CN109145356B - Method for determining broken area range of rock mass tunnel excavation - Google Patents
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Abstract
The invention discloses a method for determining the range of a rock mass tunnel excavation crushing zone, which is characterized in that a method for determining the stress state of an interface between a crushing zone and a plastic zone in a surrounding rock disturbance zone through different surrounding pressure indoor unloading tests of surrounding rock samples is established for isotropic rock masses based on the unloading damage characteristics of a tunnel surrounding rock crushing zone, a curve of the unloading damage process of the rock mass of the surrounding rock crushing zone is obtained, and a calculation method for calculating the radius of the crushing zone is established by adopting a layering method. The method reflects the process of loosening the surrounding rock of the tunnel, separates the reinforcing area and the crushing area of the surrounding rock, has more definite concept and reliable calculation result, and provides a new basis for tunnel support design and displacement calculation.
Description
Technical Field
The invention relates to a method for determining an excavation region of a rock mass tunnel, in particular to a method for determining the range of an excavation crushing region of the rock mass tunnel.
Background
The circular tunnel of excavation in infinite isotropic rock mass, whole region has an initial stress field before tunnel excavation, to weak broken rock mass tunnel, generally thinks that the surrounding rock divides into three typical regions after the excavation: an elastic zone, a plastic zone, and a fragmentation zone. In combination with a stress-strain curve for unloading the surrounding rock and in combination with the theory of the Fenner's formula, it is assumed that the strain of the surrounding rock body in the plastic region is 0, that is, although plastic deformation is generated, the total volume strain is not increased relative to the initial value. The unloading stress-strain curve of the surrounding rock corresponds to one point on the boundary of the crushing area for the ultimate strength under a certain surrounding pressure, the surrounding rock of the crushing area usually shows obvious expansion effect due to the expansion of cracks, but no method for determining the range of the crushing area exists at present, and the method brings difficulties for reinforcement design and displacement calculation.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a method for determining the range of a rock mass tunnel excavation crushing area, and solves the problem that no method for determining the range of the crushing area brings difficulties to reinforcement design and displacement calculation.
The technical scheme is as follows: the method for determining the range of the rock mass tunnel excavation crushing area comprises the following steps:
(1) estimating the maximum tangential stress sigma of the tunnel wall by adopting an elastic mechanics theory solution or an elastic finite element method according to the actually measured initial ground stresstmaxCarrying out unloading failure tests on the surrounding rock samples under different surrounding pressures to obtain unloading curves under different surrounding pressures, and carrying out dimensionless treatment on the curves to obtain a crushing area calculation basis curve;
(2) stress states of boundary points of the surrounding rock crushing area and the plastic area corresponding to the highest point A on the curve obtained in the step (1) and residual strength stress states of unloading damage of rocks at the hole wall of the lowest point B after the curve is stable are divided into n layers equally, and the corresponding surrounding rock crushing area is also divided into n layers equally;
(3) according to the equilibrium condition that the sum of all forces along the radial axis of the unit cell is zero:
the thickness of the nth layer of the crushing area is obtained after the formula is simplified:
wherein b is the radius of the hole wall, hnIs the thickness of the n-th layer, σrnIs the n-th layer upper boundary radial stress, σrn+1Is the n-th layer lower boundary radial stress, σθnFor the upper boundary tangential stress, σ, of the n-th layerθn+1Is the lower boundary tangential stress of the nth layer;
(4) according to the same equilibrium conditions: thickness of the ith layer when i < n:
wherein b is the radius of the hole wall, hiIs the thickness of the i-th layer, σriIs the i-th layer upper boundary radial stress, σri+1Is the i-th layer lower boundary radial stress, σθiIs the i-th layer upper boundary tangential stress, σθi+1Is the ith layer lower boundary tangential stress;
(5) and (4) accumulating the thicknesses of the layers according to the steps (3) and (4) to obtain the radius of the crushing area:
and (2) in the step (1), taking the maximum axial pressure of 2 gamma H when the initial ground stress is not measured, wherein gamma is the weight of the rock measured through the test, and H is the tunnel burial depth. N in the step (2) is more than or equal to 10. The sigmatmaxThe radius of the crushing area is 0 when the crushing area is smaller than the unconfined compressive strength of the rock mass.
