CN116467898A - Calculation method for butt-joint tunneling limit support pressure in shield ground - Google Patents

Calculation method for butt-joint tunneling limit support pressure in shield ground Download PDF

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CN116467898A
CN116467898A CN202310730932.0A CN202310730932A CN116467898A CN 116467898 A CN116467898 A CN 116467898A CN 202310730932 A CN202310730932 A CN 202310730932A CN 116467898 A CN116467898 A CN 116467898A
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butt
soil
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CN116467898B (en
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姚占虎
魏涛
张亚洲
梁玉强
张雷
刘福友
张习颖
魏驰
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CCCC First Highway Engineering Co Ltd
CCCC Tunnel Engineering Co Ltd
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CCCC Tunnel Engineering Co Ltd
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Abstract

The invention provides a calculation method of limit support pressure of butt joint in shield ground, which relates to the technical field of shield calculation, is more accurate and reasonable and is applicable to setting of limit support pressure under special working conditions of butt joint in shield ground, and comprises the following steps: step a: constructing a three-dimensional mechanical model under the shield butt joint working condition; step b: comprehensively considering the distance from the top of the shield to the surface of the river bed and the distance between the cutter heads of the preceding shield and the following shield, and classifying the conditions of the three-dimensional mechanical model; step c: stress analysis is carried out on the three-dimensional mechanical model based on condition classification, and a balance equation of the total horizontal acting force P is established; step d: solving the total horizontal acting force P; step e: considering the horizontal acting force of the soil in the depth range from the top of the shield to the lower part of the unloading arch, and solving the horizontal acting force acting on the tunnel face based on the total horizontal acting force P; step f: and solving the limit support pressure in the shield butt-joint tunneling process based on the horizontal acting force acting on the tunnel face.

Description

Calculation method for butt-joint tunneling limit support pressure in shield ground
Technical Field
The invention relates to the technical field of shield calculation, in particular to a method for calculating the butt tunneling limit support pressure in shield ground.
Background
The shield tunneling support pressure calculation method is mainly calculated by adopting a traditional Rankine soil pressure theory or a Taisha foundation loose soil pressure theory, and according to the test results of related shield tunneling limit support pressure models at home and abroad, the front part of the shield is a wedge body when the tunneling excavation face in sandy soil is damaged, the upper part of a damaged area is a silo-shaped model, and a model schematic diagram is shown in figure 1.
If the result of calculation is larger according to the Taisha loose soil pressure theory under the shield ground abutting working condition, the main reason is that the sliding body is blocked to slide along the original sliding surface due to the existence of the preceding shield in the abutting tunneling process, which is equivalent to the reduction of the soil body of the original sliding body which is movable along the sliding surface, the existence of the preceding shield plays a role in indirectly supporting the soil body in front of the following shield, the supporting pressure in the abutting tunneling process of the following shield is correspondingly reduced, and the model schematic diagrams are shown in fig. 2 and 3.
CN 108830014A discloses a method for calculating minimum supporting force of a shield tunnel excavation surface of a sandy pebble stratum, which comprises the steps of establishing a three-dimensional mechanical model according to S1 and the shape of the shield tunnel excavation surface when the shield tunnel excavation surface collapses, making basic assumption according to actual stratum conditions and calculation requirements, carrying out stress analysis on the three-dimensional mechanical model under an active limit state according to the basic assumption, solving other unknowns in a balance equation according to S3, calculating limit supporting pressure, dividing the limit supporting pressure by an excavation area by S5, and simply calculating the minimum supporting force of the shield tunnel excavation surface of the sandy pebble stratum according to the basic assumption.
The calculation method has great limitation in butt joint in shield ground:
1. the influence of the existence of the preceding shield on the front soil pressure of the backward shield under the butt joint working condition in the shield ground is not considered in the calculation model;
2. the minimum supporting force calculation method is suitable for the sandy pebble stratum, and has low applicability to the general stratum condition.
Based on the original calculation model and method, the limit support pressure under the shield ground butt joint working condition cannot be determined, if the support pressure calculation is performed under the shield ground butt joint working condition according to the traditional calculation model and method, the support pressure can be excessively large, and the following risk problems are caused:
1. and the face is unstable in the process of the butt tunneling of the backward shield.
2. The advanced shield is subjected to excessive disturbance, so that the advanced shield body retreats, deviates and the like, and the risk of butt joint positioning misalignment is caused.
In view of the foregoing, there is a need for a reasonable calculation model and method to accurately guide the setting of the limit support pressure under the butt-joint condition in the shield.
Disclosure of Invention
The invention aims at solving the problems in the prior art, and overcomes the defects in the prior art, and by designing a calculation method for the limit support pressure of the butt joint tunneling in the shield ground, the model stress analysis is comprehensive, the calculation method is simple and convenient, the limit support pressure of the shield butt joint is calculated by carrying out the limit balance stress analysis, the instability of the face in the butt joint tunneling process of the trailing shield and the overlarge disturbance to the leading shield can be effectively avoided, the beneficial guarantee is provided for the precise butt joint of the shield, and the technical blank of setting the limit support pressure in the butt joint in the shield ground is filled.
