CN113239510A - Method for calculating optimal excavation slope rate of mine side slope - Google Patents
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Abstract
The invention discloses a method for calculating the optimal excavation slope rate of a mine side slope, which takes the mine side slope as a research object, establishes a multi-objective optimization nonlinear mathematical programming model of the stability safety and the excavation economy of the mine side slope, and takes the maximum value of a safety coefficient and the maximum value of excavation benefit as objective functions at the same time; the excavation slope rate, the shearing force and the normal force of the structural surface are used as decision variables, the balance equation constraint condition of the side slope slide body and the yield condition of the structural surface are used as constraint conditions, and meanwhile, the gravity function constructed in the constraint conditions can change along with the change of the excavation slope rate, so that the constraint conditions of the limit balance of the side slope slide body can well relate to the safety and the economy of the mine side slope, and the actual mine side slope excavation requirements can be better met; the method can directly obtain the optimal excavation slope rate of the mine side slope, so that the stability and safety factor are the maximum while the excavation benefit is the highest, and further the unity of the excavation economy and the stability and safety is achieved.
Description
Technical Field
The invention relates to a method for calculating the optimal excavation slope rate of a mine side slope, and belongs to the technical field of analysis of stability of the mine side slope.
Background
In recent years, the problem of slope stability caused by excavation of mine slopes is receiving wide attention of a great number of geotechnical engineers. Two problems are often involved in performing mine slope excavation: firstly, the stability and safety of the mine side slope after excavation and secondly, the excavation economy caused by the excavation volume. The stability and safety of the excavated mine side slope mainly depend on the property and spatial combination of the structural surface, and the bedding surface, the weak interlayer, the fault and the joint surface in the mine side slope are all main reasons for causing instability and damage of the side slope in the excavation process; larger excavation volumes result in higher excavation economics and vice versa. In actual engineering, excavation slope rate design is usually performed by adopting an excavation slope rate method, which is mainly used for determining the excavation slope rate of an excavation slope according to the suggestions of geological specialties and similar engineering experiences, such as: the recommended excavation slope rate of the mine slope is given by the technical Specification of building slope engineering (GB 50330-2013). The proposed excavation slope rate is an empirical value, and the safety factor and the excavation benefit of the mine side slope cannot be guaranteed to be optimal at the same time, namely the purposes of safety and economy are achieved.
The current mine side slope excavation design has the following problems:
(1) in actual engineering, the excavation slope rate of a side slope is determined according to the suggestions of geological specialties and similar engineering experiences, and relevant principles and theories are still to be studied;
(2) the mine side slope suggested excavation slope rate given by the specification is adopted, and the stability, the safety and the excavation economy are not guaranteed to be optimal;
(3) the mine side slope excavation design is a multi-target problem of seeking the mine side slope excavation benefit as large as possible and seeking the mine side slope safety factor as high as possible at the same time, and no good method is considered comprehensively at present;
based on the current situation, a method for calculating the optimal excavation slope rate of the mine side slope is needed to satisfy stable safety and excavation economy.
Disclosure of Invention
The invention provides a method for calculating the optimal excavation slope rate of a mine side slope, which can obtain the optimal stable safety coefficient, optimal excavation benefit and optimal excavation slope rate which simultaneously meet the requirements of stable safety and optimal excavation economy.
The technical scheme of the invention is as follows: a method for calculating the optimal excavation slope rate of a mine side slope comprises the following steps:
step 1, drawing up geometric parameters of a drawn-up mine side slope;
step 2, drawing up physical and mechanical parameters of the mine side slope;
step 3, analyzing the stress of the mine slope slide body;
step 4, establishing a stable safety objective function and an excavation economy objective function of the mine side slope;
step 5, establishing a constraint condition of the limit balance of the mine slope landslide;
step 6, establishing a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy;
and 7, solving a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy, and obtaining stability safety factor, excavation benefit and optimal excavation slope rate when the stability safety and the excavation economy are optimal.