Has the advantages that: the method for determining the stress state of the interface between the crushing area and the plastic area in the surrounding rock disturbance ring by adopting the indoor unloading tests of different surrounding pressures of the surrounding rock sample obtains the unloading failure process curve of the rock mass in the surrounding rock crushing area, establishes the radius of the calculated crushing area by adopting a layering method, reflects the loosening process of the tunnel surrounding rock, separates the surrounding rock strengthening area from the failure area, has more definite concept and reliable calculation result, and provides a new basis for tunnel support design and displacement calculation.
Drawings
FIG. 1 is a schematic diagram of distribution of surrounding rock influence zones of a circular cavern;
FIG. 2 is a wall rock unload stress-strain curve;
FIG. 3 is a graph of the unloading process at different confining pressures;
FIG. 4 is a schematic diagram of the stratification pattern of the crushing zone;
FIG. 5 is a schematic view of the force analysis of the nth layer in the crushing zone;
FIG. 6 is a measured rock unloading stress-strain curve;
FIG. 7 is a plot of measured plastic fracture zone offset stress versus strain;
FIG. 8 is a force analysis diagram of layer 30 of the crushing zone;
fig. 9 is a measured curve of the radius of the crushing zone as a function of the retaining force.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the surrounding rock after excavation is generally considered to be divided into three typical areas: an elastic zone, a plastic zone, and a fragmentation zone. In conjunction with the wall rock stress-strain relief curve 2, AB corresponds to the plastic phase, so point a in fig. 2 corresponds to point F on the elastic-plastic boundary in fig. 1. According to the theory of the penner equation, it is assumed that the strain of the surrounding rock mass in the plastic region is 0, i.e., although plastic deformation occurs, the total volume strain is not increased relative to the initial value. Point B in fig. 2 is the ultimate strength at a certain confining pressure and point B in fig. 2 corresponds to a point G on the boundary of the crushing zone in fig. 1. Estimating the maximum tangential stress sigma of the tunnel wall by adopting an elastic mechanics theory solution or an elastic finite element method according to the actually measured initial ground stresstmaxAnd when the initial ground stress is not measured, according to experience, most of deeply buried tunnels have approximately equal initial stress fields in the horizontal direction and the vertical direction and are both p0When the round cavity is excavated, according to the theory of elasticity mechanics, the stress sigma is tangential to the periphery of the cavityθI.e. sigmatmaxThe increase becomes 2 gammah and the radial pressure sigmarAnd gradually decreases in the opposite direction along the radial direction, and the point G in figure 1 reaches the critical value of the crushing area corresponding to the point B in the unloading curve chart 2, and the rock body at the position reaches the unloading peak intensity. In the crushing zone, in the opposite radial direction, radiallyThe pressure is continuously and gradually reduced, the hole wall is reduced to 0, and the rock mass is in the unloading, destroying and softening stage, so that the stress state of each surrounding rock along the radial path, which is homogeneous in the initial state of the rock in the destroying area, can be described by an indoor rock sample unloading and surrounding rock destroying process.
Assuming that the range of the crushing zone is relatively small, the tangential stress of the G point in the boundary diagram 1 of the crushing zone is close to the maximum value sigmaθWhere γ is the rock weight as determined by the test and H is the tunnel burial depth. Because the radial stress is reduced along the radial direction and the rock sample is continuously unloaded and destroyed, each point on the unloading destruction curve corresponds to each point state on the radial path of the crushing area, so that an indoor test method can be established to determine the boundary point stress state of the surrounding rock crushing area, and the specific method comprises the following steps:
estimating the maximum tangential stress sigma of the tunnel wall by adopting an elastic mechanics theory solution or an elastic finite element method according to the actually measured initial ground stresstmaxAiming at unloading failure tests of M groups of surrounding rock samples under different surrounding pressures (the maximum surrounding pressure is not less than the initial horizontal stress), the test method refers to 'rock physical mechanical property test regulation' DZ/T0276.21-2015, the surrounding pressure is firstly applied to the rock samples and then applied by 1 time, 1.5 times can be taken when the rock samples are few, the unloading failure tests (the unloading and loading rates are the same) of surrounding pressure unloading are carried out while the axial pressure of the initial ground stress is increased, and M groups of unloading peak stress states are respectively obtained as shown in figure 3, namely the maximum axial pressure value under different surrounding pressures is close to sigma, and the maximum axial pressure is close to sigmatmaxThe curve of (2) is used as the critical stress state of the boundary of the surrounding rock crushing zone, the maximum axial pressure is 2 gamma H when the initial stress is not actually measured, wherein gamma is the weight of the rock measured through the test, and H is the unloading curve obtained according to the group of rock samples by the tunnel burial depth and used as the curve calculated by the crushing zone layer summation method. For the convenience of calculation, the rock unloading offset stress-strain curve is subjected to non-dimensionalization treatment as shown in FIG. 4. Wherein when σtmaxThe radius of the crushing area is 0 when the crushing area is smaller than the unconfined compressive strength of the rock mass.
