CN106021840A - Method for inverting transverse isotropic rock mass ground stress - Google Patents
Method for inverting transverse isotropic rock mass ground stress Download PDFInfo
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- CN106021840A CN106021840A CN201610085454.2A CN201610085454A CN106021840A CN 106021840 A CN106021840 A CN 106021840A CN 201610085454 A CN201610085454 A CN 201610085454A CN 106021840 A CN106021840 A CN 106021840A
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Abstract
The invention relates to a method for inverting transverse isotropic rock mass ground stress. Through rock mass displacement in a roadway, transverse isotropic rock mass ground stress is inverted. The method comprises the following steps: establishing a transverse isotropic rock mass model in an x-y-z coordinate system, a roadway cross section being parallel to an isotropic plane; determining the direction of ground stress in the transverse isotropic rock mass; taking a rock mass sample in the roadway, measuring transverse isotropic rock mass parameters of the rock mass sample; measuring deformation displacement of the rock mass in the roadway; and according to a roadway displacement analytic formula, obtaining a ground stress expression. The method can obtain a set of specific formulas to calculate transverse isotropic rock mass ground stress just by substituting the rock mass parameter measured values and a displacement measured value into the displacement analytic formula. The method prevents problems of complex equipment arrangement, large errors, and limited application range caused by measuring ground stress on site. The calculation method is simple and fast, and the method is mainly used for calculating transverse isotropic rock mass ground stress.
Description
Technical field
The invention belongs to Geotechnical Engineering field, particularly relate to a kind of side for inverting transverse isotropic rockmass crustal stress
Method.
Background technology
At present, in Geotechnical Engineering, the method for stress mainly carries out on-the-spot test definitely, in rock mass surface or inside
Arranging various test instrunment or equipment, the data obtained by measurement carry out analysis and the calculating of crustal stress, draw crustal stress
The regularity of distribution and result.But, geostress survey is at present mostly just for isotropism rock mass, and the cost of the equipment of measurement is relatively
Height, arranges and installs the most sufficiently complex, can expend substantial amounts of manpower and materials, arranges and improper also can cause bigger measurement by mistake
Difference.And process of the test often destroys structure and the character of rock mass itself in measured zone at the scene, also makes to measure knot
Fruit is accurate not, and the scope of application of measurement result is also subject to certain restrictions.And for rock mass itself parametric elasticity modulus and
The test of Poisson's ratio is measured comparatively easily and accurate, and, the deformation of rock mass and displacement data are also easier to measure.Cause
This, the present invention is theoretical by backanalysis on displacements, uses a kind of method of theoretical formula method to carry out inverting crustal stress.So that rock mass to be opened
Based on digging the surface in tunnel or the displacement data of inside and the elastic modelling quantity of rock itself, Poisson's ratio data, by simply
Theoretical Calculation obtains the crustal stress data of rock mass, thus avoids complexity and the bigger mistake of measurement result that measurement equipment is installed
Difference.The method is mainly used in transverse isotropic rockmass, it is possible to degenerate for isotropism rock mass.
Summary of the invention
The invention provides a kind of in the method for inverting transverse isotropic rockmass crustal stress, ask solving above-mentioned technology
Topic.
In order to achieve the above object, the technical scheme is that and be achieved in that: a kind of for inverting horizontal sight each to
The method of property rock mass crustal stress, carrys out the crustal stress of inverting transverse isotropic rockmass by the rock displacement in tunnel, including with
Lower step:
(1) setting up transverse isotropic rockmass model in x-y-z coordinate system, the transverse section in tunnel is parallel to xoy plane,
Tunnel is excavated along oz axle, and wherein xoy plane is transverse isotropy face, and oz axle is axis of symmetry;
(2) direction of transverse isotropic rockmass crustal stress is determined, at vertical direction initial field stress the most along the y-axis direction
For p, horizontal direction initial field stress the most along the x-axis direction is q;
(3) take rock mass sample in tunnel, measure the elastic modulus E in (xoy face), pool in rock mass sample transverse isotropy face
Pine ratio μ, and it is perpendicular to the elastic modulus E ' of direction, transverse isotropy face (oz axle), Poisson's ratio μ ';
(4) the deformational displacement u of rock mass in measurement tunnel;
(5) when tunnel is circular tunnel, according to displacement analytic formula
Prove uniquely inverting to obtain rock mass by rock displacement in tunnel by backanalysis on displacements uniqueness theory
Crustal stress, and the expression formula obtaining crustal stress p and q is respectively as follows:
Wherein, the radius of circular tunnel be a, r and θ be the radius under polar coordinate system and level angle, θ be by x-axis forward calculate
Rising, along the angle rotated counterclockwise, point (r, θ) represents the coordinate of a point, u in polar coordinate system1And u2Represent two points respectively
(r1, θ1) and (r2, θ2) rock displacement value.