The drawing up of the geometric parameters of the drawn-up mine slope comprises the following steps: height of mine side slope H and distance H from bottom end of structural surface to x axis1(ii) a The natural slope rate beta of the mine side slope; and (4) the excavation slope rate theta of the mine side slope.
The physical and mechanical parameters of the drawn up mine slope comprise: volume weight gamma of mine slope slide, inclination angle alpha of structural surface, cohesion c of structural surface and friction angle of structural surface
The stress analysis of the mine side slope slide body is specifically as follows: gravity G acting on the centroid of the mine slope slide body, and shear force F acting on the mine slope slide body structural surfaceSAnd normal force FNIn which F isSTurning in the counterclockwise direction negative, FNThe pressure is positive.
The establishment of the stable safety objective function and the excavation economy objective function of the mine side slope specifically comprises the following steps:
firstly, establishing a stable safety objective function of a mine side slope
Taking the stability safety coefficient of the mine slope as a stability safety objective function, seeking the maximum value of the stability safety coefficient of the mine slope, and establishing the stability safety objective function as follows:
Maximize:K
in the formula: maximize means "max"; k is the mine slope stability safety coefficient;
establishing an excavation economy objective function of the mine side slope
Taking the excavation benefit, which is the product of the price of the unit volume of the excavation slope sliding body and the excavation volume, as an excavation economic objective function, seeking the maximum value of the excavation benefit, and establishing the objective function of the excavation economic as follows:
Maximize:J
in the formula: maximize means "max"; j is mine side slope excavation benefit, and when a side slope sliding body with unit width is taken for calculation:
in the formula: k is a radical of1The unit volume selling price of the mine side slope sliding body is H, the height of the mine side slope, theta, the excavation slope rate of the mine side slope and beta, the natural slope rate of the mine side slope.
The constraint conditions for establishing the limit balance of the mine slope landslide body are as follows:
the constraint conditions of the limit balance of the mine slope landslide body comprise: the balance equation constraint condition of the mine slope landslide body and the yield condition of the structural plane;
balance equation constraint conditions of mine slope landslide:
the balance equation of the mine slope sliding body in the horizontal direction is established as follows:
FS cosα-FN sinα＝0
the balance equation in the vertical direction of the mine slope sliding body is established as follows:
G+FS sinα+FN cosα＝0
wherein:
g is the gravity acting on the mine slope slide centroid, FSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; h is the height of the mine side slope1The distance from the bottom end of the structural plane to the x axis is used, and theta is the excavation slope rate of the mine side slope; gamma is the volume weight of the mine slope sliding body;
secondly, the yield condition of the mine side slope slide body structure surface is as follows:
in the formula: k is the mine slope stability safety coefficient; c.
respectively the cohesion and friction angle of the structural surface; l is the length of the structural plane.
The establishment of the multi-objective optimization nonlinear mathematical programming model for the mine slope stability safety and the excavation economy is as follows:
the method comprises the following steps of establishing a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy, which takes mine slope stability safety factors and excavation benefits as dual objective function and simultaneously meets constraint conditions of mine slope slide mass balance equations and yield conditions of structural surfaces, as follows:
in the formula: k is the mine slope stability safety coefficient; j, mine side slope excavation benefit; fSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; g is the gravity acting on the centroid of the mine slope slide body; c.
respectively the cohesion and friction angle of the structural surface; l is the length of the structural plane; k is a radical of1The unit volume selling price of the mine slope slide body is obtained; h is the height of the mine side slope; theta is the excavation slope rate of the mine side slope; beta is the natural slope rate of the mine side slope.