A calculation method for the pressure of a butt-joint tunneling limit support in shield ground comprises the following steps:
step a: constructing a three-dimensional mechanical model under the shield butt joint working condition;
step b: comprehensively considering the distance from the top of the shield to the surface of the river bed and the distance between the cutter heads of the preceding shield and the following shield, and classifying the conditions of the three-dimensional mechanical model;
step c: stress analysis is carried out on the three-dimensional mechanical model based on condition classification, and a balance equation about the total horizontal acting force P in the butt tunneling process is established;
step d: solving the total horizontal acting force P;
step e: considering the horizontal acting force of the soil in the depth range from the top of the shield to the lower part of the unloading arch, and solving the horizontal acting force acting on the tunnel face based on the total horizontal acting force P;
step f: and solving the limit support pressure in the shield butt-joint tunneling process based on the horizontal acting force acting on the tunnel face.
Step a, assuming that the distance of influence of the backward shield on the forward shield is equal to the excavation diameter, when the distance S of a cutterhead between the forward shield and the backward shield is larger than the excavation diameter D of the shield, assuming that an initial sliding surface with influence is a fan-shaped structure with a radius D, the upper part of the fan-shaped structure is a cuboid structure with a length and a width equal to D and a depth equal to 2D,
when S is less than or equal to D, the sliding body is blocked from sliding along the original sliding surface due to the existence of the preceding shield after the shield enters the butt joint influence range, the existence of the preceding shield plays a role in indirectly supporting the soil body in front of the rear shield, the sliding soil body in front of the butt joint tunneling of the rear shield is regarded as a triangular prism body with the volume continuously reduced along with the continuous reduction of the distance between the cutter heads, the inclined edge of the triangular prism body is the connecting line between the bottom of the rear shield and the top of the preceding shield and is prolonged and intersected with the initial sliding line, the horizontal line is along the intersection point and is intersected with the extension line of the excavation surface of the cutter head of the rear shield, and the upper part of the triangular prism body is deepCuboid structure with degree reduced along with continuous reduction of cutter head distance, triangular prism with width of D and height of D+h 0 The length of the cuboid structure is D, the width is D, and the height is 2S-h 0 Wherein θ is the angle between the hypotenuse of the triangular prism and the horizontal plane,，h 0 is the depth of the triangular prism above the top of the shield,。
further, the classifying in the step2 includes:
category 1: h >2D and S <0.5D, wherein H represents the distance from the shield top to the surface of the river bed;
category 2: h is more than 2D, and S is more than or equal to 0.5D and less than or equal to D;
category 3: h >2D and S > D;
category 4: h is less than or equal to 2D, and S is less than 0.5D;
category 5: h is less than or equal to 2D, and S is less than or equal to 0.5D and less than or equal to D;
category 6: h is less than or equal to 2D and S is greater than D.
Further, the expression of P is:
；
wherein:is the floating degree of soil mass->Is the friction force between soil bodies>，/>Is the internal friction angle of the soil, and is the internal friction angle of the soil,is an active soil pressure coefficient->。
Further, for category 3 and category 6, the expression of P is:
；
wherein alpha is the inclination angle of the sliding block, is the included angle between the inclined edge of the soil body sliding block in front of the cutter head and the horizontal plane, beta is the included angle between the balance arch and the retaining wall, epsilon is the simplified representation parameter I of the formula,is the cohesive force of soil->Is the floating degree of soil mass->For balancing the included angle between the arch and the retaining wall, +.>Is water pressure->Is the three-dimensional loose soil pressure.
Preferably, the method comprises the steps of,
inclination angle of sliding blockSatisfies the following formula:
；
ε satisfies the following formula:
；
satisfies the following formula:
；
wherein,,is the coefficient of static side pressure, in%>For ground load->Depth of earth>For simplifying the expression representing the parameter II, the following formula is satisfied:
。
further preferably, for category 5, the expression for p is:
；
wherein,,is the distance from the top of the shield to the surface of the river bed.
Further, for category 1 and category 4, the expression for P is:
。
further, step e is calculated according to the following formula:
。
wherein:for horizontal forces acting on the face +.>For the horizontal acting force of the soil in the depth range from the top of the shield to the lower part of the unloading arch,
(1) when S is more than or equal to 0.5 and less than or equal to D,
；
wherein,,for the depth of the triangular prism above the top of the shield, the expression is as follows:
；
(2) when S is less than 0.5D,
。
further, in the step f, the limit supporting pressure in the shield butt tunneling process is calculated according to the following formula:
；
wherein, p is the limit supporting pressure in the butt tunneling process,the water pressure is calculated by the following formula:
；
wherein,,severe water, jersey>Is the depth of the water.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a calculation method of the limit support pressure of butt joint in shield ground, which is designed according to the special working condition of butt joint in shield ground, is simple and reasonable, is fit in practice, has comprehensive model stress analysis consideration, is simple and convenient, calculates the limit support pressure of shield butt joint through limit balance stress analysis, takes the average value of the limit support pressure and the upper limit value calculated by the Rankine soil pressure theory as the set value of the limit support pressure of shield butt joint in the shield butt joint process, can effectively avoid the instability of the face of a tunnel and the overlarge disturbance to a preceding shield in the follow-up shield butt joint process, provides favorable guarantee for precise shield butt joint, and fills the technical blank of setting the limit support pressure in the shield ground butt joint process.