In order to achieve the above object, technical scheme is it may also is that realize: a kind of each for the horizontal sight of inverting
To the method for same sex rock mass crustal stress, carried out the crustal stress of inverting transverse isotropic rockmass by the rock displacement in tunnel, bag
Include following steps:
(1) setting up transverse isotropic rockmass model in x-y-z coordinate system, the transverse section in tunnel is parallel to xoy plane,
Tunnel is excavated along oz axle, and wherein xoy plane is transverse isotropy face, and oz axle is axis of symmetry;
(2) direction of transverse isotropic rockmass crustal stress is determined, at vertical direction initial field stress the most along the y-axis direction
For p, horizontal direction initial field stress the most along the x-axis direction is q;
(3) take rock mass sample in tunnel, measure the elastic modulus E in (xoy face), pool in rock mass sample transverse isotropy face
Pine ratio μ, and it is perpendicular to the elastic modulus E ' of direction, transverse isotropy face (oz axle), Poisson's ratio μ ';
(4) the deformational displacement u of rock mass in measurement tunnel;
(5) when tunnel is complicated shape tunnel, according to displacement analytic formula
Prove uniquely inverting to obtain rock mass by rock displacement in tunnel by backanalysis on displacements uniqueness theory
Crustal stress, and the expression formula obtaining crustal stress p and q is respectively as follows:
Wherein,
F1Z () is to F4Z () (z=z+iy) is complex function, their concrete form depends on roadway shape, Ro[Fj
(z)] and Im[Fj(z)] (j=1,2,3,4) represent real part and the imaginary part of corresponding complex function respectively, θ is the level under polar coordinate system
Angle, z=x+iy, (x, y) coordinate of a point in expression xoy plane, point (z, θ) represents the seat of a point in polar coordinate system to point
Mark, u1And u2Represent two point (z respectively1, θ1) and (z2, θ2) rock displacement value.
Further, the method for inverting transverse isotropic rockmass crustal stress as claimed in claim 1 or 2, it is special
Levy and be: as E '=E, during μ '=μ, then expression formula (1) to (4) can be used for calculating the crustal stress of isotropism rock mass.
Further, roadway surrounding rock is continuous, the transverse isotropic rockmass of homogenizing, linear elasticity.
Further, tunnel cross dimension is much smaller than tunnel axial length, for the plane strain problems in xoy face.
Further, the buried depth in tunnel is more than 10 times of size of tunnel cross section.
Further, the deadweight of rock mass in coverage is ignored.
Further, in step (4), when measuring the deformational displacement u of rock mass in tunnel, the selection principle of measuring point is: a, position
Move the point the most applicable layout measuring point that absolute value is the biggest;B, it is suitable at bigger principal direction of stress and the direction neighbouring with bigger principal stress
Close the direction arranging survey line;C, it is optimal point layout region at bigger principal direction of stress near the region of wall.
Compared with prior art, it is an advantage of the current invention that: according to displacement analytic formula, be derived by the horizontal sight of a set of calculating
The concrete formula of isotropism rock mass crustal stress, the parameter included in formula all can be obtained by simple rock mass test and measurement
Accurate result, substitute into formula and carry out calculating and i.e. can get crustal stress result;Avoid caused by field measurement crustal stress
Equipment arrange complicated, error compared with big and that the scope of application is limited phenomenon, to be more easy to convenient accurately measure the rock in the tunnel arrived
Based on displacement body and rock mass parameter, in the way of inverting, try to achieve crustal stress by the method for Theoretical Calculation;Design parameter is divided into
Two classes: one is rock mass parameter, i.e. elastic modelling quantity and Poisson's ratio, can draw data by traditional rock mechanics;Two are
Rock displacement in tunnel, can obtain displacement data by rock mass surface in tunnel or internal layout measuring point;The present invention is only
Just need to can be obtained by calculating be relatively as the criterion via rock displacement measurement data in simple rock mass parameter experiment with measuring and tunnel
The crustal stress data of true transverse isotropic rockmass, computational methods are simple and efficient, are mainly used in calculating transverse isotropy rock
Mass ground stress.