Solving a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy to obtain stability safety factor, excavation benefit and optimal excavation slope rate when the stability safety and the excavation economy are optimal, specifically:
solving a nonlinear mathematical programming model with optimal stability and safety by adopting a penalty function method, wherein the nonlinear mathematical programming model with optimal stability and safety is as follows:
in the formula:
the stability and safety factor of the side slope when the excavation stability and safety are optimal is obtained; fSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; g is the gravity acting on the centroid of the mine slope slide body; c.
respectively the cohesion and friction angle of the structural surface; l is the length of the structural plane; k is a radical of1The unit volume selling price of the mine slope slide body is obtained; h is the height of the mine side slope; j. the design is a square1The side slope excavation benefit is achieved when the excavation stability and safety are optimal; thetaKExcavating slope rate for the side slope with optimal excavation stability and safety; beta is the natural slope rate of the mine side slope;
solving the nonlinear mathematical programming model with the optimal excavation economy by adopting a penalty function method, wherein the nonlinear mathematical programming model with the optimal excavation economy is as follows:
in the formula:
the side slope excavation benefit is achieved when the excavation economy is optimal; k1The safety coefficient is stabilized for the side slope when the excavation economy is optimal; thetaJExcavating slope rate for the side slope with optimal excavating economy;
and thirdly, constructing an objective function with optimal stability, safety and excavation economy as follows:
in the formula: z is an objective function when the stability safety and the excavation economy are optimal;
the method is used for realizing the slope excavation benefit when the stability safety and the excavation economy are optimal;
the slope stability safety factor is the slope stability safety factor when the stability safety and the excavation economy are both optimal;
solving the nonlinear mathematical programming model of the mine slope excavation economy and the stable safety by adopting a penalty function method, wherein the nonlinear mathematical programming model of the mine slope excavation economy and the stable safety is as follows:
in the formula: thetaoptThe optimal excavation slope rate is achieved when the stability, the safety and the excavation economy are optimal.
The invention has the beneficial effects that:
the method takes the mine side slope as a research object, establishes a multi-objective optimization nonlinear mathematical programming model of the stability safety and the excavation economy of the mine side slope, and simultaneously takes the maximum value of the safety coefficient and the maximum value of the excavation benefit as objective functions; the excavation slope rate, the shearing force and the normal force of the structural surface are used as decision variables, the balance equation constraint condition of the side slope slide body and the yield condition of the structural surface are used as constraint conditions, and meanwhile, the gravity function constructed in the constraint conditions can change along with the change of the excavation slope rate, so that the constraint conditions of the limit balance of the side slope slide body can well relate to the safety and the economy of the mine side slope, and the actual mine side slope excavation requirements can be better met; the model is different from the traditional method that the model is established by combining theory and practice according to the suggestions of geological specialties and similar engineering experiences, and the optimal excavation slope rate of the mine side slope can be directly obtained by the method, so that the stable safety factor is the maximum while the excavation benefit is the highest, and the unification of the excavation economy and the stable safety is further achieved.
The method is suitable for calculating the optimal excavation slope rate of the mine with comprehensive consideration of stable safety and excavation economy, and has the characteristics of clear concept, high calculation precision and simple and convenient engineering application.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of an excavation area of a mine slope according to the present invention;
FIG. 3 is a schematic view of a mine slope of the present invention;
FIG. 4 is a schematic view of a mine slope according to an embodiment of the present invention;
fig. 5 is a schematic view of the force applied to the side slope sliding body according to the embodiment of the invention.
Detailed Description
Example 1: as shown in fig. 1 to 5, a method for calculating an optimal excavation slope rate of a mine side slope includes:
step 1, drawing up geometric parameters of a drawn-up mine side slope;
step 2, drawing up physical and mechanical parameters of the mine side slope;
step 3, analyzing the stress of the mine slope slide body;
step 4, establishing a stable safety objective function and an excavation economy objective function of the mine side slope;
step 5, establishing a constraint condition of the limit balance of the mine slope landslide;
step 6, establishing a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy;
step 7, solving a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy, and obtaining a stability safety coefficient when the stability safety and the excavation economy are optimal
Benefits of excavation
And optimum excavation slope rate θopt。
Further, the invention provides the following implementation processes:
(1) drawing up the geometric parameters of mine side slope
As shown in fig. 4, the mine slope of the embodiment is established by a coordinate system: and (3) taking an angular point A on the outer side of the slope top of the mine slope as a vertical line, intersecting the slope bottom with a point O, taking a straight line where BO is located as an x-axis, taking the x-axis as a right positive, taking a straight line where OA is located as a y-axis, and taking the y-axis as a positive, and establishing a coordinate system as shown in the figure. Drawing up the geometric parameters of the side slope according to the actual situation of the mine side slope, comprising the following steps: the height H of the mine side slope is 50 m; the distance from the bottom end of the structural surface to the x axis is 8.49 m; AB is a natural face of the mine side slope, and the natural slope rate beta is 60 degrees; OC is the face-to-air surface after the excavation of the mine side slope, and the excavation slope rate is theta.
