CN113553653B - Method for determining surrounding rock pressure of deeply buried unequal-span tunnel in lithologic stratum - Google Patents

Method for determining surrounding rock pressure of deeply buried unequal-span tunnel in lithologic stratum Download PDF

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CN113553653B
CN113553653B CN202110865062.9A CN202110865062A CN113553653B CN 113553653 B CN113553653 B CN 113553653B CN 202110865062 A CN202110865062 A CN 202110865062A CN 113553653 B CN113553653 B CN 113553653B
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tunnel
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CN113553653A (en
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安永林
李佳豪
刘文娟
贺建清
周进
谭格宇
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Hunan University of Science and Technology
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Abstract

The invention discloses a method for determining surrounding rock pressure of a deeply buried unequal-span tunnel in a lithologic stratum. The method mainly comprises the following steps: establishing a rock stratum deep-buried unequal-span tunnel destruction mode; the equivalent cohesive force and the internal friction angle of the lithologic stratum are obtained according to the HockBrown criterion; calculating the speed relation and the side length relation between the destructive bodies; calculating the gravity working power of the rock surrounding rock in the peripheral damage range of the deep tunnel; calculating the internal energy dissipation power of the rock mass surrounding rock in the peripheral damage range of the deeply buried unequal-span tunnel; calculating the work power of the support counter force; according to the energy conservation principle and the constraint condition, the supporting counter force is solved, and the surrounding rock pressure can be obtained. The method can be applied to surrounding rock pressure calculation and lining safety assessment of deep-buried underground engineering with unequal spans and small distances, so that an asymmetric design and support construction scheme is adopted, materials can be saved, the cost is reduced, and the construction safety of the tunnel is facilitated.

Description

Method for determining surrounding rock pressure of deeply buried unequal-span tunnel in lithologic stratum
Technical Field
The invention relates to the technical field of tunnel design and construction, in particular to a method for determining surrounding rock pressure of a rock stratum deeply buried unequal-span tunnel.
Background
How to calculate the surrounding rock pressure is a problem which needs to be considered before the design of tunnel support and is also a key of tunnel safety construction, and if the surrounding rock pressure is high, the required support needs to be strong; the surrounding rock pressure is small, the support can be relatively weak, and the surrounding rock pressure is also closely related to the tunnel construction safety. The invention is provided by the condition that the tunnel ramp (2 lanes with small span) and the main tunnel (3 lanes with large span) have unequal spans on the background. And part of the field is II-level surrounding rock, and the part of the field is deeply buried in the tunnel body. In design and construction, how to determine the pressure of surrounding rock and the damage range directly relates to support design and tunnel construction safety. At present, relevant tunnel specifications such as highway tunnel design specifications, railway tunnel design specifications and subway design specifications do not relate to calculation of the surrounding rock pressure of the unequal-span tunnel, and few documents are available on how to calculate the surrounding rock pressure of the deeply-buried unequal-span tunnel.
Disclosure of Invention
The invention aims to provide a method for determining the pressure of surrounding rock of a rock stratum deeply buried unequal-span tunnel aiming at the technical problems in the prior art.
The above object of the present invention is achieved by the following technical solutions:
the method for determining the pressure of the surrounding rock of the tunnel with unequal deep burial spans of the lithologic stratum comprises the following steps of:
(1) establishing T1Hole and T2A tunnel rock mass deep-buried unequal-span tunnel surrounding rock pressure failure mode; in the damage mode, due to deep burying, the surrounding rock damage only exists at the periphery of the tunnel and does not reach the ground surface; the failure mode can consider the condition that the spans of two tunnels are unequal and the burial depths are unequal, namely T1Hole and T2Different span of hole, T1Hole and T2The buried depths of the holes are different; wherein, T1The hole is a large span hole, T2The hole is a small span hole;
(2) the equivalent cohesive force and the equivalent internal friction angle of the lithologic formation are obtained by quasi-equivalence of HockBron's criterion, and are specifically determined by the following formula:
Figure BDA0003187012140000021
Figure BDA0003187012140000022
in the formula (I), the compound is shown in the specification,
Figure BDA0003187012140000023
is the equivalent internal friction angle; c. CtEquivalent cohesive force; sigmaciUniaxial compressive strength of intact rock material; m isbS, ξ are semi-empirical parameters of rock properties that can be calculated from the GSI index using the following equation:
Figure BDA0003187012140000024
Figure BDA0003187012140000025
Figure BDA0003187012140000026
in the formula, Dam is the disturbance degree of the tunnel excavation to the surrounding rock, and the value is 0.5; GSI is a geological strength index; m isiEmpirical parameters that are rock properties;