Accompanying drawing explanation
In order to be illustrated more clearly that the specific embodiment of the invention or technical scheme of the prior art, below will be to specifically
In embodiment or description of the prior art, the required accompanying drawing used is briefly described, it should be apparent that, in describing below
Accompanying drawing is some embodiments of the present invention, for those of ordinary skill in the art, before not paying creative work
Put, it is also possible to obtain other accompanying drawing according to these accompanying drawings.
Fig. 1 is the embodiment of the present invention 1 transverse isotropy illustraton of model;
Fig. 2 is the embodiment of the present invention 1 circular tunnel illustraton of model;
Fig. 3 is the embodiment of the present invention 2 complicated shape Roadway model figure;
Detailed description of the invention
Below with reference to accompanying drawing, the technical scheme of various embodiments of the present invention is carried out clear, complete description, it is clear that retouched
The embodiment stated is only a part of embodiment of the present invention rather than whole embodiments.Based on the embodiment in the present invention,
All other embodiments that those of ordinary skill in the art are obtained on the premise of not making creative work, broadly fall into this
The scope that invention is protected.
Below by specific embodiment and combine accompanying drawing the present invention is described in further detail.
Embodiment 1
The present invention relates to a kind of method for inverting transverse isotropic rockmass crustal stress, by the rock mass position in tunnel
The crustal stress of in-migration inverting transverse isotropic rockmass, comprises the following steps:
(1) setting up transverse isotropic rockmass model in x-y-z coordinate system, the transverse section in tunnel is parallel to xoy plane,
Tunnel is excavated along oz axle, and wherein xoy plane is transverse isotropy face, and oz axle is axis of symmetry;
(2) direction of transverse isotropic rockmass crustal stress is determined, at vertical direction initial field stress the most along the y-axis direction
For p, horizontal direction initial field stress the most along the x-axis direction is q;
(3) take rock mass sample in tunnel, measure the elastic modulus E in (xoy face) in rock mass sample transverse isotropy face,
Poisson's ratio μ, and it is perpendicular to the elastic modulus E ' of direction, transverse isotropy face (oz axle), Poisson's ratio μ ';
(4) the deformational displacement u of rock mass in measurement tunnel;
(5) when tunnel is circular tunnel, according to displacement analytic formula
Prove uniquely inverting to obtain rock mass by rock displacement in tunnel by backanalysis on displacements uniqueness theory
Crustal stress, and obtain the expression formula of crustal stress p and q.
Wherein, the radius of circular tunnel be a, r and θ be the radius under polar coordinate system and level angle, θ be by x-axis forward calculate
Rising, along the angle rotated counterclockwise, point (r, θ) represents the coordinate of a point, u in polar coordinate system1And u2Represent two points respectively
(r1, θ1) and (r2, θ2) rock displacement value.
Proved by backanalysis on displacements uniqueness theory: if it is known that 4 rock mass parameter number E, μ, E ' and μ ', then can lead to
Excess displacement value is uniquely finally inversed by crustal stress p and q.Therefore, for circular tunnel, if it is known that 4 rock mass parameter E, μ,
E ' and μ ' and the shift value u of two measuring points1And u2, bring in displacement analytic formula respectively, can express in the hope of corresponding crustal stress
Formula (1) and (2):
For circular tunnel, choose two point (r1, θ1) and (r2, θ2), measure the shift value u obtaining them respectively1And u2,
It is brought in circular tunnel displacement analytic formula and can obtain below equation group:
In above equation group, regard p and q as unknown number, equation group is deformed, solves, the table of p and q can be obtained
Reach formula for (1) and (2):
Preferably, in order to guaranteed discharge records the most accurate and applicable rock displacement data, in tunnel, arrange that displacement is surveyed
The optimizing the locations of the measuring points principle of point is:
(1) criterion of displacement measuring points preferred arrangement can be summarized simply as follows: the most applicable layout of point that displacement absolute value is the biggest
Measuring point;
(2) at bigger principal direction of stress and the direction neighbouring with bigger principal stress it is the direction being suitable for arranging survey line;
(3) it is optimal point layout region at bigger principal direction of stress near the region of hole wall.
