CN110243526B - Method for determining three-dimensional initial ground stress of rock mass based on flat jack measurement - Google Patents
Method for determining three-dimensional initial ground stress of rock mass based on flat jack measurement Download PDFInfo
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- CN110243526B CN110243526B CN201910592852.7A CN201910592852A CN110243526B CN 110243526 B CN110243526 B CN 110243526B CN 201910592852 A CN201910592852 A CN 201910592852A CN 110243526 B CN110243526 B CN 110243526B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
- G01L5/16—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes for measuring several components of force
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- G—PHYSICS
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Abstract
The invention discloses a method for determining three-dimensional initial crustal stress of a rock mass based on flat jack measurement, and belongs to the technical field of crustal stress measurement. Firstly, selecting 6 measurable measuring points on the same cross section or the area near the same cross section on the rock wall of the tunnel by adjusting the included angle theta between the measuring points and the horizontal plane of the tunnel and the included angle alpha between the flat groove and the axis of the tunnel; respectively measuring the normal stress component sigma of the flat groove of each measuring point by adopting a flat jack methodθ"; determining the Poisson's ratio v of the rock near the measuring point through a rock mechanical test or a geological report; and calculating the three-dimensional initial stress component of the rock mass in the area near the measuring point by combining the elasticity mechanics. The method expands the flat jack measurement method from one dimension to three dimensions under the condition of ensuring the measurement accuracy, and has the characteristics of simple operation, economy and convenient measurement.
Description
Technical Field
The invention relates to the technical field of ground stress measurement, in particular to a method for determining three-dimensional initial ground stress of a rock mass based on flat jack measurement.
Background
Due to the self weight of the rock mass and the movement of the geological structure, a complex ground stress field exists in the rock mass, and the ground stress is the fundamental acting force which causes the deformation and the destruction of the underground engineering. Obtaining the initial ground stress magnitude and direction of the underground engineering area is important for the arrangement of the underground engineering axis, the excavation mode and the selection of reasonable supporting parameters.
There are many measurement methods available in the world, and the measurement methods are mainly classified into direct measurement methods and indirect measurement methods according to the principle. The direct measurement method is to obtain corresponding stress component values through direct measurement; and the indirect measurement mainly utilizes an elastic mechanics formula to calculate the initial stress of the rock mass according to the deformation of the rock.
At present, the conventional ground stress direct measurement methods at home and abroad mainly comprise a hydraulic fracturing method, an acoustic emission method and a flat jack method. Although the field of stress measurement has made great advances in technology and equipment, they still have limitations. The hydraulic fracturing method is a method which is widely applied at present, and is a two-dimensional stress measurement method in principle. When the hydrofracturing method is adopted for measurement, deeper drilling needs to be drilled, the operation is complex, the measurement cost is high, the main stress direction is assumed to be parallel to the drilling direction, and if the drilling direction deviates from the main stress direction greatly, the obtained result has great problems in precision. In order to determine the three-dimensional stress state of a measuring point by using the acoustic emission method, test pieces must be prepared in 6 different directions in a rock sample of the point, more than 4 samples need to be taken in each direction, the total number of the samples reaches more than 24, the sampling number is large, and the operation is difficult.
