使得计算所得的围岩压力较小; 对于中洞, 工序3由于先施工中洞, 左右洞施工时, 都会对中洞上方围岩造成较大的扰动, 因此中洞围岩压力最大. 对于右洞, 工序1围岩压力最大, 工序2和工序3围岩压力基本相同.
施工工序不同导致的围岩压力分布特征对于指导工程支护设计具有重要意义. 若按照传统的状态载荷计算结果进行支护设计, 会低估相邻洞室施工对先行洞围岩压力的影响, 导致支护安全性不足, 且无法有效对不同工序进行支护参数设计. 采用本文推导的计算公式, 可以更好满足工程实际需要.
4.2 中隔墙宽度对围岩压力的影响
中隔墙宽度Bz对围岩压力的影响主要体现在以下两个方面: (1)直接影响各简化导洞压力拱高度的确定, 进而影响到基本围岩压力q1的大小; (2)通过间接影响Gm与qz的取值大小进而影响松散围岩压力q2大小的确定. 当Rs较小时, qz取值很小, 可以忽略, 此时Bz主要通过影响Gm来影响围岩压力的分布; 当Rs较大时, 则是在Gm与qz的综合作用下影响围岩压力分布. 因此取Rs = 100, 2000 kPa两种工况对中隔墙宽度对围岩压力的影响进行分析(图24 ~ 图27).
结果表明, (1)当中隔墙岩体抗压强度Rs较小时, 此时随着中隔墙宽度Bz的增加, 隧道竖向和侧向围岩压力均呈略微增加趋势, 且中洞围岩压力增加速率较左右两洞较快. 因此, 当中隔墙岩体抗压强度Rs较小时, 中隔墙宽度Bz的增加并不会改善围岩压力分布, 反而会增大隧道围岩压力, 出现该情况的原因可能是中隔墙强度较低, 此时可能已经到达了极限抗压强度, 墙体出现了开裂现象, 此时再增加中隔墙宽度则会加大偏压力矩, 加剧中隔墙的开裂, 从而加大隧道围岩压力. 不利于隧道结构安全, 需要及时对中隔墙上方土体采取一定的加固措施. (2)当中隔墙岩体抗压强度Rs较大时, 此时中隔墙宽度Bz对围岩压力分布具有明显的改善作用, 宽度越大, 围岩压力越小. 此时中隔墙能够一定程度上阻碍各洞室压力拱的联结, 提高围岩稳定性. 且对中洞的改善效果明显优于左洞和右洞.
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图 24 竖向围岩压力与中隔墙宽度关系曲线(Rs = 100 kPa)Figure 24. Relationship curve between vertical surrounding rock pressure and middle partition wall’s width (Rs = 100 kPa)![]()
图 25 侧向围岩压力与中隔墙宽度关系曲线(Rs = 100 kPa)Figure 25. Relationship curve between lateral surrounding rock pressure and middle partition wall’s width (Rs = 100 kPa)![]()
图 26 竖向围岩压力与中隔墙宽度关系曲线(Rs = 2000 kPa)Figure 26. Relationship curve between vertical surrounding rock pressure and middle partition wall’s width (Rs = 2000 kPa)![]()
图 27 侧向围岩压力与中隔墙宽度关系曲线(Rs = 2000 kPa)Figure 27. Relationship curve between lateral surrounding rock pressure and middle partition wall’s width (Rs = 2000 kPa)4.3 围岩等级对围岩压力的影响
由于普氏理论是基于围岩为松散体的假设, 并不太适用于I ~ II级坚硬围岩. 因此主要分析研究III ~ V级围岩条件下三连拱隧道的围岩压力分布规律, 如图28和图29. 结果显示: (1)围岩等级对三连拱隧道的围岩压力分布具有显著影响, V级围岩由于岩体质量较差, 因此围岩压力远大于III和IV级围岩下的数值, 而III和IV级围岩下的隧道围岩压力差距较小; (2)围岩条件越差, 隧道各相邻洞室间的施工引起的偏压效应越显著; (3)围岩条件对中洞围岩压力也有显著影响. 由于隧道上方围岩质量越差, 复合压力拱越容易形成, 导致中洞拱顶围岩压力增大. 而围岩条件越好, 三连拱隧道各洞室更倾向于形成单个独立的压力拱.