(3) calculating the speed relation and the side length relation between the damaged blocks, which comprises the following steps:
determining the velocity field of each destroyed mass part:
T1the upper part of the hole is broken into a triangular block delta B1J1O1And a trapezoidal block body O1J1OC1Velocity v0Vertically downward; t is1The breaking block at the left side of the hole is a triangular block delta B1AB, moving speed v1Relative velocity is v0,1(ii) a The included angle between the velocity vector and the break line between each damaged block is equal to the calculated friction angle of the rock surrounding rock, namely the equivalent internal friction angle
Figure BDA0003187012140000027
Each failure mass velocity satisfies a vector closure; alpha is T1Hole left block BA side and BB1The included angle of the edges; beta is T1Block AB on left side of hole1Side and BB1The included angle of the edges;
other mass velocity vector relationships can be derived in the same way; wherein, T1Cavern right side destruction block CDC1M0The angle and speed of (a) are marked by alpha ', beta', theta, v ', alpha' is CD edge and CM0The angle between the edges, beta', is CD edge and DM0Angle of side, theta being DC1Edge and DM0Angle of sides, v' being breakdown blocks Δ DC1M0The speed of (a); t is2Left-side destruction block M0F1The angle and speed of EF are marked by α ', β ', θ ', v ', where α ' is the FE edge and FM edge0The angle between the edges, beta' being FE edge and EM0The angle of the sides, theta' being EF1Edge and EM0Angle of the edges, v' being the breakdown mass Δ EF1M0The speed of (d); t is2Hole right side destruction block Δ G1HG angle and speed are marked by alpha ', beta', v ', and alpha' is GH side and GG1The angle of the sides, beta' being G1H edge and GG1Angle of the edges, v' being the breaking block Δ G1The speed of the HG;
(II) calculating the relation between the speed and the side length of each damaged block:
from the above-mentioned geometrical relationship between the respective failure blocks in the failure mode, the following relationship between the side lengths of the respective failure blocks can be obtained:
for T1Triangular block delta B on left side of hole1AB：
AB1＝ABtanα＝h1tanα
BB1＝AB/cosα＝h1/cosα；
In the formula, alpha is T1Left block B of hole1The included angle between the side B and the side AB; h is1Is T1The height of the hole;
for T1Hole right block CDC1M0：
Figure BDA0003187012140000031
In the formula, alpha' is T1Right side block CD edge and CM0The included angle of the edges; theta is DC1Edge and DM0The included angle of the edges;
for T1Block B on top of hole1J1OC1：
Figure BDA0003187012140000041
In the formula, BT1Is T1The span of the hole;
from the above-mentioned relationship between the failure mode and the velocity vector, T can be obtained1Triangular block delta B on left side of hole1AB velocity v1、v0,1And velocity v0The relationship of (a) to (b) is as follows:
Figure BDA0003187012140000042
Figure BDA0003187012140000043
for T1Hole right block CDC1M0V 'speed'1、v'0,1、v1'1、v1'0,1And velocity v0The relationship of (a) to (b) is as follows:
Figure BDA0003187012140000044
Figure BDA0003187012140000045
Figure BDA0003187012140000046
Figure BDA0003187012140000047
(4) calculating the gravity working power of the rock surrounding rock in the peripheral damage range of the deeply buried tunnel, which comprises the following steps:
(Ⅰ)T1the hole periphery destruction block body consists of the following parts: t is1Triangle block body delta B on upper part of hole1J1O1And a trapezoidal block body O1J1OC1，T1Triangular block delta B on left side of hole1AB，T1Delta CDM of triangular block on right side of hole0And triangular block Delta DC1M0(ii) a The area of each failure block was calculated:
Figure BDA0003187012140000051
Figure BDA0003187012140000052
Figure BDA0003187012140000053
(II) determining the gravity work-done power calculation formula of each damaged block rock mass at the periphery of the tunnel as follows:
for T1The hole and rock mass gravity work power is as follows:
Figure BDA00031870121400000512
for T in the same way2The hole and rock mass gravity work power is as follows:
Figure BDA0003187012140000054
Figure BDA0003187012140000055
in the formula: gamma is the rock mass gravity;
Figure BDA0003187012140000056
is T1The gravity acting power of each block rock mass is destroyed around the hole;
Figure BDA0003187012140000057
is T2The gravity acting power of each block rock mass is destroyed around the hole; pWFor two unequal-span tunnels, i.e. T1Hole and T2The gravity acting power of the block rock mass is destroyed around the hole;
Figure BDA0003187012140000058
is T2Quadrilateral block G on top of hole1J2OF1The area of (d);
Figure BDA0003187012140000059
is T2Triangular block HG on right side of hole1The area of G;
Figure BDA00031870121400000510
is T2Triangular block EF on left side of hole1M0The area of (d);
Figure BDA00031870121400000511
is T2Hole left side triangle block EFM0The area of (d);
(5) calculating the internal energy dissipation power of the rock mass surrounding rock in the deep-buried unequal-span tunnel peripheral damage range, wherein the internal energy dissipation power is determined by the following formula:
internal energy dissipated power PCFor the sum of the energy dissipated on each broken block break line, for break line B1J1And J1The energy dissipated power over O is:
Figure BDA0003187012140000061
Figure BDA0003187012140000062
the energy dissipation power is then:
Figure BDA0003187012140000063
Figure BDA0003187012140000064
Figure BDA0003187012140000065
in the formula (I), the compound is shown in the specification,
Figure BDA0003187012140000066