Drawings
FIG. 1 is a prior art home and abroad ultimate support pressure test model;
FIG. 2 is a schematic diagram of a normal tunneling model of the shield;
FIG. 3 is a schematic view of a shield tunneling model;
FIG. 4 is a schematic diagram of a shield tunneling initial slider model;
FIG. 5 is a schematic view of a shield front slider model under docking conditions;
FIG. 6 is a schematic diagram of a sliding body model of H >2D, S > D;
FIG. 7 is a schematic diagram of a slider model with H >2D, 0.5D.ltoreq.S.ltoreq.D;
FIG. 8 is a schematic diagram of a sliding body model of H >2D, S <0.5D;
FIG. 9 is a schematic diagram of a sliding body model with H.ltoreq.2D, S > D;
FIG. 10 is a schematic diagram of a slider model with H.ltoreq.2D, 0.5D.ltoreq.S.ltoreq.D;
FIG. 11 is a schematic diagram of a sliding body model with H.ltoreq.2D, S <0.5D;
FIG. 12 is a schematic diagram of a stress analysis of an H >2D,0.5 D.ltoreq.S.ltoreq.D spacer;
FIG. 13 is a schematic diagram of H >2D, S <0.5D isolator stress analysis;
FIG. 14 is a schematic diagram of a stress analysis of H.ltoreq.2D, 0.5D.ltoreq.S.ltoreq.D spacers;
FIG. 15 is a schematic diagram of stress analysis of H.ltoreq.2D, S <0.5D spacers;
FIG. 16 is a graph of calculated results versus analysis line.
Detailed Description
The method for calculating the butt tunneling limit support pressure in the shield tunneling machine is further described in detail below with reference to the accompanying drawings and the specific implementation method.
1. Three-dimensional mechanical model establishment under shield butt joint working condition
Assuming that the distance of the influence of the backward shield on the forward shield is 1 time the excavation diameter D, the initial sliding surface when the influence exists is assumed to be a sector structure with a radius D, and a rectangular parallelepiped structure with a length D and a width D and a depth 2D is arranged at the upper part, as shown in fig. 4.
After the shield enters the butt joint influence range, the sliding body is blocked from sliding along the original sliding surface due to the existence of the preceding shield, the soil body which is equivalent to the original sliding body and movable along the sliding surface is reduced, the existence of the preceding shield plays a role in indirectly supporting the soil body in front of the rear shield, the sliding soil body in front of the butt joint tunneling of the rear shield is regarded as a triangular prism structure, the inclined edge is a connecting line between the bottom of the rear shield and the top of the preceding shield and extends to intersect at an initial sliding line, the connecting line is a horizontal line along the intersection point to intersect with an extension line of the excavation surface of a cutter head of the rear shield, the width of the triangular prism is D, and the height is D+h 0 The length of the cuboid structure is D, the width is D, and the height is 2S-h 0 As shown in fig. 5, where θ is the angle between the hypotenuse of the triangular prism and the horizontal plane,，h 0 is the depth of the triangular prism above the top of the shield, which is +.>。
2. And comprehensively considering the distance condition from the top of the shield to the surface of the river bed, and establishing a calculation model by the cutter head distance.
(1) H >2D, when the distance from the top of the shield to the surface of the river bed is more than 2 times of the shield excavation diameter.
(1) S > D, the shield cutter head spacing is larger than 1 time of the shield excavation diameter, and a model schematic diagram is shown in figure 6.
(2) S is more than or equal to 0.5 and less than or equal to D, the distance between shield cutterheads is between 0.5 and 1 time of shield excavation diameter, and a model schematic diagram is shown in figure 7.
(3) S <0.5D, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the model schematic diagram is shown in figure 8.
(2) H is less than or equal to 2D, and when the distance from the top of the shield to the surface of the river bed is less than 2 times of the shield excavation diameter
(1) S > D, the shield cutter head spacing is larger than 1 time of the shield excavation diameter, and a model schematic diagram is shown in figure 9.
(2) S is more than or equal to 0.5 and less than or equal to D, the distance between shield cutterheads is between 0.5 and 1 time of shield excavation diameter, and a model schematic diagram is shown in figure 10.
(3) S <0.5D, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the model schematic diagram is shown in figure 11.
3. And taking out the calculation models respectively as the separators for stress analysis, and establishing a force balance equation by using a limit balance method.
(1) H >2D, when the distance from the top of the shield to the surface of the river bed is more than 2 times of the shield excavation diameter
(1) S > D, the distance between shield cutterheads is larger than 1 time of the shield excavation diameter, and the minimum supporting pressure is calculated by applying the Taisha loose soil pressure theory:
；
wherein:
the diameter of the equivalent excavation surface;
the inclination angle of the sliding block is the inclined edge of the soil body sliding block in front of the cutter headThe included angle of the horizontal plane meets the following formula:
；
the floating degree of the soil body;
the included angle between the balance arch and the retaining wall;
is the internal friction angle of the soil;
is the cohesive force of the soil;
is water pressure;
is the pressure of the three-dimensional loose soil;
is the resting side pressure coefficient;
is the depth of the soil;
is ground load.
(2) S is more than or equal to 0.5 and less than or equal to D, the distance between shield cutterheads is between 0.5 and 1 time of shield excavation diameter, and a stress analysis schematic diagram of the isolator is shown in figure 12.
Horizontal direction:
；
wherein:
the total horizontal acting force of the isolator;
normal supporting force is applied to the sliding surface of the isolator;
friction force for the sliding surface of the separator;
is the included angle between the hypotenuse of the isolator and the horizontal plane;
is the friction force between soil bodies.
