图  1  翼裂纹模型示意图

${\sigma _1}$—最大主应力，MPa；${\sigma _3}$—最小主应力，MPa

Figure  1.  Schematic diagram of the wing crack model

${\sigma _1}$−maximum principal stress, MPa; ${\sigma _3}$−minimum principal stress, MPa

图  2  渗压−应力作用下微裂纹起裂示意图

${\sigma _1}$—最大主应力，MPa；${\sigma _3}$—最小主应力，MPa；$l$—翼裂纹长度，m；$a$—裂纹半径，m；${F_{\mathrm{p}}}$—裂纹有效法向力，N；${F_{\mathrm{e}}}$—裂纹有效切向力，N；${F_{\mathrm{w}}}$—楔入力，N；$\varphi $—裂纹与最大主应力方向的夹角

Figure  2.  Schematic diagram of microcrack initiation under osmotic pressure stress

${\sigma _1}$−maximum principal stress, MPa; ${\sigma _3}$−minimum principal stress, MPa; $l$−wing crack length, m; $a$−crack radius, m; ${F_{\mathrm{p}}}$−effective normal force of the crack, N; ${F_{\mathrm{e}}}$−effective tangential force of the crack, N; ${F_{\mathrm{w}}}$−wedging force, N; $\varphi $−angle between the crack and the direction of the maximum principal stress

图  3  渗压−应力环境下翼型裂纹扩展贯通示意图

${\sigma _1}$—最大主应力，MPa；${\sigma _3}$—最小主应力，MPa；${F_{\mathrm{w}}}$—楔入力，MPa；$p$—渗压，MPa；$\sigma _3^{\,\mathrm{i}} $—有效张拉应力，MPa

Figure  3.  Schematic diagram of wing crack propagation and penetration under an osmotic stress environment

${\sigma _1}$−maximum principal stress, MPa; ${\sigma _3}$−minimum principal stress, MPa; ${F_{\mathrm{w}}}$−wedge force, N; $p$−osmotic pressure, MPa; $\sigma _3^{\mathrm{i}} $−effective tensile stress

图  4  DK262+018.1里程掌子面渗水与失稳情况

Figure  4.  Seepage and instability situation of a tunnel face at D6K262+018.1 mileage

图  5  最小安全厚度示意图

h—最小安全厚度，m；h_c—岩体抗劈裂厚度，m；h_f—裂隙带区厚度，m

Figure  5.  Schematic diagram of the minimum safety thickness

h−minimum safety thickness, m; h_c−anti-splitting thickness of the rock mass, m; h_f−fracture zone thickness, m

图  6  TSP成果图

Figure  6.  TSP achievement chart

图  7  断层水压力对岩体抗劈裂厚度的影响

$\gamma $—岩层容重，N/m³；H—隧道埋深，m；D—开挖扰动因子

Figure  7.  The influence of the fault water pressure on the anti-splitting thickness of a rock mass

$\gamma $−rock unit weight, N/m³; H−tunnel burial depth, m; D−excavation disturbance factor

图  8  竖向应力对岩体抗劈裂厚度的影响

D—开挖扰动因子；${p_{\mathrm{w}}}$—断层水压力，MPa

Figure  8.  The influence of vertical stress on the anti-splitting thickness of rock mass

D−excavation disturbance factor; ${p_{\mathrm{w}}}$−fault water pressure, MPa

图  9  开挖扰动因子对岩体抗劈裂厚度的影响

$\gamma $—岩层容重，N/m³；H—隧道埋深，m；${p_{\mathrm{w}}}$—断层水压力，MPaa—不同断层水压力条件下；b—不同竖向应力条件下

Figure  9.  The influence of the excavation disturbance factor on the anti-splitting thickness of a rock mass

(a) Under different fault water pressures; (b) Under different vertical stresses $\gamma $−rock unit weight, N/m³; H −tunnel burial depth, m; ${p_{\mathrm{w}}}$−fault water pressure, MPa