(2) Drawing up physical and mechanical parameters of mine side slope
The physical and mechanical parameters of the side slope are drawn up according to the actual situation of the mine side slope, and the drawing comprises the following steps: the volume weight gamma of the side slope slide is 19.00kN/m3The inclination angle of the structural plane is alpha, the cohesion c of the structural plane is 40kPa, and the friction angle of the structural plane
Is 40 deg..
(3) Stress analysis of mine slope slide
As shown in fig. 5, which is a schematic diagram of a mine slope slide body, the stress analysis is performed on the slope slide body, the centroid of the slope slide body acts on the gravity G in the y direction, and the shearing force F acts on the structural surface of the slope slide bodySAnd normal force FNIn which F isSTurning in the counterclockwise direction negative, FNThe pressure is positive.
(4) Establishing stable safety objective function and excavation economy objective function of mine side slope
Firstly, establishing a stable safety objective function of a mine side slope
The obtained strength reserve coefficient is the stability safety coefficient, and the stability safety coefficient is higher. Taking the mine slope stability safety coefficient as a stability safety objective function, seeking the maximum value of the mine slope stability safety coefficient, and establishing the stability safety objective function as follows:
Maximize:K (1)
in the formula: maximize means "max"; k is the mine slope stability safety coefficient.
Establishing an excavation economy objective function of the mine side slope
The excavation economy of mine side slope embodies through the size of excavation volume, and the excavation volume is big more, and the excavation economy is higher, will excavate the product of the price of side slope landslide unit volume and excavation volume, excavate the benefit promptly as excavation economy objective function to seek the maximum value of excavation benefit, then the objective function of excavation economy can write:
Maximize:J (2)
in the formula: maximize means "max"; j, the slope excavation benefit;
fig. 2 is a mine slope excavation area diagram, where the excavation benefit is the product of the unit volume selling price of the slope sliding body and the excavation volume, and when the slope sliding body with unit width is taken for calculation:
in the formula: k is a radical of1The unit volume selling price of the side slope sliding body is 1000, and theta is the excavation slope rate of the mine side slope;
(5) constraint condition for establishing limit balance of mine slope landslide
The constraint conditions of the limit balance of the mine slope landslide body comprise: the balance equation constraint condition of the mine slope landslide body and the yield condition of the structural plane;
the mine side slope slide body balance equation constraint conditions are as follows:
the mine slope slide body is kept balanced by gravity on the centroid, shearing force on the structural surface and normal force on the structural surface.
The balance equation of the mine slope sliding body in the horizontal direction is established as follows:
FS cosα-FN sinα＝0 (4)
the balance equation in the vertical direction of the mine slope sliding body is established as follows:
G+FS sinα+FN cosα＝0 (5)
wherein:
g is the gravity of the slide centroid of the side slope along the y direction, FSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, alpha rotates in the counterclockwise direction as positive, and gamma is the volume weight of the mine slope slide.
Secondly, the yield condition of the mine side slope slide body structure surface is as follows:
assuming that the mine slope sliding body is a rigid body block which cannot generate any damage, the damage of the mine slope only occurs on a structural plane, the structural plane meets the Mohr-Coulomb yield condition, and the yield condition on the structural plane is written as follows:
K|FS|-FN tan40°-40×l≤0 (6)
in the formula: fSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; l is the length of the structural plane; c.
respectively the cohesion and friction angle of the structural surface; k is the mine slope stability safety coefficient.