The flat jack method is a method for measuring the surface stress of rock wall, also called rock mass surface stress recovery method. The method is one of the suggested methods for determining rock stress by the test method committee of the international rock mechanics society. The method has simple operation; the measurement cost is low; the test equipment is simple, durable and stable. However, in principle, it is only a one-dimensional stress measurement method, and the measurement of one flat slot can only determine the normal stress component perpendicular to the direction of the flat jack at the measurement point. If 6 stress components of the point are determined, 6 flat grooves need to be cut in different directions at the point, so that mutual interference among the flat grooves can cause excessive errors, and the significance of measurement is lost. Due to the above reasons, the flat jack method cannot be widely applied in practice, and cannot fully exert the advantages of simple operation, economy and convenience in measurement. Therefore, a ground stress measuring method which is cheap, simple and applicable is needed in the field of geotechnical engineering.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for determining the three-dimensional initial ground stress of a rock mass based on the measurement of a flat jack, and the flow of the technical scheme is shown in figure 1 and comprises the following steps:
step 1: selecting a measuring point;
selecting 6 different measuring points to be recorded as P by adjusting the included angle theta between the measuring point and the horizontal plane of the tunnel and the included angle alpha between the flat groove and the axis of the tunnel in the same section or the area near the same section on the rock wall of the tunnel1～P6；
Step 2: respectively measuring the normal stress component sigma of the flat groove of each measuring point by adopting a flat jack methodθ”；
And step 3: determining the Poisson's ratio v of the rock near the measuring point through a rock mechanical test or a geological report;
and 4, step 4: calculating the three-dimensional initial ground stress component of the rock mass in the area near the measuring point, wherein the process is as follows;
step 4-1: rotating the rectangular space coordinate system around the z-axis in the tunnel axis direction to make the included angle between the new and old coordinate systems form θ degrees, as shown in fig. 2, according to the stress conversion relationship under the new and old coordinate systems of the elasticity mechanics:
wherein, σ (r, theta, z) is a stress component matrix under a cylindrical coordinate system; qijA stress transformation matrix of the new and old coordinate systems at the moment; sigma (x, y, z) is a stress component matrix under a space rectangular coordinate system;
calculating by a formula to obtain tauθz＝-sinθτzx+cosθτzy；
Step 5-2: rotating the cylindrical coordinate system around the r axis in the radius direction of the tunnel to make the included angle between the new and old coordinate systems form an angle of alpha degrees, as shown in fig. 3, according to the stress conversion relationship under the new and old coordinate systems of the elasticity mechanics:
wherein, sigma (r ', theta ', z ') is a disturbance stress component matrix after the tunnel is excavated under the new cylindrical coordinate system; qij' is the stress transformation matrix of the new and old coordinate systems at the moment; sigma (r, theta, z) is a disturbance stress component matrix after the tunnel is excavated under the old cylindrical coordinate system;
the formula is used for calculating: sigmaθ”＝cos2ασθ-sin2ατθz+sin2ασz'；
Subjecting tau obtained in step 4-1 toθzSubstituting the formula to obtain: sigmaθ”＝cos2ασθ+sin2α(sinθτzx-cosθτzy)+sin2ασz'；
Step 4-3: assuming that no tunnel deformation is caused by excavation along the z direction of the tunnel axis, the near sigma of the tunnel can be obtainedzThe stress variation amount of (a) is:
Δσz＝νΔ(σx+σy)＝ν[(σx'+σy')-(σx+σy)]
wherein, Delta sigmazThe z-direction stress component variation caused by excavation; sigmax' and σy' is disturbance stress component after tunnel excavation;
according to the first stress invariant sigmay'+σx'＝σr+σθWe can get:
Δσz＝ν[(σr+σθ)-(σx+σy)]
σz'＝σz+Δσz＝σz+ν[(σr+σθ)-(σx+σy)]
wherein σz' is disturbance stress component after tunnel excavation;
will obtain sigmaz' substitution into σ obtained in step 4-2θ"in the formula:
σθ”＝cos2ασθ+sin2α(sinθτzx-cosθτzy)+sin2α(σz+ν[(σr+σθ)-(σx+σy)])