is T1Internal energy dissipation power among all the destruction blocks at the periphery of the hole;
Figure BDA0003187012140000067
is T2Internal energy dissipation power among all the destruction blocks at the periphery of the hole; pCFor two unequal-span tunnels, i.e. T1Hole and T2The internal energy of the whole damage block body at the periphery of the hole dissipates power;
(6) calculating the work power of the support reaction force, which is determined by the following steps:
in a deep-buried tunnel, the tunnel roof support reaction force q and the side wall support reaction force e have the following relationship:
q＝Ke；
order: k is a radical of1＝(q2-q1)/qaBT1；k2＝(q3-q4)/qbBT2；qa＝(q1+q2)/2；qb＝(q3+q4)/2；
In the formula, qaIs T1Average supporting force of the tunnel top plate; q. q.sbIs T2Average supporting force of the tunnel top plate; q. q.s1Is T1Supporting counter force on the left side of the tunnel top plate; q. q.s2Is T1Supporting counter force on the right side of the tunnel top plate; q. q.s3Is T2Supporting counter force on the left side of the tunnel top plate; q. q.s4Is T2Supporting counter force on the right side of the tunnel top plate; K. k1, k2Is the undetermined coefficient; BT (BT)1Is T1The span of the hole; BT (BT)2Is T2The span of the hole;
(II) the working power of the support reaction force is determined by the following formula:
Figure BDA0003187012140000068
Figure BDA0003187012140000069
Figure BDA00031870121400000610
in the formula (I), the compound is shown in the specification,
Figure BDA00031870121400000611
is T1The hole support counter-force acting power;
Figure BDA00031870121400000612
is T2The hole support counter-force acting power; pTFor two unequal-span tunnels, i.e. T1Hole and T2The total work power of the hole support counterforce; h is1Is T1The height of the hole; h is2Is T2The height of the hole;
(7) according to the energy conservation principle and in combination with constraint conditions, the supporting counter force is solved, and the surrounding rock pressure can be obtained, and the method comprises the following steps:
according to the energy conservation principle, the difference value of the gravity acting power and the internal energy dissipation power of the rock mass is equal to the support counter-force acting power, namely:
PW-PC＝PT；
(II) obtaining the support reaction force q according to the formulaa、qbComprises the following steps:
Figure BDA0003187012140000071
(III) according to the closing of the velocity vector and the geometrical conditions of each damaged block, each angle parameter needs to satisfy the constraint condition shown in the following formula:
Figure BDA0003187012140000072
wherein BD is T1Hole and T2Clear spacing between holes;
(IV) because of mutual influence among the small-clear-distance tunnels, in order to ensure that the calculation result of the tunnel surrounding rock pressure is reliable, the tunnel span value is taken as the support counter force to calculate the safety coefficient, and m is made1＝BT1/(BT1+BT2)，m2＝BT2/(BT1+BT2) Let q be (q)a*m1)+(qb*m2) Wherein m is1、m2According to T1Hole, T2Determining the span value of the hole, and representing the size of the relative span of the two tunnels; q is T taking into account the influence of the span1Hole, T2Average vertical supporting force of the hole;
(V) is defined by a set of angles α, α ', θ', and GSI, mi、σciThe shape of the failure mode can be determined, the shape can be completely determined, and a corresponding true value solution q is obtained, namely under the condition that constraint conditions are met, the maximum value of q is obtained by adopting an optimization method, and the supporting reaction force of the two tunnels can be obtained, namely the surrounding rock pressure values of all the unequal cross tunnels under the deep burying of the rock texture layer.
Compared with the prior art and research methods, the invention has the advantages that: the prior art mainly analyzes the surrounding rock pressure of a single tunnel or the surrounding rock pressure of an equivalent cross tunnel; the research aiming at the unequal-span tunnel is few, and individual documents provide the surrounding rock pressure according to the slump arch method aiming at the deep-buried tunnel, but lack theoretical basis.
The invention provides a theoretical calculation method for determining the pressure of rock surrounding rock of a deeply buried unequal-span tunnel in a lithologic stratum; by changing the nonlinear parameters, the relative burial depths of the two tunnels and the relative sizes of the two tunnels, the surrounding rock pressures under different burial depths and different relative sizes can be obtained, thereby providing a basis for designing unequal-span tunnels; under the condition that the resistance of the support is known, whether the support meets the requirements can be judged, and therefore the safety of tunnel construction is guaranteed. The method can be applied to the surrounding rock pressure calculation and lining safety assessment of deep-buried underground engineering with unequal spans and small distances, such as adjacent roadways in mining, adjacent tunnels in hydraulic engineering, adjacent interval tunnels of subways, crossover line sections and other engineering.
Drawings
Fig. 1 is a schematic view of a failure mode of a rock stratum deeply buried under unequal tunnel surrounding rock pressure according to an embodiment of the invention.
In FIG. 1, h3For large-span tunnel T1Tunnel arch top and small-span tunnel T2Height difference of the arch top of the tunnel; BT (BT)1Is T1A hole span; BT (BT)2Is T2A hole span; h is1Is T1The height of the hole; h is2Is T2The height of the hole; BD is the clear distance between the two tunnels.