Vertical direction:
wherein:
is the gravity of the isolator;
unloading the gravity of the soil body for the upper part of the isolator;
friction force between soil bodies in a depth range from the top of the shield to the bottom of the unloading arch is generated;
the horizontal acting force of the soil in the depth range from the top of the shield to the lower part of the unloading arch is adopted.
Gravity of the separator:
；
wherein:
is the floating degree of the soil body;
the diameter of the excavation of the first and the second shield;
is the depth of the triangular prism above the top of the shield.
Gravity of the soil body unloaded from the upper part of the separator:
；
wherein:
the distance between the cutter heads of the shield is the distance between the cutter heads of the shield which move firstly and then.
h 0 Horizontal force of depth range soil:
；
wherein:
is the active soil pressure coefficient.
Active soil pressure coefficient:
；
wherein:is the internal friction angle of the soil body.
The depth of the triangular prism above the top of the shield is obtained by the similar triangle theorem:
；
included angle of hypotenuse of spacer and horizontal plane:
；
(3) s <0.5D, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the isolation body stress analysis schematic diagram is shown in figure 13.
Horizontal direction:
；
wherein:
the total horizontal acting force of the isolator;
normal supporting force is applied to the sliding surface of the isolator;
friction force for the sliding surface of the separator;
is the included angle between the hypotenuse of the isolator and the horizontal plane;
is the friction force between soil bodies.
Vertical direction:
；
wherein:
is the gravity of the isolator;
friction force between soil bodies in a depth range from the top of the shield to the bottom of the unloading arch is generated;
the horizontal acting force of the soil in the depth range from the top of the shield to the lower part of the unloading arch is adopted.
Gravity of the separator:
；
wherein:
is the floating degree of the soil body;
the diameter of the excavation of the first and the second shield;
defining a side length of the lower upper portion for the separator at a 2S height;
the distance between the cutter heads of the shield is the distance between the cutter heads of the shield which move firstly and then.
From the similar triangle theorem:
；
horizontal acting force from top of shield to unloading arch depth range soil:
；
active soil pressure coefficient:
；
wherein:and excavating an internal friction angle of the soil body for the shield.
Included angle of hypotenuse of spacer and horizontal plane:；
(2) H is less than or equal to 2D, and when the distance from the top of the shield to the surface of the river bed is less than 2 times of the shield excavation diameter
(1) S > D, the distance between shield cutterheads is larger than 1 time of the shield excavation diameter, and the minimum supporting pressure is calculated by applying the Taisha loose soil pressure theory:
；
wherein:
the diameter of the equivalent excavation surface;
the inclination angle of the sliding block is the included angle between the inclined edge of the soil body sliding block in front of the cutter head and the horizontal plane, and the inclination angle is +.>；
The floating degree of the soil body;
the included angle between the balance arch and the retaining wall;
is the internal friction angle of the soil;
is the cohesive force of the soil;
is water pressure;
is the pressure of the three-dimensional loose soil;
is the resting side pressure coefficient;
is the depth of the soil;
is ground load.
(2) S is more than or equal to 0.5 and less than or equal to D, the distance between shield cutterheads is between 0.5 and 1 time of shield excavation diameter, and a stress analysis schematic diagram of the isolator is shown in fig. 14.
Horizontal direction:
；
wherein:
the total horizontal acting force of the isolator;
normal supporting force is applied to the sliding surface of the isolator;
friction force for the sliding surface of the separator;
is the included angle between the hypotenuse of the isolator and the horizontal plane;
is the friction force between soil bodies.
Vertical direction:
；
wherein:
is the gravity of the isolator;
unloading the gravity of the soil body for the upper part of the isolator;
friction force between soil bodies in a depth range from the top of the shield to the bottom of the unloading arch is generated;
from the top of the shield to the unloading archHorizontal force of the earth in the lower depth range.
Gravity of the separator:
wherein:
is the floating degree of the soil body;
the diameter of the excavation of the first and the second shield;
is the depth of the triangular prism above the top of the shield.
Gravity of the soil body unloaded from the upper part of the separator:
；
wherein:
is the distance from the top of the shield to the surface of the river bed.
h 0 Horizontal force of depth range soil:
；
wherein:
is the active soil pressure coefficient.
Active soil pressure coefficient:
；
wherein:is the internal friction angle of the soil body.
The depth of the triangular prism above the top of the shield is obtained by the similar triangle theorem:
；
included angle of hypotenuse of spacer and horizontal plane:
；
(3) s <0.5D, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the stress analysis schematic diagram of the isolator is shown in figure 15.
Horizontal direction:
；
wherein:
the total horizontal acting force of the isolator;
normal supporting force is applied to the sliding surface of the isolator;
friction force for the sliding surface of the separator;
is the included angle between the hypotenuse of the isolator and the horizontal plane;
is between soil bodiesIs used for the friction force of the steel plate.
Vertical direction:
；
wherein:
is the gravity of the isolator;
friction force between soil bodies in a depth range from the top of the shield to the bottom of the unloading arch is generated;
the horizontal acting force of the soil in the depth range from the top of the shield to the lower part of the unloading arch is adopted.
Gravity of the separator:
；
wherein:
is the floating degree of the soil body;
the diameter of the excavation of the first and the second shield;
defining a side length of the lower upper portion for the separator at a 2S height;
the distance between the cutter heads of the shield is the distance between the cutter heads of the shield which move firstly and then.