Preferably, as E '=E, during μ '=μ, then expression formula (1) and (2) can be used for calculate isotropism rock mass ground should
Power.
Preferably, roadway surrounding rock is continuously, the transverse isotropic rockmass of homogenizing, linear elasticity, and displacement and strain are small
's.
Preferably, tunnel cross dimension is much smaller than tunnel axial length, for the plane strain problems in xoy face.
Preferably, the degree of depth in tunnel is more than 10 times of the size of tunnel cross section, for Deep Roadway.
Preferably, the deadweight of roadway surrounding rock is less for whole initial field stress, ignores oneself in coverage
Weight.
Embodiment 2
As it is shown on figure 3, the difference that this enforcement is fallen with embodiment 1 is when tunnel is complicated shape tunnel, according to displacement
Analytic formula
Prove uniquely inverting to obtain rock mass by rock displacement in tunnel by backanalysis on displacements uniqueness theory
Crustal stress, and obtain the expression formula of crustal stress p and q.
F1Z () is to F4Z () (z=x+iy) is complex function, their concrete form depends on roadway shape, ro[Fj
(z)] and Im[Fj(z)] (j=1,2,3,4) represent real part and the imaginary part of corresponding complex function respectively, θ is the level under polar coordinate system
Angle, z=x+iy, (x, y) coordinate of a point in expression xoy plane, point (z, θ) represents the seat of a point in polar coordinate system to point
Mark, u1And u2Represent two point (z respectively1, θ1) and (z2, θ2) rock displacement value.
During for complicated shape tunnel, choose two point (z1, θ1) and (z2, θ2), measure the shift value obtaining them respectively
u1And u2, be brought into complicated shape roadway displacement analytic formula can obtain following
Equation group:
In above equation group, regard p and q as unknown number, equation group is deformed, solves, the table of p and q can be obtained
Reach formula for (3) and (4):
In formula (3) and (4):
Transverse section, complicated shape tunnel can be arbitrary complicated shape.
Embodiment 3
Circular tunnel in a transverse isotropic rockmass is provided anti-below by Theoretical Calculation and the mode of numerical simulation
Drill the example of crustal stress.
Certain tunnel radius a=2m, rock mass parameter is as follows: E=1Gpa, E '=0.8Gpa, μ=0.25, μ '=0.3,.Choose
Two points (2,0) and (2,45), even r1=2m, θ1=0 °;r2=2m, θ2=45 °, record the shift value of the two point respectively
It is u1=5.89cm and u2=3.68cm, is brought into them and rock mass parameter in formula (1) and (2), unify measurement unit with
After, being calculated crustal stress numerical value is p=9.92Mpa, q=19.52Mpa.
Then using computer software FLAC3D to verify, detailed process is as follows: initially with numerical computations software
FLAC3D sets up circular tunnel model in a transverse isotropic rockmass, and design parameter is as follows: tunnel radius a=2m, rock mass
Parameter is as follows: E=1Gpa, E '=0.8Gpa, μ=0.25, μ '=0.3.Crustal stress is carried out according to the most calculated data
Set: vertically stress p=9.92Mpa, flatly stress q=19.52Mpa, by the position of FLAC3D this model calculated
Move cloud atlas, displacement cloud atlas two points (2,0) and shift value u of (2,45) in can reading in model1=5.73cm and u2=
3.61cm, by the u of they pre-tests therewith1=5.89cm and u2=3.68cm contrasts, the effect of checking inverting.Can see
Going out the shift value calculated with measured value closely, absolute error is less than 0.2cm, and relative error is less than 3%, and this also demonstrates that
The correctness of this inversion method.