(6) Multi-objective optimization nonlinear mathematical programming model for establishing mine slope stability safety and excavation economy
The method comprises the following steps of establishing a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy, which takes mine slope stability safety factors and excavation benefits as dual objective function and simultaneously meets constraint conditions of mine slope slide mass balance equations and yield conditions of structural surfaces, as follows:
in the formula: k is a slope stability safety coefficient; j, the slope excavation benefit; theta is the slope rate of slope excavation(ii) a G is the gravity acting on the centroid of the side slope slide body; fSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; l is the length of the structural plane; c.
respectively, the cohesion and the friction angle of the structural surfaces.
The formula (7) is a multi-target nonlinear mathematical programming model, and the stability safety factor when the stability safety and the excavation economy are optimal cannot be obtained simultaneously
Benefits of excavation
And optimum excavation slope rate θoptTherefore, the invention firstly solves the nonlinear mathematical programming model with optimal stability and safety to obtain
Then solving a nonlinear mathematical programming model with optimal excavation economy to obtain
And then according to the solution
Constructing an objective function with optimal stability safety and optimal excavation economy so as to obtain the stability safety coefficient when the stability safety and the excavation economy are optimal
Benefits of excavation
And optimum excavation slope rate θopt(ii) a In this wayThe deficiency that ideal solutions cannot be obtained simultaneously is avoided (an ideal solution can be determined for a nonlinear mathematical programming model with optimal excavation economy)
An ideal solution can be determined for a nonlinear mathematical programming model that optimizes stability and safety
Generally speaking of'i≠α″iThis makes it impossible to obtain ideal solutions of the multi-objective functions simultaneously, and therefore by solving them according to
Constructing a target function with optimal stability safety and excavation economy, thereby realizing finding an alphaiSo that J (alpha)i) And
and K (alpha)i) And
as close as possible). The method comprises the following specific steps:
(7) solving a nonlinear mathematical programming model for multi-objective optimization of mine slope stability safety and excavation economy to obtain a stability safety coefficient when the stability safety and the excavation economy are both optimal
Benefits of excavation
And optimum excavation slope rate θopt。
step 1: nonlinear mathematical programming model for solving optimal stability and safety
According to the target function formula (1) and the constraint condition formulas (3), (4), (5) and (6), obtaining a nonlinear mathematical programming model with optimal stability and safety of mine slope excavation:
in the formula:
the stability and safety factor of the side slope when the excavation stability and safety are optimal is obtained; j. the design is a square1The side slope excavation benefit is achieved when the excavation stability and safety are optimal; thetaKExcavating slope rate for the side slope with optimal excavation stability and safety; g is the gravity of the slide centroid of the side slope along the y direction; fSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; l is the length of the structural plane.
The invention discloses a non-linear mathematical programming model for solving the optimal safety of mine slope stability in a formula (8) by adopting a penalty function method.
step 2: nonlinear mathematical programming model for solving optimal excavation economy
According to the target function formula (2) and the constraint condition formulas (3), (4), (5) and (6), obtaining a nonlinear mathematical programming model with optimal mine slope excavation economy as follows:
in the formula: k1The safety coefficient is stabilized for the side slope when the excavation economy is optimal;
the side slope excavation benefit is achieved when the excavation economy is optimal; thetaJExcavating slope rate for the side slope with optimal excavating economy; g is the gravity of the slide centroid of the side slope along the y direction; fSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, whichMiddle FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; l is the length of the structural plane.
And (3) solving the nonlinear mathematical programming model with the optimal economic performance of the mine slope excavation by adopting a penalty function method (9).