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图 28 竖向围岩压力与围岩等级关系曲线Figure 28. Relationship curve between vertical surrounding rock pressure and surrounding rock grade![]()
图 29 侧向围岩压力与围岩等级关系曲线Figure 29. Relationship curve between lateral surrounding rock pressure and surrounding rock grade5. 总结
基于普氏压力拱理论和过程载荷理念, 考虑三连拱隧道施工工法及工序的影响, 建立了不同工序下的载荷理论模型, 进而推导了深埋三连拱隧道围岩压力理论公式, 推动了三连拱隧道的围岩压力理论研究. 该模型分析了施工工序、中隔墙和围岩等级等因素对三连拱隧道围岩压力的影响, 通过研究得出以下结论.
(1)深埋三连拱隧道次行洞、后行洞的开挖都会导致先行洞上方围岩的进一步破碎和松散载荷的加大, 形成较为明显的偏压现象.
(2)中隔墙对于三连拱隧道的载荷分布模式具有显著影响. 中隔墙岩体抗压强度的不同, 对围岩压力的改善作用也会不同.
(3)围岩等级对三连拱隧道的围岩压力大小也具有显著影响. 围岩条件越差, 偏压现象更加显著. 此外, 围岩越破碎越易导致极限承载大拱的形成, 中洞安全性也越低.
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图 4 普氏理论围岩压力示意图
Figure 4. Calculation diagram of surrounding rock pressure based on Protodyakonov's theory
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图 6 小净距模式载荷模型1附加围岩压力(Lz > 0)
Figure 6. Load distribution 1 additional surrounding rock pressure of closely spaced mode (Lz > 0)
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图 7 小净距模式载荷模型2附加围岩压力(Lz = 0)
Figure 7. Load distribution 2 additional surrounding rock pressure of closely spaced mode (Lz = 0)
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图 8 连拱模式载荷模型附加围岩压力
Figure 8. Additional surrounding rock pressure of multi-arch load model
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图 10 全断面载荷模型附加围岩压力
Figure 10. Additional surrounding rock pressure of full section load model
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图 13 工序1双洞室断面(小净距模式)载荷分布图
Figure 13. Procedure 1 load distribution of double tunnels section (closely spaced mode)
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图 14 工序3双洞室断面(连拱模式)载荷分布图
Figure 14. Procedure 3 load distribution of double tunnels section (multi-arch mode)
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图 18 双洞式断面监测点布置
Figure 18. Layout of double-hole cross-section monitoring measurement points
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图 20 双洞室断面围岩压力理论值与实测值对比结果
Figure 20. Comparison between theoretical value and the measured value of double tunnels section surrounding rock pressure
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图 21 全断面围岩压力理论值与实测值对比结果
Figure 21. Comparison between theoretical value and the measured value of full section surrounding rock pressure
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图 22 竖向围岩压力与施工工序关系曲线
Figure 22. Relationship curve between vertical surrounding rock pressure and construction procedure
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图 23 侧向围岩压力与施工工序关系曲线
Figure 23. Relationship curve between lateral surrounding rock pressure and construction procedure
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图 24 竖向围岩压力与中隔墙宽度关系曲线(Rs = 100 kPa)
Figure 24. Relationship curve between vertical surrounding rock pressure and middle partition wall’s width (Rs = 100 kPa)
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图 25 侧向围岩压力与中隔墙宽度关系曲线(Rs = 100 kPa)
Figure 25. Relationship curve between lateral surrounding rock pressure and middle partition wall’s width (Rs = 100 kPa)
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图 26 竖向围岩压力与中隔墙宽度关系曲线(Rs = 2000 kPa)
Figure 26. Relationship curve between vertical surrounding rock pressure and middle partition wall’s width (Rs = 2000 kPa)
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图 27 侧向围岩压力与中隔墙宽度关系曲线(Rs = 2000 kPa)
Figure 27. Relationship curve between lateral surrounding rock pressure and middle partition wall’s width (Rs = 2000 kPa)
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图 28 竖向围岩压力与围岩等级关系曲线
Figure 28. Relationship curve between vertical surrounding rock pressure and surrounding rock grade
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图 29 侧向围岩压力与围岩等级关系曲线
Figure 29. Relationship curve between lateral surrounding rock pressure and surrounding rock grade
表 1 围岩基本参数
Table 1 Basic parameters of surrounding rock
Surrounding rock grade γ/(kN·m−3) φ/(°) φg/(°) Rc/MPa V 20 20 40 15 
下载: 导出CSV
表 2 各断面围岩压力数值
Table 2 Surrounding rock pressure of each section
Pressure η1q11/kPa — q13/kPa q22/kPa q21/kPa — Double hole 128.3 — 111.6 236.6 236.6 — Pressure η1η2q11/kPa q12/kPa η2q13/kPa q22/kPa q21/kPa q3/kPa Full section 219.5 88.8 190.9 333.9 71.4 80.0
下载: 导出CSV
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