FIG. 2 and FIG. 3 are respectively a T diagram of an embodiment of the present invention1Triangles on the left side of the hole destroy the mass velocity field schematic and the vector relationship diagram.
FIG. 4 and FIG. 5 are diagrams illustrating T of an embodiment of the present invention1Triangles on the right side of the hole destroy the speed schematic diagram and the vector relation diagram of the block.
FIG. 6 shows an embodiment of the present invention T1Hole and T2The holes each destroy the angle and speed identification map of the block.
FIG. 7 is a simplified diagram of the wall pressure according to an embodiment of the present invention.
FIG. 8 shows T at different GSIs according to an embodiment of the present invention1Hole and T2And (4) a curve chart of calculated values of the surrounding rock pressure of the hole.
Detailed Description
The invention is further described below with reference to the figures and examples.
The specific data of the project of the embodiment are as follows: deep burying of certain rock mass with unequal spans of tunnel h1＝10.7m，BT1＝14.1m，h2＝8.79m，BT2＝12.34m，BD＝5m，K＝0.6，k1＝k2＝0.02，γ＝20kN/m3，σci＝300kPa，mi＝10，h 31 is ═ 1; the GSI values of the parameters are respectively: 10. 15, 20, 25, 30, 35, 40.
Referring to fig. 1, the method for determining the pressure of the rock stratum deeply buried unequal-span tunnel surrounding rock in the embodiment is as follows:
(1) establishing T1Hole and T2A tunnel rock mass deep-buried unequal-span tunnel surrounding rock pressure failure mode; in the damage mode, due to deep burying, the surrounding rock damage only exists at the periphery of the tunnel and does not reach the ground surface; the failure mode can consider the condition that the two tunnels have unequal spans and unequal burial depths, namely T1Hole and T2Different span of hole, T1Hole and T2The burial depth of the holes is different; wherein, T1The hole is a large span hole, T2The hole is a small span hole.
(2) The equivalent cohesive force and the equivalent internal friction angle of the lithologic formation are obtained by quasi-equivalence of HockBron's criterion, and are specifically determined by the following formula:
Figure BDA0003187012140000091
Figure BDA0003187012140000092
in the formula (I), the compound is shown in the specification,
Figure BDA0003187012140000093
is the equivalent internal friction angle; c. CtEquivalent cohesive force; sigmaciUniaxial compressive strength of intact rock material; m isbS, ξ are semi-empirical parameters of rock properties that can be calculated from the GSI index using the following equation:
Figure BDA0003187012140000101
Figure BDA0003187012140000102
Figure BDA0003187012140000103
in the formula, Dam is the disturbance degree of the tunnel excavation to the surrounding rock, and the value is 0.5; GSI is a geological strength index; m isiIs an empirical parameter of rock properties.
(3) Calculating the speed relation and the side length relation between the damaged blocks, which comprises the following steps:
determining the velocity field of each destroyed mass part:
T1the upper part of the hole is broken into a triangular block delta B1J1O1And a trapezoidal block body O1J1OC1Velocity v0Vertically downwards, see fig. 2 to 5; t is1The breaking block at the left side of the hole is a triangular block delta B1AB, moving speed v1Relative velocity is v0,1(ii) a The included angle between the velocity vector and the break line between each damaged block is equal to the calculated friction angle of the rock surrounding rock, namely the equivalent internal friction angle
Figure BDA0003187012140000104
Each failure mass velocity satisfies a vector closure; alpha is T1Hole left block BA side and BB1The included angle of the edges; beta is T1Block AB on left side of hole1Side and BB1The included angle of the edges;
other mass velocity vector relationships can be derived in the same manner, as shown in FIG. 6; wherein, T1Cavern right side destruction block CDC1M0The angle and speed of (a) are marked by alpha ', beta', theta, v ', alpha' is CD edge and CM0The angle between the edges, beta', is CD edge and DM0Angle of side, theta being DC1Edge and DM0Angle of sides, v' being breakdown blocks Δ DC1M0The speed of (d); t is2Left-side destruction block M0F1The angle and speed of EF are marked by α ', β ', θ ', v ', where α ' is the FE edge and FM edge0The angle between the edges, beta' being FE edge and EM0Angle of sides, theta' being EF1Edge and EM0Angle of the edges, v' being the breakdown mass Δ EF1M0The speed of (d); t is2Hole right side destruction block Δ G1HG angle and speed are marked by alpha ', beta', v ', and alpha' is GH side and GG1The angle of the sides, beta' being G1H edge and GG1Angle of the edges, v' being the breaking block Δ G1The speed of the HG;
(II) calculating the relation between the speed and the side length of each damaged block:
from the above-mentioned geometrical relationship between the respective failure blocks in the failure mode, the following relationship between the side lengths of the respective failure blocks can be obtained:
for T1Triangular block delta B on left side of hole1AB：
AB1＝ABtanα＝h1tanα
BB1＝AB/cosα＝h1/cosα；