σ in the partial stress-strain curve1And σ3Respectively corresponding to sigma in the crushing zoneθAnd σrThe maximum point A of the right curve of FIG. 4 isThe stress state of the boundary point of the surrounding rock crushing area and the plastic area, and the point B is the residual strength stress state of the unloading damage of the rock at the hole wall, so the idea of the layering summation method is as follows: equally dividing AB into n layers corresponding to the n layers of the crushing zone, wherein the thickness of the ith layer in the crushing zone is hiIf n is large enough, the damage state of the surrounding rock of the ith layer can be approximately uniform, and the mechanical parameters such as expansion strain and the like are constant. When the layer separation calculation is adopted, the number of layers is preferably more than 10, namely n is more than or equal to 10.
Thus, in the nth layer, as in FIG. 5, the sum of all forces along the radial axis of the cell body is zero, i.e., Sigma F, depending on the equilibrium conditionrWhen the ratio is 0, the following:
the thickness of the n-th layer can be obtained by simplification
Wherein b is the radius of the hole wall, hnIs the thickness of the n-th layer, σrnIs the n-th layer upper boundary radial stress, σrn+1Is the n-th layer lower boundary radial stress, σθnFor the upper boundary tangential stress, σ, of the n-th layerθn+1The lower boundary tangential stress of the nth layer is distributed in a trapezoidal shape. σ in FIG. 43 0Is the initial confining pressure.
The thickness of the n-1 th layer can be obtained with the same equilibrium conditions for the n-1 th layer:
wherein b is the radius of the hole wall, hnIs the thickness of the n-th layer, hn-1Is the n-1 th layer thickness, σrn-1Is the n-1 th layer upper boundary radial stress, σrnIs the n-1 th layer lower boundary radial stress, σθn-1Is the upper boundary tangential stress of the n-1 th layer, sigmaθnIs the lower boundary tangential stress of the (n-1) th layer and the tangential stressThe distribution is trapezoidal.
At the ith layer (when i < n)
Wherein b is the radius of the hole wall, hiIs the thickness of the i-th layer, σriIs the i-th layer upper boundary radial stress, σri+1Is the i-th layer lower boundary radial stress, σθiIs the i-th layer upper boundary tangential stress, σθi+1The lower boundary tangential stress of the ith layer is distributed in a trapezoidal shape. Wherein sigmaθi+1、σri+1、σθiAnd σriAll can be obtained on the obtained test curve, and the radius R of the crushing zone can be obtained by accumulating the thickness of each layerc
When the method is adopted to calculate the range of the tunnel excavation crushing area, the burial depth of a certain circular tunnel is 1120m, the excavation radius is 3.7m, and the physical and mechanical parameters of rocks obtained through a rock unloading test are shown in table 1.
TABLE 1 petrophysical mechanical parameters
σ at the fracture boundary due to tunnel burial depth 1160mθAccording to the method for determining the range of the crushing zone provided by the invention, the stress-strain curve of rock unloading test under different confining pressures is 58MPa, and the confining pressure is 10MPa (namely sigma delta)3 010Mpa) is closest to 58Mpa, so that the curve is taken as the unloading failure process curve of the rock mass in the fracture zone, as shown in fig. 6. Carrying out layering calculation in a plastic crushing zone, and therefore, intercepting a partial stress-strain curve graph 7 at the beginning of expansion (corresponding to the stress state of an interface between the crushing zone and the plastic zone), wherein the layering method comprises the following steps: assuming no bracing stress pi, in this exampleThe resulting curve is divided equally in 30 layers on the vertical axis, corresponding to 30 layers of different thickness in the crushing zone.
The calculation is started from the layer 30, and the sigma corresponding to the upper boundary and the lower boundary of the layer 30 of the measured curve is respectively taken in the graph 71And σ3The upper boundary of the 30 th floor in fig. 7 corresponds to the upper boundary of the 30 th floor of the crushing zone in fig. 8, and the lower boundary of the 30 th floor in fig. 7 corresponds to the lower boundary in fig. 8. And sigma1And σ3Respectively correspond to sigmaθAnd σr. The value of each layer is calculated according to the method, the thickness of the 30 th layer is calculated by the formula (2) n which is 30, the thicknesses of other layers of the crushing zone are calculated by the formula (4), and the thickness of each layer is accumulated to obtain the influence range of the crushing zone and further obtain the radius of the crushing zone.