Embodiment 4
For the tunnel of complicated shape, first determine complex function F according to tunnel concrete shape1(z)F4(z), then by testing
Determine rock mass parameter E, μ, E ' and μ ', and arrange in tunnel according to optimizing the locations of the measuring points principle and measure two measuring point c1(z1,
θ1) and c2(z2, θ2) shift value u1And u2, (in order to obtain higher precision, the measuring point fetch bit of multiple same coordinate can be arranged
Move meansigma methods), finally bring in formula (3) and (4), try to achieve the numerical value of crustal stress p and q.
The above, be only the preferably enforcement side of the present invention, the present invention not make any pro forma restriction, appoints
What those skilled in the art, in the range of without departing from technical solution of the present invention, when in the technology of available the disclosure above
Hold and make a little change or be modified to the Equivalent embodiments of equivalent variations, as long as being the content without departing from technical solution of the present invention,
Any simple modification, equivalent variations and the modification made above example according to the technical spirit of the present invention, all still falls within this
In the range of inventive technique scheme.
Claims (8)
1., for a method for inverting transverse isotropic rockmass crustal stress, carry out the horizontal sight of inverting by the rock displacement in tunnel
The crustal stress of isotropism rock mass, it is characterised in that comprise the following steps:
(1) setting up transverse isotropic rockmass model in x-y-z coordinate system, the transverse section in tunnel is parallel to xoy plane, tunnel
Excavating along oz axle, wherein xoy plane is transverse isotropy face, and oz axle is axis of symmetry;
(2) determine the direction of transverse isotropic rockmass crustal stress, be p at vertical direction initial field stress the most along the y-axis direction,
Horizontal direction initial field stress the most along the x-axis direction is q;
(3) take rock mass sample in tunnel, measure the elastic modulus E in (xoy face), Poisson's ratio in rock mass sample transverse isotropy face
μ, and it is perpendicular to the elastic modulus E ' of direction, transverse isotropy face (oz axle), Poisson's ratio μ ';
(4) the deformational displacement u of rock mass in measurement tunnel;
(5) when tunnel is circular tunnel, according to displacement analytic formula
Prove uniquely inverting to obtain the ground of rock mass by rock displacement in tunnel by backanalysis on displacements uniqueness theory
Stress, and the expression formula obtaining crustal stress p and q is respectively as follows:
Wherein, the radius of circular tunnel be a, r and θ be the radius under polar coordinate system and level angle, θ is to be counted by the forward of x-axis, edge
The angle rotated counterclockwise, point (r, θ) represents the coordinate of a point, u in polar coordinate system1And u2Represent two point (r respectively1, θ1)
(r2, θ2) rock displacement value.
2., for a method for inverting transverse isotropic rockmass crustal stress, carry out inverting by the rock displacement in tunnel horizontal
See the crustal stress of isotropism rock mass, it is characterised in that comprise the following steps:
(1) setting up transverse isotropic rockmass model in x-y-z coordinate system, the transverse section in tunnel is parallel to xoy plane, tunnel
Excavating along oz axle, wherein xoy plane is transverse isotropy face, and oz axle is axis of symmetry;
(2) determine the direction of transverse isotropic rockmass crustal stress, be p at vertical direction initial field stress the most along the y-axis direction,
Horizontal direction initial field stress the most along the x-axis direction is q;
(3) take rock mass sample in tunnel, measure the elastic modulus E in (xoy face), Poisson's ratio in rock mass sample transverse isotropy face
μ, and it is perpendicular to the elastic modulus E ' of direction, transverse isotropy face (oz axle), Poisson's ratio μ ';
(4) the deformational displacement u of rock mass in measurement tunnel;
(5) when tunnel is complicated shape tunnel, according to displacement analytic formula
Prove uniquely inverting to obtain the ground of rock mass by rock displacement in tunnel by backanalysis on displacements uniqueness theory
Stress, and the expression formula obtaining crustal stress p and q is respectively as follows:
Wherein,
F1Z () is to F4Z () (z=x+iy) is complex function, their concrete form depends on roadway shape, Re[Fj(z)] and Im
[Fj(z)] (j=1,2,3,4) represent real part and the imaginary part of corresponding complex function respectively, θ is the level angle under polar coordinate system, z=x+
Iy, (x, y) coordinate of a point in expression xoy plane, (z, θ) represents the coordinate of a point, u in polar coordinate system to point1And u2Respectively
Represent two point (z1, θ1) and (z2, θ2) rock displacement value.