From the similar triangle theorem:
；
horizontal acting force from top of shield to unloading arch depth range soil:
；
active soil pressure coefficient:
；
wherein:and excavating an internal friction angle of the soil body for the shield.
Included angle of hypotenuse of spacer and horizontal plane:；
4. and (3) solving an expression of the total horizontal force P of the model isolator and the distance S between the shield cutterheads by combining the balance equations, and calculating the assignment of the distance S between the shield cutterheads in the P-S relation expression to obtain the total horizontal acting force P of the isolator at different distances.
(1) When the distance between shield cutterheads is larger than 1 time of the shield excavation diameter (S > D), the minimum supporting pressure can be calculated directly by utilizing the Taisha loose soil pressure theory without considering the distance from the top of the shield to the surface of the river bed:
；/>
(2) When the distance from the top of the shield to the surface of the river bed is more than 2 times of the shield excavation diameter (H > 2D), the distance between shield cutterheads is 0.5 times to 1 time of the shield excavation diameter (S is more than or equal to 0.5D and less than or equal to D), and the expression of the P-S can be obtained by the simultaneous formula as follows:
；
(3) When the distance from the top of the shield to the surface of the river bed is less than or equal to 2 times of the shield excavation diameter (H is less than or equal to 2D), the distance between shield cutterheads is between 0.5 times and 1 time of the shield excavation diameter (S is less than or equal to 0.5D and less than or equal to D), and the expression of the P-S can be obtained by the simultaneous formula as follows:
；
(4) When the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter S <0.5D, the distance from the top of the shield to the surface of the river bed can be not considered, and the expression of the P-S can be obtained by the simultaneous formula as follows:
；
5. and (3) calculating to obtain the total horizontal acting force, subtracting the horizontal acting force of the soil in the depth range from the top of the shield to the position below the unloading arch, and solving to obtain the horizontal acting force acting on the tunnel face.
；
Wherein:is a horizontal acting force acting on the face.
The calculation formula is as follows:
the shield cutter head spacing is between 0.5 and 1 times of shield excavation diameter (S is more than or equal to 0.5D and less than or equal to D)
；
The shield cutter head spacing is smaller than 0.5 times shield excavation diameter (S < 0.5D)
；
6. The limit supporting pressure in the shield butt-joint tunneling process can be obtained by dividing the horizontal acting force acting on the tunnel face by the area of the tunnel face.
；
Wherein: p is the limit supporting pressure in the butt tunneling process;is water pressure->，/>Severe water, jersey>Is the depth of water (including river water and groundwater). />
Taking the construction of a certain Yangtze river tunnel by a shield method as an example, the diameter D of the shield excavation is 16m, the shield penetrates through the tunnel in a river-to-river butt joint mode, the earthing depth H of the butt joint position is about 27m, and the water depth H of the river is about w About 27m, the soil layer floating weight of the butt joint position is gamma of 9.6kN/m 3 The cohesion c is 10kPa, the internal friction angle psi is 25 DEG, and the lateral pressure coefficient K 0 0.51.
The calculation of the shield tunneling limit support pressure within a distance range of 1 time of the excavation diameter D during shield butt joint is taken as an example.
Step1, comprehensively considering the distance condition from the top of the shield to the surface of the river bed, selecting a calculation model and a corresponding P-S calculation expression.
According to H= 27,2D =32m, H is less than or equal to 2D, the limit support pressure in the shield butt tunneling process is calculated by using the following equation:
the shield cutter head spacing is between 0.5 and 1 time of shield excavation diameter (S is more than or equal to 0.5 and less than or equal to D), and the expression of P-S is as follows:
；
the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter S <0.5D, and the expression of P-S is as follows:
；
step2, determining the assignment range of S, and taking different S into the P-S expression to calculate the total horizontal force P at different positions.
The assignment range of S is selected to be within 1D (namely, less than or equal to 16 m)
When S=16m, the shield cutter head distance is between 0.5 times and 1 time of shield excavation diameter, S=16m is brought into a P-S expression when S is more than or equal to 0.5D and less than or equal to D, and P= 35779.73kN is solved.
When S=15m, the shield cutter head distance is between 0.5 and 1 time of shield excavation diameter, S=15m is brought into a P-S expression when S is more than or equal to 0.5D and less than or equal to D, and P= 36910.76kN is solved.
When S=14m, the shield cutter head distance is between 0.5 times and 1 time of shield excavation diameter, S=14m is brought into a P-S expression when S is more than or equal to 0.5D and less than or equal to D, and P= 37774.35kN is solved.
When S=13m, the shield cutter head distance is between 0.5 times and 1 time of shield excavation diameter, S=13m is brought into a P-S expression when S is more than or equal to 0.5D and less than or equal to D, and P= 38284.90kN is solved.
When S=12m, the shield cutter head distance is between 0.5 and 1 time of shield excavation diameter, S=12m is brought into a P-S expression when S is more than or equal to 0.5D and less than or equal to D, and P= 38319.91kN is solved.
When S=11m, the shield cutter head distance is between 0.5 times and 1 time of shield excavation diameter, S=11m is brought into a P-S expression when S is more than or equal to 0.5D and less than or equal to D, and P= 37699.30kN is solved.
When S=10m, the shield cutter head distance is between 0.5 and 1 time of shield excavation diameter, S=10m is brought into a P-S expression when S is more than or equal to 0.5D and less than or equal to D, and P= 36149.49kN is solved.