When the support stress pi is not equal to 0, σ is found in fig. 73And (4) performing layering from the point corresponding to pi, and performing the calculation of the range of the area to be crushed by the same method. The crushing zone layering treatment is divided into 30 layers and the crushing zone is not layered, namely only one layer of radius of the obtained crushing zone is compared, then a curve of the radius of the crushing zone layering treatment and the radius of the crushing zone non-layering treatment along with the change of the supporting force is obtained, as shown in fig. 9, the fact that the radius of the crushing zone calculated by layering is larger than that calculated by non-layering, the supporting stress pi is smaller, and the difference is larger. With the increase of the supporting force, namely pi is increased, the radius of the crushing area is exponentially attenuated, gradually reduced and approaches to 0, namely when pi is large, the crushing area disappears, and only the elastoplastic area exists in the surrounding rock.
The stress state of the boundary of the plastic zone and the crushing zone is determined by the strength characteristic of rock mass materials and is independent of the supporting pressure, so that the stress state of the boundary of the plastic zone is fixed as long as the crushing zone exists, and the stress state is fixed along with the supporting force piThe radius of the crushing area is increased and gradually reduced until the radius disappears, namely, when the supporting force is large, the crushing area does not appear in the surrounding rock. Therefore, if the rock mass is of good quality, there may be no fracture zone after excavation. The method reflects the rule to meet the actual condition, and overcomes the defect that the actual project cannot determine the range of the crushing area through an indoor test at present.
Claims (4)
1. A method for determining the range of a rock mass tunnel excavation crushing area is characterized by comprising the following steps:
(1) estimating the maximum tangential stress sigma of the tunnel wall by adopting an elastic mechanics theory solution or an elastic finite element method according to the actually measured initial ground stresstmaxCarrying out unloading failure tests on the surrounding rock samples under different confining pressures to obtain unloading curves under different confining pressures, and enabling the maximum axial pressure to be close to sigmatmaxCarrying out non-dimensionalization treatment on the curve to obtain a crushing area calculation basis curve;
(2) stress states of boundary points of the surrounding rock crushing area and the plastic area corresponding to the highest point A on the curve obtained in the step (1) and residual strength stress states of unloading damage of rocks at the hole wall corresponding to the lowest point B after the curve is stable are divided into n layers, and the corresponding surrounding rock crushing area is also divided into n layers;
(3) according to the equilibrium condition that the sum of all forces along the radial axis of the unit cell is zero:
the thickness of the nth layer of the crushing area is obtained after the formula is simplified:
wherein b is the radius of the hole wall, hnIs the thickness of the n-th layer, σrnIs the n-th layer upper boundary radial stress, σrn+1Is the n-th layer lower boundary radial stress, σθnFor the upper boundary tangential stress, σ, of the n-th layerθn+1Is the lower boundary tangential stress of the nth layer;
(4) according to the same equilibrium conditions: thickness of the ith layer when i < n:
wherein b is the radius of the hole wall, hiAs the i-th layerThickness, σriIs the i-th layer upper boundary radial stress, σri+1Is the i-th layer lower boundary radial stress, σθiIs the i-th layer upper boundary tangential stress, σθi+1Is the ith layer lower boundary tangential stress;
(5) and (4) accumulating the thicknesses of the layers according to the steps (3) and (4) to obtain the radius of the crushing area:
2. the method for determining the range of the broken zone of the rock mass tunnel excavation according to claim 1, wherein the maximum axial pressure in the step (1) is 2 γ H when the initial stress is not measured, wherein γ is the rock weight measured by the test, and H is the tunnel burial depth.
3. The method for determining the range of the rock mass tunnel excavation fracture area in claim 1, wherein n is greater than or equal to 10 in the step (2).
4. The method for determining the extent of a fractured zone of rock mass tunnel excavation according to claim 1, wherein the σ istmaxThe radius of the crushing area is 0 when the crushing area is smaller than the unconfined compressive strength of the rock mass.
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| CN111400886B (en) * | 2020-03-05 | 2022-04-15 | 河海大学 | Displacement calculation method for enclosed pressure arch circular tunnel with unevenly distributed surrounding rock space |
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