3. the method for inverting transverse isotropic rockmass crustal stress as claimed in claim 1 or 2, it is characterised in that: when
When E '=E, μ '=μ, then expression formula (1) to (4) can be used for calculating the crustal stress of isotropism rock mass.
4. the method for inverting transverse isotropic rockmass crustal stress as claimed in claim 1 or 2, it is characterised in that: lane
Road country rock is continuously, the transverse isotropic rockmass of homogenizing, linear elasticity.
5. the method for inverting transverse isotropic rockmass crustal stress as claimed in claim 1 or 2, it is characterised in that: lane
Road cross dimension is much smaller than tunnel axial length, for the plane strain problems in xoy face.
6. the method for inverting transverse isotropic rockmass crustal stress as claimed in claim 1 or 2, it is characterised in that: lane
The buried depth in road is more than 10 times of the size of tunnel cross section.
7. the method for inverting transverse isotropic rockmass crustal stress as claimed in claim 1 or 2, it is characterised in that: neglect
The slightly deadweight of rock mass in coverage.
8. the method for inverting transverse isotropic rockmass crustal stress as claimed in claim 1 or 2, it is characterised in that:
In step (4), when measuring the deformational displacement u of rock mass in tunnel, the selection principle of measuring point is: the biggest point of a, displacement absolute value is more
It is suitable for arranging measuring point;B, bigger principal direction of stress and the direction neighbouring with bigger principal stress be suitable for arrange survey line direction;
C, it is optimal point layout region at bigger principal direction of stress near the region of wall.
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CN106932275A (en) * | 2017-03-10 | 2017-07-07 | 中国石油天然气股份有限公司 | A kind of transverse isotropy rock mechanics test and analysis method |
CN107607232A (en) * | 2017-09-07 | 2018-01-19 | 张重远 | A kind of method for continuous measuring and system of earth's crust rock plane stress |
CN110176069A (en) * | 2019-04-25 | 2019-08-27 | 华北水利水电大学 | The building of the characterization and its characterization model of transverse isotropic rockmass three-dimensional creep properties |
CN111794732A (en) * | 2020-05-22 | 2020-10-20 | 中国科学院武汉岩土力学研究所 | Method for estimating ground stress of soft rock in fault fracture zone |
CN114417488A (en) * | 2022-03-29 | 2022-04-29 | 中交第一航务工程局有限公司 | Railway deep-buried soft rock large-deformation tunnel ground stress field inversion method |
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Cited By (8)
Publication number | Priority date | Publication date | Assignee | Title |
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CN106932275A (en) * | 2017-03-10 | 2017-07-07 | 中国石油天然气股份有限公司 | A kind of transverse isotropy rock mechanics test and analysis method |
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CN107607232A (en) * | 2017-09-07 | 2018-01-19 | 张重远 | A kind of method for continuous measuring and system of earth's crust rock plane stress |
CN110176069A (en) * | 2019-04-25 | 2019-08-27 | 华北水利水电大学 | The building of the characterization and its characterization model of transverse isotropic rockmass three-dimensional creep properties |
CN110176069B (en) * | 2019-04-25 | 2023-08-04 | 华北水利水电大学 | Characterization of three-dimensional creep characteristics of transverse isotropic rock mass and construction of characterization model thereof |
CN111794732A (en) * | 2020-05-22 | 2020-10-20 | 中国科学院武汉岩土力学研究所 | Method for estimating ground stress of soft rock in fault fracture zone |
CN111794732B (en) * | 2020-05-22 | 2022-01-28 | 中国科学院武汉岩土力学研究所 | Method for estimating ground stress of soft rock in fault fracture zone |
CN114417488A (en) * | 2022-03-29 | 2022-04-29 | 中交第一航务工程局有限公司 | Railway deep-buried soft rock large-deformation tunnel ground stress field inversion method |
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