When S=9m, the shield cutter head distance is between 0.5 times and 1 time of shield excavation diameter, S=9m is brought into a P-S expression when S is more than or equal to 0.5D and less than or equal to D, and P= 33238.61kN is solved.
When S=8m, the shield cutter head distance is between 0.5 and 1 time of shield excavation diameter, S=8m is brought into a P-S expression when S is more than or equal to 0.5D and less than or equal to D, and P= 28252.14kN is solved.
When s=7m, the shield cutter head distance is smaller than 0.5 times of the shield excavation diameter, and the s=7m is brought into an expression of P-S when S <0.5D, so that p= 24123.63kN is obtained.
When s=6m, the shield cutter head distance is smaller than 0.5 times of the shield excavation diameter, and the s=6m is brought into an expression of P-S when S <0.5D, so that p= 20092.37kN is obtained.
When s=5m, the shield cutter head distance is smaller than 0.5 times of the shield excavation diameter, and the s=5m is brought into an expression of P-S when S <0.5D, so that p= 16201.87kN is obtained.
When s=4m, the shield cutter head distance is smaller than 0.5 times of the shield excavation diameter, and the s=4m is brought into an expression of P-S when S <0.5D, so that p= 12492.08kN is obtained.
When s=3m, the shield cutter head distance is smaller than 0.5 times of the shield excavation diameter, and the s=3m is brought into an expression of P-S when S <0.5D, so that p= 8997.64kN is obtained.
When s=2m, the shield cutter head distance is smaller than 0.5 times of the shield excavation diameter, and the s=2m is brought into an expression of P-S when S <0.5D, so that p= 5745.18kN is obtained.
When s=1m, the shield cutter head distance is smaller than 0.5 times of the shield excavation diameter, and the s=1m is brought into an expression of P-S when S <0.5D, so that p= 2748.50kN is obtained.
Step3, carrying corresponding formulas according to different distances of the cutterhead to solve the horizontal acting force of the soil in the depth range from the top of the shield to the position below the unloading arch.
The distance between shield cutterheads is 0.5 to 1 time of shield excavation diameter, and horizontal acting force of soil in the depth range from above the top of the shield to below the unloading arch is as follows:
；
the distance between shield cutterheads is smaller than 0.5 times of the shield excavation diameter, and horizontal acting force of soil in the depth range from the top of the shield to the lower part of the unloading arch is smaller than that of the shield:
；
when s=16m, the shield cutter head spacing is between 0.5 and 1 time of the shield excavation diameter, and the s=16m is carried in to obtain0kN。
When s=15m, the shield cutter head spacing is between 0.5 and 1 time of the shield excavation diameter, and the s=15m is carried in to obtain35.46kN。
When s=14m, the shield cutter head spacing is between 0.5 and 1 time of the shield excavation diameter, and the s=14m is carried in to obtain162.85kN。
When s=13m, the shield cutter head spacing is between 0.5 and 1 time of the shield excavation diameter, and the S=13m is carried in to obtain424.94kN。
When s=12m, the shield cutter head spacing is between 0.5 and 1 time of the shield excavation diameter, and the s=12m is carried in to obtain886.61kN。
When s=11m, the shield cutter head spacing is between 0.5 and 1 time of the shield excavation diameter, and the s=11m is carried in to obtain1648.66kN。/>
When s=10m, the shield cutter head spacing is between 0.5 and 1 time of the shield excavation diameter, and the s=10m is carried in to obtain2872.62kN。
When s=9m, the shield cutter head spacing is between 0.5 and 1 time of the shield excavation diameter, and the s=9m is carried in to obtain4827.11kN。
When s=8m, the shield cutter head spacing is between 0.5 and 1 time of the shield excavation diameter, and the s=8m is carried in to obtain7979.50kN。
When s=7m, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the S=7m is carried in to obtain6109.31kN。
When s=6m, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the S=6m is carried in to obtain4488.47kN。
When s=5m, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the S=5m is carried in to obtain3116.99kN。
When s=4m, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the S=4m is carried in to obtain1994.88kN。
When s=3m, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the S=3m is carried in to obtain1122.12kN。
When s=2m, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the S=2m is carried in to obtain498.72kN。
When s=1m, the shield cutter head spacing is smaller than 0.5 times of the shield excavation diameter, and the S=1m is carried in to obtain124.68kN。
Step4, subtracting the horizontal acting force of the soil in the depth range from the upper part of the shield to the lower part of the unloading arch from the total horizontal acting force to obtain the horizontal acting force acting on the tunnel face;
horizontal force acting on the face:
。
when s=16m, the horizontal force acting on the tunnel face: p (P) 1 =35779.73kN。
When s=15m, the horizontal force acting on the tunnel face: p (P) 1 =36875.29kN。
When s=14m, the horizontal force acting on the tunnel face: p (P) 1 =37611.51kN。
When s=13m, horizontal force acting on the tunnel face: p (P) 1 =37859.96kN。
When s=12m, the horizontal force acting on the tunnel face: p (P) 1 =37433.30kN。
When s=11m, the horizontal force acting on the tunnel face: p (P) 1 =36050.64kN。
When s=10m, the horizontal force acting on the tunnel face: p (P) 1 =33276.88kN。
When s=9m, horizontal force acting on the tunnel face: p (P) 1 =28411.50kN。
When s=8m, the horizontal force acting on the tunnel face: p (P) 1 =20272.64kN。
When s=7m, the horizontal force acting on the tunnel face: p (P) 1 =18014.32kN。
When s=6m, the horizontal force acting on the tunnel face: p (P) 1 =15603.90kN。
When s=5m, the horizontal force acting on the tunnel face: p (P) 1 =13084.88kN。
When s=4m, horizontal force acting on the tunnel face: p (P) 1 =10497.20kN。
When s=3m, the horizontal force acting on the tunnel face: p (P) 1 =7875.52kN。
When s=2m, the horizontal force acting on the tunnel face: p (P) 1 =5246.46kN。
When s=1m, the horizontal force acting on the tunnel face: p (P) 1 =2623.82kN。
Step5, dividing the horizontal acting force acting on the face by the area of the face to obtain the limit support pressure in the shield butt tunneling process.