In the formula, alpha is T1Left block B of hole1The included angle between the side B and the side AB; h is1Is T1The height of the hole;
for T1Hole right block CDC1M0：
Figure BDA0003187012140000111
In which α' is T1Right block of hole CD edge and CM0The included angle of the edges; theta is DC1Edge and DM0The included angle of the edges;
for T1Block B on top of hole1J1OC1：
Figure BDA0003187012140000112
In the formula, BT1Is T1The span of the hole;
from the above-mentioned relationship between the failure mode and the velocity vector, T can be obtained1Triangular block delta B on left side of hole1AB velocity v1、v0,1And velocity v0The relationship of (a) to (b) is as follows:
Figure BDA0003187012140000113
Figure BDA0003187012140000121
for T1Hole right block CDC1M0V 'speed'1、v'0,1、v1'1、v1'0,1And velocity v0The relationship of (a) to (b) is as follows:
Figure BDA0003187012140000122
Figure BDA0003187012140000123
Figure BDA0003187012140000124
Figure BDA0003187012140000125
(4) calculating the gravity working power of the rock surrounding rock in the peripheral damage range of the deeply buried tunnel, which comprises the following steps:
(Ⅰ)T1the hole periphery destruction block body consists of the following parts: t is1Triangle block body delta B on upper part of hole1J1O1And a trapezoidal block body O1J1OC1，T1Triangular block delta B on left side of hole1AB，T1Triangle block on right side of hole delta CDM0And triangular block Delta DC1M0(ii) a The area of each failure block was calculated:
Figure BDA0003187012140000126
Figure BDA0003187012140000127
Figure BDA0003187012140000128
(II) determining the gravity work-done power calculation formula of each damaged block rock mass at the periphery of the tunnel as follows:
for T1The work power of the gravity of the rock mass is as follows:
Figure BDA0003187012140000129
for T in the same way2The work power of the gravity of the rock mass is as follows:
Figure BDA0003187012140000131
Figure BDA0003187012140000132
in the formula: gamma is the rock mass gravity;
Figure BDA0003187012140000133
is T1The gravity acting power of each block rock mass is destroyed around the hole;
Figure BDA0003187012140000134
is T2The gravity acting power of each block rock mass is destroyed around the hole; pWFor two unequal-span tunnels, i.e. T1Hole and T2The gravity acting power of the block rock mass is destroyed around the hole;
Figure BDA0003187012140000135
is T2Quadrilateral block G on top of hole1J2OF1The area of (d);
Figure BDA0003187012140000136
is T2Triangular block HG on right side of hole1The area of G;
Figure BDA0003187012140000137
is T2Triangular block EF on left side of hole1M0The area of (d);
Figure BDA0003187012140000138
is T2Hole left side triangle block EFM0The area of (a).
(5) Calculating the internal energy dissipation power of the rock mass surrounding rock in the deep-buried unequal-span tunnel peripheral damage range, wherein the internal energy dissipation power is determined by the following formula:
internal energy dissipated power PCFor the sum of the energy dissipated on each broken block break line, for break line B1J1And J1The energy dissipated power over O is:
Figure BDA0003187012140000139
Figure BDA00031870121400001310
the energy dissipation power is then:
Figure BDA00031870121400001311
Figure BDA00031870121400001312
Figure BDA00031870121400001313
in the formula (I), the compound is shown in the specification,
Figure BDA00031870121400001314
is T1Internal energy dissipation power among all the destruction blocks at the periphery of the hole;
Figure BDA00031870121400001315
is T2Internal energy dissipation power among all the destruction blocks at the periphery of the hole; pCFor two unequal-span tunnels, i.e. T1Hole and T2The entire periphery of the hole destroys the internal energy of the block to dissipate power.
(6) Calculating the work power of the support reaction force, which is determined by the following steps:
in a deep-buried tunnel, the tunnel roof support reaction force q and the side wall support reaction force e have the following relationship:
q＝Ke；
order: k is a radical of1＝(q2-q1)/qaBT1；k2＝(q3-q4)/qbBT2；qa＝(q1+q2)/2；qb＝(q3+q4)/2；
In the formula, qaIs T1Average supporting force of the tunnel top plate; q. q.sbIs T2Average supporting force of the tunnel top plate; q. q.s1Is T1Supporting counter force on the left side of the tunnel top plate; q. q.s2Is T1Supporting counter force on the right side of the tunnel top plate; q. q.s3Is T2Supporting counter force on the left side of the tunnel top plate; q. q.s4Is T2The counter force of the support on the right side of the tunnel top plate is shown in figure 7; K. k is a radical of1、k2Is the undetermined coefficient; BT (BT)1Is T1The span of the hole; BT (BT)2Is T2The span of the hole;
(II) the working power of the support reaction force is determined by the following formula:
Figure BDA0003187012140000141
Figure BDA0003187012140000142
Figure BDA0003187012140000143
in the formula (I), the compound is shown in the specification,
Figure BDA0003187012140000144
is T1The hole support counter-force acting power;
Figure BDA0003187012140000145
is T2The hole support counter-force acting power; pTFor two unequal-span tunnels, i.e. T1Hole and T2The total work power of the hole support counterforce; h is1Is T1The height of the hole; h is2Is T2The hole height.