step 4-4: substituting the existing theoretical calculation formula for measuring the initial ground stress component of the x-y plane of the tunnel section by using the flat jack method into the sigma obtained in the step 4-3θ"in the formula;
the existing theoretical calculation formula for measuring the initial ground stress component of the x-y plane of the tunnel section by using a flat jack method is as follows:
wherein σrIs the radial stress; sigmaθIs tangential stress; tau isrθIs a shear stress; a is the tunnel radius; r is the distance between the measuring point and the center of the tunnel; theta is an anticlockwise rotation included angle between the measuring point and the horizontal plane of the tunnel; sigmax、σyAnd τxyIs a stress component;
assuming that a is r, the above formula is substituted into σ obtained in step 4-3θ"in the formula, get:
wherein σθ"is the normal stress value of the flat slot actually measured on site by the flat jack method; theta is an anticlockwise rotation included angle between the measuring point and the horizontal plane of the tunnel; alpha is a clockwise rotation included angle between the flat groove and the axis of the tunnel; v is the poisson's ratio of the rock near the measurement point; sigmax、σy、σz、τxy、τzxAnd τzy6 initial ground stress components;
and 4-5: the included angles theta, alpha of the 6 final measurement points described in claim 3; the poisson's ratio v of the rock near the measurement point of step 3 in claim 1; the flat groove normal stress component σ of each measurement point of step 2 in claim 1θ"substitute into the formula obtained in step 4-4, calculate 6 initialThe ground stress component σx、σy、σz、τxy、τzxAnd τzyFinally, 6 initial ground stress components sigma are obtained through calculationx、σy、σz、τxy、τzxAnd τzy。
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: compared with the existing method for measuring the crustal stress by using the flat jack, the method for determining the three-dimensional initial crustal stress of the rock mass based on the flat jack provides a theoretical formula for solving the six components of the three-dimensional initial crustal stress field; compared with other direct stress measurement methods, the method can measure the three-dimensional initial ground stress component in the rock mass more simply, economically and conveniently; the method also improves the application range of the flat jack method, and is beneficial to popularization and application of the method in underground engineering.
Drawings
FIG. 1 is a flow chart of a method for determining three-dimensional initial ground stress of a rock mass based on flat jack measurement according to the present invention;
FIG. 2 is a schematic diagram of the present invention rotating a spatial rectangular coordinate system around a z-axis in a tunnel axis direction to make an included angle between a new coordinate system and an old coordinate system form a θ degree angle;
FIG. 3 is a schematic diagram of the present invention rotating a cylindrical coordinate system around an r-axis in a tunnel radius direction to make an included angle between a new coordinate system and an old coordinate system form an angle of α degrees;
FIG. 4 is a schematic view of a slot of a flat jack in a tunnel during selection of a measurement point according to embodiment 1 of the present invention;
FIG. 5 is a schematic diagram of an angle between a slot position of a flat jack and a tunnel axis according to embodiment 1 of the present invention;
FIG. 6 is a schematic view showing the arrangement of slots of a flat jack in a tunnel during the selection of a measurement point in the embodiment 2 of the present invention;
FIG. 7 is a schematic diagram of an angle between a slot position of a flat jack and a tunnel axis according to embodiment 2 of the present invention.
Wherein: 1-a tunnel; 2-flat jack mounting groove.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
Example 1:
the circular tunnel is taken as an example for detailed description, and the specific implementation steps are as follows:
step 1: selecting a position where the rock is firm and flat and the rock surface has no obvious geological discontinuity on the same section or an area near the same section on the rock wall of the tunnel, and selecting 6 different measuring points P by adjusting an included angle theta between the measuring point and the horizontal plane of the tunnel and an included angle alpha between the flat groove and the axis of the tunnel1～P6The arrangement of the slot position of the flat jack in the tunnel is shown in figure 4, and the included angle between the slot position of the flat jack and the axis of the tunnel is shown in figure 5;