Limit supporting pressure in the shield butt tunneling process:
；
when s=16m, the limit support pressure is: p= 679.76kPa.
When s=15m, the limit support pressure is: p= 684.04kPa.
When s=14m, the limit support pressure is: p= 686.92kPa.
When s=13m, the limit support pressure is: p= 687.89kPa.
When s=12m, the limit support pressure is: p= 686.22kPa.
When s=11m, the limit support pressure is: p= 680.82kPa.
When s=10m, the limit support pressure is: p= 669.99kPa.
When s=9m, the limit support pressure is: p= 650.98kPa.
When s=8m, the limit support pressure is: p= 619.19kPa.
When s=7m, the limit support pressure is: p= 610.37kPa.
When s=6m, the limit support pressure is: p= 600.95kPa.
When s=5m, the limit support pressure is: p= 591.11kPa.
When s=4m, the limit support pressure is: p= 581.00kPa.
When s=3m, the limit support pressure is: p= 570.76kPa.
When s=2m, the limit support pressure is: p= 560.49kPa.
When s=1m, the limit support pressure is: p= 550.25kPa.
And (3) calculating value analysis:
according to theory, as the shield abutting distance is continuously reduced, the sliding soil body at the front part of the backward shield is continuously reduced, the required supporting pressure is continuously reduced, and as can be seen from a comparison analysis line diagram of the calculation result of fig. 16, the limit supporting pressure of the backward shield shows a gradually reduced trend along with the reduction of the distance between shield cutterheads, the trend of the calculation result is matched with the actual situation, and the reasonable calculation model is verified.
The calculated values are all smaller than Yu Langken soil pressure calculated values due to the influence of the unloading arch, and the calculated values of the calculated method are reasonable.
The set value of the supporting pressure is the average value of the upper limit and the lower limit calculated by the Rankine soil pressure theory during normal tunneling of the shield. In order to ensure the safety of the face in front of the shield, the average value of the limit support pressure and the upper limit value calculated by the Rankine soil pressure theory can be taken as the set value of the limit support pressure for shield butt tunneling.
The present invention provides a method for calculating the pressure of the butt tunneling limit support in the shield land, and the above embodiments are only for illustrating the technical concept and the characteristics of the present invention, and the purpose of the present invention is to enable those skilled in the art to understand the content of the present invention and implement the present invention accordingly, and not to limit the protection scope of the present invention. All equivalent changes or modifications made in accordance with the spirit of the present invention should be construed to be included in the scope of the present invention.

Claims (10)

1. The calculation method of the shield tunneling limit support pressure in the ground is characterized by comprising the following steps:
step a: constructing a three-dimensional mechanical model under the shield butt joint working condition;
step b: comprehensively considering the distance from the top of the shield to the surface of the river bed and the distance between the cutter heads of the preceding shield and the following shield, and classifying the conditions of the three-dimensional mechanical model;
step c: stress analysis is carried out on the three-dimensional mechanical model based on condition classification, and a balance equation about the total horizontal acting force P in the butt tunneling process is established;
step d: solving the total horizontal acting force P;
step e: considering the horizontal acting force of the soil in the depth range from the top of the shield to the lower part of the unloading arch, and solving the horizontal acting force acting on the tunnel face based on the total horizontal acting force P;
step f: and solving the limit support pressure in the shield butt-joint tunneling process based on the horizontal acting force acting on the tunnel face.
2. The method for calculating the pressure of the butt-joint tunneling limit support in the shield tunneling machine according to claim 1, which is characterized by comprising the following steps:
step a, assuming that the distance of influence of the backward shield on the forward shield is equal to the excavation diameter, when the distance S of a cutterhead between the forward shield and the backward shield is larger than the excavation diameter D of the shield, assuming that an initial sliding surface with influence is a fan-shaped structure with a radius D, the upper part of the fan-shaped structure is a cuboid structure with a length and a width equal to D and a depth equal to 2D,
when S is less than or equal to D, after the shield enters the butt joint influence range, the sliding body is blocked to slide along the original sliding surface due to the existence of the preceding shield, the existence of the preceding shield plays a role in indirectly supporting the soil body in front of the rear shield, the sliding soil body in front of the butt joint tunneling of the rear shield is regarded as a triangular prism body with the volume being continuously reduced along with the continuous reduction of the distance between the cutterhead, the bevel edge of the triangular prism body is the connecting line of the bottom of the rear shield and the top of the preceding shield and is prolonged and intersected at the initial sliding line, the horizontal line is taken along the intersection point and is intersected at the extension line of the excavation surface of the cutterhead of the rear shield, the cuboid structure with the depth being reduced along with the continuous reduction of the distance between the cutterhead is arranged above the triangular prism body, the width of the triangular prism body is D, and the height of the triangular prism body is D+h 0 The length of the cuboid structure is D, the width is D, and the height is 2S-h 0 Wherein θ is the angle between the hypotenuse of the triangular prism and the horizontal plane,，h 0 is the depth of the triangular prism above the top of the shield,。
3. the method for calculating the pressure of the butt tunneling limit support in the shield tunneling machine according to claim 2, wherein the classification in the step2 comprises:
category 1: h >2D and S <0.5D, wherein H represents the distance from the shield top to the surface of the river bed;
category 2: h is more than 2D, and S is more than or equal to 0.5D and less than or equal to D;
category 3: h >2D and S > D;
category 4: h is less than or equal to 2D, and S is less than 0.5D;
category 5: h is less than or equal to 2D, and S is less than or equal to 0.5D and less than or equal to D;
category 6: h is less than or equal to 2D and S is greater than D.