(7) According to the energy conservation principle and in combination with constraint conditions, the supporting counter force is solved, and the surrounding rock pressure can be obtained, and the method comprises the following steps:
according to the energy conservation principle, the difference value of the gravity acting power and the internal energy dissipation power of the rock mass is equal to the support counter-force acting power, namely:
PW-PC＝PT；
(II) obtaining the support reaction force q according to the formulaa、qbComprises the following steps:
Figure BDA0003187012140000146
(III) according to the closing of the velocity vector and the geometrical conditions of each damaged block, each angle parameter needs to satisfy the constraint condition shown in the following formula:
Figure BDA0003187012140000151
wherein BD is T1Hole and T2Clear spacing between holes;
(IV) because of mutual influence among the small-clear-distance tunnels, in order to ensure that the calculation result of the tunnel surrounding rock pressure is reliable, the tunnel span value is taken as the support counter force to calculate the safety coefficient, and m is made1＝BT1/(BT1+BT2)，m2＝BT2/(BT1+BT2) Let q be (q)a*m1)+(qb*m2) Wherein m is1、m2According to T1Hole, T2Determining the span value of the hole, and representing the size of the relative span of the two tunnels; q is T taking into account the influence of the span1Hole, T2Average vertical supporting force of the hole;
(V) is defined by a set of angles α, α ', θ', and GSI, mi、σciThe shape of the failure mode can be determined, the shape can be completely determined, and a corresponding true value solution q is obtained, namely under the condition that constraint conditions are met, the maximum value of q is obtained by adopting an optimization method, and the supporting reaction force of the two tunnels can be obtained, namely the surrounding rock pressure values of all the unequal cross tunnels under the deep burying of the rock texture layer.
According to the steps of the method, T under different GSI can be obtained1Hole and T2The magnitude of the cavern wall pressure is shown in fig. 8. As can be seen from fig. 8, the average vertical wall rock pressure is related to the change in the GSI value. Under the nonlinear H-B criterion, the surrounding rock pressure value is in a nonlinear reduction trend along with the increase of the GSI value, the variation range of the surrounding rock pressure value is large, and the surrounding rock pressure difference value of the two holes is gradually reduced along with the increase of the GSI value from the general trend. The change of the GSI value has obvious influence on the surrounding rock pressure solution value, and parameters need to be reasonably selected when the surrounding rock pressure is calculated, so that the design safety is ensured. Simultaneous large span T1Pressure of surrounding rock in hole, T of smaller span2The hole is large, and the pressure difference of the surrounding rocks of the two holes is larger when the GSI value is smaller (the surrounding rocks are worse), namely the T of different spans is more suitable for1Hole and T2The holes adopt different support parameters, thereby ensuring the construction safety, being beneficial to saving materials and reducing the cost.

Claims (1)

1. A method for determining the pressure of surrounding rocks of a rock stratum deeply buried unequal-span tunnel is characterized by comprising the following steps:
(1) establishing T1Hole and T2A tunnel rock mass deep buries a surrounding rock pressure failure mode with unequal spans of the tunnel; in the damage mode, due to deep burying, the surrounding rock damage only exists at the periphery of the tunnel and does not reach the ground surface; the failure mode can consider the condition that the two tunnels have unequal spans and unequal burial depths, namely T1Hole and T2Different span of hole, T1Hole and T2The buried depths of the holes are different; wherein, T1The hole is a large span hole, T2The hole is a small span hole;
(2) the equivalent cohesive force and the equivalent internal friction angle of the lithologic formation are obtained by quasi-equivalence of HockBron's criterion, and are specifically determined by the following formula:
Figure FDA0003516484940000011
Figure FDA0003516484940000012
in the formula (I), the compound is shown in the specification,
Figure FDA0003516484940000013
is the equivalent internal friction angle; c. CtEquivalent cohesive force; sigmaciUniaxial compressive strength of intact rock material; m isbS, ξ are semi-empirical parameters of rock properties that can be calculated from the GSI index using the following equation:
Figure FDA0003516484940000014
Figure FDA0003516484940000015
Figure FDA0003516484940000016
in the formula, Dam is the disturbance degree of the tunnel excavation to the surrounding rock, and the value is 0.5; GSI is geological strength index; m isiEmpirical parameters that are rock properties;
(3) calculating the speed relation and the side length relation between the damaged blocks, which comprises the following steps:
determining the velocity field of each destroyed mass part:
T1the upper part of the hole is a triangular block delta B1J1O1And a trapezoidal block body O1J1OC1Velocity v0Vertically downward; t is1The breaking block at the left side of the hole is a triangular block delta B1AB, moving speed v1Relative velocity is v0,1(ii) a The included angle between the velocity vector and the break line between each damaged block is equal to the calculated friction angle of the rock surrounding rock, namely the equivalent internal friction angle