step 2: respectively measuring the normal stress component sigma of the flat groove of the 6 measuring points by adopting a flat jack methodθ", 6 measurement points P1～P6The included angle theta of anticlockwise rotation between the horizontal plane of the tunnel, the included angle alpha of clockwise rotation between the flat groove and the axis of the tunnel, and the normal stress component sigma of the flat groove obtained by field actual measurementθ"are shown in Table 1;
TABLE 1 arrangement position of the mounting groove of the flat jack in the tunnel and the measured ground stress results
And step 3: determining the Poisson ratio v of the rock near the measuring point to be 0.3 through a rock mechanics test; :
and 4, step 4: by a theoretical formula, a matrix expression for solving the three-dimensional initial ground stress component can be deduced as follows, and the matrix expression can be solved by matrix calculation software such as MATLAB and the like during specific calculation;
finally, the three-dimensional initial of the rock mass in the area near the measuring point is obtained through calculationThe result of the initial stress component is: sigmax＝-8.59MPa；σy＝-4.86MPa；σz＝-14.17MPa；τxy＝-1.78MPa；τzx＝-1.05MPa；τzy＝3.12MPa。
Example 2:
the circular tunnel is taken as an example for detailed description, and the specific implementation steps are as follows:
step 1: selecting a position where the rock is firm and flat and the rock surface has no obvious geological discontinuity on the same section or an area near the same section on the rock wall of the tunnel, and selecting 6 different measuring points P by adjusting an included angle theta between the measuring point and the horizontal plane of the tunnel and an included angle alpha between the flat groove and the axis of the tunnel1～P6The arrangement of the slot position of the flat jack in the tunnel is shown in figure 6, and the included angle between the slot position of the flat jack and the axis of the tunnel is shown in figure 7;
step 2: respectively measuring the normal stress component sigma of the flat groove of the 6 measuring points by adopting a flat jack methodθ", 6 measurement points P1～P6The included angle theta of anticlockwise rotation between the horizontal plane of the tunnel, the included angle alpha of clockwise rotation between the flat groove and the axis of the tunnel, and the normal stress component sigma of the flat groove obtained by field actual measurementθ"are shown in Table 2;
TABLE 2 arrangement position of the mounting groove of the flat jack in the tunnel and the measured ground stress results
| Position of | P1 | P2 | P3 | P4 | P5 | P6 |
| θ/° | 0 | 0 | 20 | 60 | 100 | 100 |
| α/° | 0 | 60 | 30 | 0 | 90 | 0 |
| σθ”/MPa | -15 | -18 | -15 | -13 | -18 | -11 |
And step 3: determining the Poisson ratio v of the rock near the measuring point to be 0.25 through a rock mechanics test; :
and 4, step 4: by a theoretical formula, a matrix expression for solving the three-dimensional initial ground stress component can be deduced as follows, and the matrix expression can be solved by matrix calculation software such as MATLAB and the like during specific calculation;
the final calculation result of the three-dimensional initial ground stress component of the rock mass in the area near the measuring point is as follows: sigmax＝-6.08MPa；σy＝-7.03MPa；σz＝-18.53MPa；τxy＝0.24MPa；τzx＝3.86Pa；τzy＝-0.003MPa。
The rock mass three-dimensional initial ground stress component obtained in the embodiment 1 and the embodiment 2 plays a vital role in the arrangement of underground engineering axes, the excavation mode and the selection of reasonable support parameters.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (2)
1. A method for determining three-dimensional initial ground stress of a rock mass based on flat jack measurement is characterized by comprising the following steps:
step 1: selecting a measuring point;
step 2: respectively measuring the normal stress component sigma of the flat groove of each measuring point by adopting a flat jack methodθ”；
And step 3: determining the Poisson's ratio v of the rock near the measuring point through a rock mechanical test or a geological report;
and 4, step 4: the process of calculating the three-dimensional initial ground stress component of the rock mass in the area near the measuring point is as follows:
step 4-1: rotating the space rectangular coordinate system around the z-axis in the axial direction of the tunnel to form an included angle between the new coordinate system and the old coordinate system into theta degrees, and according to the stress conversion relation under the new coordinate system and the old coordinate system of the elasticity mechanics:
σ(r,θ,z)＝Qij×σ(x,y,z)×Qij T
wherein, σ (r, theta, z) is a stress component matrix under a cylindrical coordinate system; qijA stress transformation matrix of the new and old coordinate systems at the moment; sigma (x, y, z) is a stress component matrix under a space rectangular coordinate system;
calculating by a formula to obtain tauθz＝-sinθτzx+cosθτzy；
Step 4-2: rotating the cylindrical coordinate system around an r axis in the radius direction of the tunnel to enable an included angle between the new coordinate system and the old coordinate system to form alpha degrees, and according to the stress conversion relation under the new coordinate system and the old coordinate system of the elastomechanics:
σ(r”,θ”,z”)＝Qij'×σ(r,θ,z)×Qij'T
wherein, sigma (r ', theta ', z ') is a disturbance stress component matrix after the tunnel is excavated under the new cylindrical coordinate system; qij' is the stress transformation matrix of the new and old coordinate systems at the moment; sigma (r, theta, z) is a disturbance stress component matrix after the tunnel is excavated under the old cylindrical coordinate system;
the formula is used for calculating: sigmaθ”＝cos2ασθ-sin2ατθz+sin2ασz'；
Subjecting tau obtained in step 4-1 toθzSubstituting the formula to obtain: sigmaθ”＝cos2ασθ+sin2α(sinθτzx-cosθτzy)+sin2ασz'；
Step 4-3: provided that there is no z-direction along the tunnel axisThe tunnel deformation caused by excavation can be obtainedzThe stress variation amount of (a) is:
Δσz＝νΔ(σx+σy)＝ν[(σx'+σy')-(σx+σy)]
wherein, Delta sigmazThe z-direction stress component variation caused by excavation; sigmax' and σy' is disturbance stress component after tunnel excavation;
according to the first stress invariant sigmay'+σx'＝σr+σθWe can get:
Δσz＝ν[(σr+σθ)-(σx+σy)]
σz'＝σz+Δσz＝σz+ν[(σr+σθ)-(σx+σy)]
wherein σz' is disturbance stress component after tunnel excavation;
will obtain sigmaz' substitution into σ obtained in step 4-2θ"in the formula:
σθ”＝cos2ασθ+sin2α(sinθτzx-cosθτzy)+sin2α(σz+ν[(σr+σθ)-(σx+σy)])
step 4-4: substituting the existing theoretical calculation formula for measuring the initial ground stress component of the x-y plane of the tunnel section by using the flat jack method into the sigma obtained in the step 4-3θ"in the formula;
the existing theoretical calculation formula for measuring the initial ground stress component of the x-y plane of the tunnel section by using a flat jack method is as follows:
wherein σrIs the radial stress; sigmaθIs tangential stress; tau isrθIs a shear stress; a is the tunnel radius; r is the distance between the measuring point and the center of the tunnel; theta is an anticlockwise rotation included angle between the measuring point and the horizontal plane of the tunnel; sigmax、σyAnd τxyIs a stress component;
assuming that a is r, the above formula is substituted into σ obtained in step 4-3θ"in the formula, get:
σθ”＝Aσx+Bσy+Cσz+Dτxy+Eτzx+Fτzy
wherein σθ"is the normal stress value of the flat slot actually measured on site by the flat jack method; theta is an anticlockwise rotation included angle between the measuring point and the horizontal plane of the tunnel; alpha is a clockwise rotation included angle between the flat groove and the axis of the tunnel; v is the poisson's ratio of the rock near the measurement point; sigmax、σy、σz、τxy、τzxAnd τzy6 initial ground stress components;
and 4-5: the included angles theta, alpha of the 6 measuring points stated in the claim 2; the poisson's ratio v of the rock near the measurement point of step 3 in claim 1; the flat groove normal stress component σ of each measurement point of step 2 in claim 1θSubstituting the obtained result into the formula obtained in the step 4-4, and finally calculating to obtain 6 initial ground stress components sigmax、σy、σz、τxy、τzxAnd τzy。
2. A chain link according to claim 1The method for determining the three-dimensional initial ground stress of the rock mass through the measurement of the jack is characterized in that in the step 1, the measurement points are selected to be in the same section or the area near the same section on the rock wall of the tunnel, 6 different measurement points are selected by adjusting the included angle theta between the measurement points and the horizontal plane of the tunnel and the included angle alpha between the flat groove and the axis of the tunnel, and the selected measurement points are marked as P1～P6。
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| CN203393687U (en) * | 2013-06-26 | 2014-01-15 | 中国水利水电科学研究院 | Prestressed concrete lined tunnel structure and circular ring-shaped flat jack thereof |
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