4. A method of calculating the pressure of a butt tunneling limit support in a shield land according to claim 3, wherein for class 2, the expression of p is:
；
wherein:is the floating degree of soil mass->Is the friction force between soil bodies>，/>Is the internal friction angle of earth->Is an active soil pressure coefficient->。
5. The method for calculating the butt tunneling limit support pressure in the shield land according to claim 4, wherein for category 3 and category 6, the expression of P is:
；
wherein alpha is the inclination angle of the sliding block, is the included angle between the inclined edge of the soil body sliding block in front of the cutter head and the horizontal plane, beta is the included angle between the balance arch and the retaining wall, epsilon is the simplified representation parameter I of the formula,is the cohesive force of soil->Is the floating degree of soil mass->For balancing the included angle between the arch and the retaining wall, +.>Is water pressure->Is the three-dimensional loose soil pressure.
6. The method for calculating the pressure of the butt tunneling limit support in the shield tunneling machine according to claim 5, wherein,
inclination angle of sliding blockSatisfies the following formula:
；
ε satisfies the following formula:
；
satisfies the following formula:
；
wherein,,is the coefficient of static side pressure, in%>For ground load->Depth of earth>For simplifying the expression representing the parameter II, the following formula is satisfied:
。
7. the method for calculating the pressure of the butt tunneling limit support in the shield tunneling machine according to claim 6, wherein for category 5, the expression of p is:
；
wherein,,is the distance from the top of the shield to the surface of the river bed.
8. The method for calculating the pressure of the butt tunneling limit support in the shield land according to claim 7, wherein the expression of p for category 1 and category 4 is:
。
9. the method for calculating the pressure of the butt tunneling limit support in the shield tunneling machine according to claim 8, wherein the step e is calculated according to the following formula:
；
wherein:for horizontal forces acting on the face +.>For the horizontal acting force of the soil in the depth range from the top of the shield to the lower part of the unloading arch,
(1) when S is more than or equal to 0.5 and less than or equal to D,
；
wherein,,for the depth of the triangular prism above the top of the shield, the expression is as follows:
；
(2) when S is less than 0.5D,
。
10. the method for calculating the limit support pressure in the shield tunneling process in the shield tunneling according to claim 9, wherein the limit support pressure in the shield tunneling process in the step f is calculated by the following formula:
；
wherein, p is the limit supporting pressure in the butt tunneling process,the water pressure is calculated by the following formula:
；
wherein,,severe water, jersey>Is the depth of the water.
CN202310730932.0A 2023-06-20 2023-06-20 Calculation method for butt-joint tunneling limit support pressure in shield ground Active CN116467898B (en)

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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20150267370A1 (en) * 2015-06-03 2015-09-24 Ramesh Chandra Gupta Test Device for Determining Three-Dimensional Consolidation Properties of Soils
CN108830014A (en) * 2018-06-29 2018-11-16 西南石油大学 A kind of Shield Tunneling containing sand-pebble layer face minimal support power calculation method
CN111695186A (en) * 2020-06-12 2020-09-22 河海大学 Method for calculating ultimate supporting force of circumferential excavation surface of shield tunnel without considering earth surface overload working condition
CN114329750A (en) * 2022-03-16 2022-04-12 北京城建集团有限责任公司 Sand-gravel stratum earth pressure balance shield earth bin pressure design and control method
CN115828627A (en) * 2022-12-23 2023-03-21 中国水利水电第八工程局有限公司 Method, system and medium for determining support pressure of tunnel face of opposite excavation tunnel

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20150267370A1 (en) * 2015-06-03 2015-09-24 Ramesh Chandra Gupta Test Device for Determining Three-Dimensional Consolidation Properties of Soils
CN108830014A (en) * 2018-06-29 2018-11-16 西南石油大学 A kind of Shield Tunneling containing sand-pebble layer face minimal support power calculation method
CN111695186A (en) * 2020-06-12 2020-09-22 河海大学 Method for calculating ultimate supporting force of circumferential excavation surface of shield tunnel without considering earth surface overload working condition
CN114329750A (en) * 2022-03-16 2022-04-12 北京城建集团有限责任公司 Sand-gravel stratum earth pressure balance shield earth bin pressure design and control method
CN115828627A (en) * 2022-12-23 2023-03-21 中国水利水电第八工程局有限公司 Method, system and medium for determining support pressure of tunnel face of opposite excavation tunnel

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