Figure FDA0003516484940000021
Each failure mass velocity satisfies a vector closure; alpha is T1Hole left block BA side and BB1The included angle of the edges; beta is T1Block AB on left side of hole1Side and BB1The included angle of the edges;
other mass velocity vector relationships can be derived in the same way; wherein, T1Cavern right side destruction block CDC1M0The angle and speed of (a) are marked by alpha ', beta', theta, v ', alpha' is CD edge and CM0The angle between the edges, beta', is CD edge and DM0Angle of side, theta being DC1Edge and DM0Angle of sides, v' being breakdown blocks Δ DC1M0The speed of (d); t is2Left-side destruction block M0F1The angle and speed of EF are marked by alpha ', beta ', theta ', v ', where alpha ' is FE edge and FM edge0The angle between the edges, beta', is FE edge and EM0Angle of sides, theta' being EF1Edge and EM0Angle of the edges, v' being breakdown blocks Δ EF1M0The speed of (d); t is2Hole right side destruction block Δ G1The HG angle and speed are marked by alpha ', beta', v ', and alpha' is GH side and GG1The angle of the sides, beta' being G1H edge and GG1Angle of the sides, v' ″ breaking block Δ G1The speed of the HG;
(II) calculating the relation between the speed and the side length of each damaged block:
from the above-mentioned geometrical relationship between the respective failure blocks in the failure mode, the following relationship between the side lengths of the respective failure blocks can be obtained:
for T1Triangular block delta B on left side of hole1AB：
AB1＝ABtanα＝h1tanα
BB1＝AB/cosα＝h1/cosα；
In the formula, alpha is T1Left block B of hole1The included angle between the side B and the side AB; h is1Is T1The height of the hole;
for T1Hole right block CDC1M0：
Figure FDA0003516484940000022
In which α' is T1Right side block CD edge and CM0The included angle of the edges; theta is DC1Edge and DM0The included angle of the edges;
for T1Block B on top of hole1J1OC1：
Figure FDA0003516484940000031
In the formula, BT1Is T1The span of the hole;
from the above-mentioned relationship between the failure mode and the velocity vector, T can be obtained1Triangular block delta B on left side of hole1AB velocity v1、v0,1And velocity v0The relationship of (a) to (b) is as follows:
Figure FDA0003516484940000032
Figure FDA0003516484940000033
for T1Hole right block CDC1M0V 'velocity'1、v'0,1、v1'1、v1'0,1And velocity v0The relationship of (a) to (b) is as follows:
Figure FDA0003516484940000034
Figure FDA0003516484940000035
Figure FDA0003516484940000036
Figure FDA0003516484940000041
in formula (II), v'1Is T1Triangular block body delta DC on right side of hole1M0The speed of (d); v'0,1Is a triangular block body Delta DC1M0With respect to the trapezoidal block O at the top of the tunnel1J1OC1The relative speed of (c); v. of1'1Is T1Delta CDM of triangular block on right side of hole0The speed of (d); v. of1'0,1Is T1Delta CDM of triangular block on right side of hole0Relative to T1Triangular block on right side of holeΔDC1M0The relative speed of (d);
(4) calculating the gravity working power of the rock surrounding rock in the peripheral damage range of the deeply buried tunnel, which comprises the following steps:
(Ⅰ)T1the hole periphery breaking block body is composed of the following parts: t is1Triangle block body delta B on upper part of hole1J1O1And a trapezoidal block body O1J1OC1，T1Triangular block delta B on left side of hole1AB，T1Delta CDM of triangular block on right side of hole0And triangular block Delta DC1M0(ii) a The area of each failure block was calculated:
Figure FDA0003516484940000042
Figure FDA0003516484940000043
Figure FDA0003516484940000044
(II) determining the gravity work-done power calculation formula of each damaged block rock mass at the periphery of the tunnel as follows:
for T1The work power of the gravity of the rock mass is as follows:
Figure FDA0003516484940000045
for T in the same way2The work power of the gravity of the rock mass is as follows:
Figure FDA0003516484940000046
Figure FDA0003516484940000047
in the formula: gamma is the rock mass gravity;
Figure FDA0003516484940000048
is T1The gravity acting power of each block rock mass is destroyed around the hole;
Figure FDA0003516484940000049
is T2The gravity acting power of each block rock mass is destroyed around the hole; pWFor two unequal-span tunnels, i.e. T1Hole and T2The gravity acting power of the block rock mass is destroyed around the hole;
Figure FDA0003516484940000051
is T2Quadrilateral block G on top of hole1J2OF1The area of (d);
Figure FDA0003516484940000052
is T2Triangular block HG on right side of hole1The area of G;
Figure FDA0003516484940000053
is T2Triangular block EF on left side of hole1M0The area of (d);
Figure FDA0003516484940000054
is T2Hole left side triangle block EFM0The area of (d);
(5) calculating the internal energy dissipation power of the rock mass surrounding rock in the deep-buried unequal-span tunnel peripheral damage range, wherein the internal energy dissipation power is determined by the following formula:
internal energy dissipated power PCFor the sum of the energy dissipated on each broken block break line, for break line B1J1And J1The energy dissipated power over O is:
Figure FDA0003516484940000055
Figure FDA0003516484940000056
the energy dissipation power is then:
Figure FDA0003516484940000057
Figure FDA0003516484940000058
Figure FDA0003516484940000059
in the formula (I), the compound is shown in the specification,
Figure FDA00035164849400000510
is T1Internal energy dissipation power among all the destruction blocks at the periphery of the hole;
Figure FDA00035164849400000511
is T2Internal energy dissipation power among all the destruction blocks at the periphery of the hole; pCFor two unequal-span tunnels, i.e. T1Hole and T2The internal energy of the whole damage block body at the periphery of the hole dissipates power;
(6) calculating the work power of the support reaction force, which is determined by the following steps:
in a deep-buried tunnel, the tunnel roof support reaction force q and the side wall support reaction force e have the following relationship:
q＝Ke；
order: k is a radical of1＝(q2-q1)/qaBT1；k2＝(q3-q4)/qbBT2；qa＝(q1+q2)/2；qb＝(q3+q4)/2；
In the formula, qaIs T1Average supporting force of the tunnel top plate; q. q.sbIs T2Average supporting force of the tunnel top plate; q. q of1Is T1Supporting counter force on the left side of the tunnel top plate; q. q.s2Is T1Supporting counter force on the right side of the tunnel top plate; q. q of3Is T2Supporting counter force on the left side of the tunnel top plate; q. q.s4Is T2Supporting counter force on the right side of the tunnel top plate; K. k is a radical of1、k2Is the undetermined coefficient; BT (BT)1Is T1The span of the hole; BT (BT)2Is T2The span of the hole;
(II) the working power of the support reaction force is determined by the following formula:
Figure FDA0003516484940000061
Figure FDA0003516484940000062
Figure FDA0003516484940000063
in the formula (I), the compound is shown in the specification,
Figure FDA0003516484940000064
is T1The hole support counter-force acting power;
Figure FDA0003516484940000065
is T2The hole support counter-force acting power; pTFor two unequal-span tunnels, i.e. T1Hole and T2The total work power of the hole support counterforce; h is1Is T1The height of the hole; h is2Is T2The height of the hole;
(7) according to the energy conservation principle and in combination with constraint conditions, the supporting counter force is solved, and the surrounding rock pressure can be obtained, and the method comprises the following steps:
according to the energy conservation principle, the difference value of the gravity acting power and the internal energy dissipation power of the rock mass is equal to the support counter-force acting power, namely:
PW-PC＝PT；
(II) according to the formula, the support reaction force q can be obtaineda、qbComprises the following steps:
Figure FDA0003516484940000066
Figure FDA0003516484940000067
(III) according to the closing of the velocity vector and the geometrical conditions of each damaged block, each angle parameter needs to satisfy the constraint condition shown in the following formula:
Figure FDA0003516484940000068
wherein BD is T1Hole and T2Clear spacing between holes;
(IV) because of mutual influence among the small-clear-distance tunnels, in order to ensure that the calculation result of the tunnel surrounding rock pressure is reliable, the tunnel span value is taken as the support counter force to calculate the safety coefficient, and m is made1＝BT1/(BT1+BT2)，m2＝BT2/(BT1+BT2) Let q be (q)a*m1)+(qb*m2) Wherein m is1、m2According to T1Hole, T2Determining the span value of the hole, and representing the size of the relative span of the two tunnels; q is T taking into account the span effect1Hole, T2Average vertical supporting force of the hole;
(V) is composed of a group of angles alpha, alpha ', theta', and GSI, mi、σciCan determine the destruction mode thereofThe shape of the formula can be completely determined, and a corresponding true value q is obtained, namely under the condition that constraint conditions are met, the maximum value of q is obtained by adopting an optimization method, and the supporting reaction force of the two tunnels can be obtained, namely the surrounding rock pressure values of all the unequal cross tunnels under the deep burying of the rock texture layer.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106682330A (en) * 2016-12-30 2017-05-17 湖南科技大学 Deep chamber surrounding rock pressure calculating method
CN108763749A (en) * 2018-05-28 2018-11-06 湖南科技大学 A method of judging different degrees of water-rich and area face stability under the full water time
CN108875152A (en) * 2018-05-28 2018-11-23 湖南科技大学 A kind of tunnel tunnel face calculating method for stability considering penetration

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018086085A1 (en) * 2016-11-12 2018-05-17 苏州大学 Method for calculating earth pressure load on tunnel
CN112632668A (en) * 2020-12-18 2021-04-09 中国电建集团贵阳勘测设计研究院有限公司 Shallow tunnel surrounding rock pressure calculation method under secondary failure mode

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106682330A (en) * 2016-12-30 2017-05-17 湖南科技大学 Deep chamber surrounding rock pressure calculating method
CN108763749A (en) * 2018-05-28 2018-11-06 湖南科技大学 A method of judging different degrees of water-rich and area face stability under the full water time
CN108875152A (en) * 2018-05-28 2018-11-23 湖南科技大学 A kind of tunnel tunnel face calculating method for stability considering penetration

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
Effect of Seepage Force on Tunnel Face Stability Using Limit Analysis with SRM;Yonglin An等;《Springer Nature Switzerland》;20201008;全文 *

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