step 3: objective function with optimal construction stability safety and optimal excavation economy
The objective function with optimal construction stability safety and excavation economy is as follows:
in the formula: z is an objective function when the stability safety and the excavation economy are both optimal,
for the side slope excavation benefit when the excavation economy is optimal,
the method is used for realizing the slope excavation benefit when the stability safety and the excavation economy are optimal;
for the stability and safety factor of the side slope when the stability and safety of excavation are optimal,
the slope stability safety factor is the slope stability safety factor when the stability safety and the excavation economy are both optimal;
step 4: nonlinear mathematical programming model for establishing mine slope excavation economy and stable safety
Converting the nonlinear mathematical programming model of the multi-objective optimization of mine slope stability safety and excavation economy into a nonlinear mathematical programming model of single-objective optimization represented by the following formula according to the objective function formula (10) and the constraint condition formulas (3), (4), (5) and (6):
in the formula: z is an objective function when the stability safety and the excavation economy are both optimal,
for the side slope excavation benefit when the excavation economy is optimal,
the method is used for realizing the slope excavation benefit when the stability safety and the excavation economy are optimal;
for the stability and safety factor of the side slope when the stability and safety of excavation are optimal,
the slope stability safety factor is the slope stability safety factor when the stability safety and the excavation economy are both optimal; thetaoptThe optimal excavation slope rate is obtained when the stability safety and the excavation economy are optimal; g is the gravity of the slide centroid of the side slope along the y direction; fSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; l is the length of the structural plane.
And (3) solving a nonlinear mathematical programming model of the mine slope excavation economy and stable safety in the formula (14) by adopting a penalty function method.
The calculation results obtained when the excavation economy is optimal under different structural surface inclination angles alpha are listed in the table 1; the results of calculations obtained when the stability and safety are optimal for different structural surface inclination angles α are listed in table 2; the stability factor obtained with the process of the invention is shown in Table 3
Benefits of excavation
And optimum excavation slope rate θopt(ii) a Table 4 compares the stability safety factor and excavation benefit obtained by the method of the present invention when the excavation economy is optimal under different structural surface inclination angles α; table 5 compares the optimum stability and safety for different structural surface inclination angles alpha with the stability and safety factor and excavation benefit obtained by the method of the present invention.
TABLE 1 example calculation results for mine slope when excavation economics are optimal
Table 2 example calculation results for mine slope when stability and safety are optimal
Table 3 example mine slope calculated results obtained by the method of the invention
TABLE 4 comparison of excavation economics optimal with stability safety factor and excavation benefit of the method of the present invention
TABLE 5 comparison of optimal stability and safety with stability, safety factor and excavation benefit of the method of the invention
As shown in table 4, the excavation efficiency obtained by the method of the present invention was found to be equal to 45 ° in the structural plane inclination angle α
Compared with the excavation benefit when the excavation economy is optimal
The stable safety factor can be realized only by reducing 2.00 percent
Compared with stable safety factor K when the excavation economy is optimal1The increase of 56.84 percent achieves the unification of stable safety and economy.
As shown in Table 5, the stability factor obtained by the process according to the invention is higher for a structural surface inclination α of 50 °
Stability factor of safety compared to stability factor of safety when optimal
The excavation benefit can be realized only by reducing 0.36 percent
Excavation benefit J compared with stable safety when optimal1The increase of 2.82 percent, and the unification of safety and economy is achieved.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (8)
1. A method for calculating the optimal excavation slope rate of a mine side slope is characterized by comprising the following steps: the method comprises the following steps:
step 1, drawing up geometric parameters of a drawn-up mine side slope;
step 2, drawing up physical and mechanical parameters of the mine side slope;
step 3, analyzing the stress of the mine slope slide body;
step 4, establishing a stable safety objective function and an excavation economy objective function of the mine side slope;
step 5, establishing a constraint condition of the limit balance of the mine slope landslide;
step 6, establishing a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy;
and 7, solving a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy, and obtaining stability safety factor, excavation benefit and optimal excavation slope rate when the stability safety and the excavation economy are optimal.
2. The method for calculating the optimal excavation slope rate of the mine side slope according to claim 1, characterized in that: the drawing up of the geometric parameters of the drawn-up mine slope comprises the following steps: height of mine side slope H and distance H from bottom end of structural surface to x axis1(ii) a The natural slope rate beta of the mine side slope; and (4) the excavation slope rate theta of the mine side slope.
3. The method for calculating the optimal excavation slope rate of the mine side slope according to claim 1, characterized in that: the physical and mechanical parameters of the drawn up mine slope comprise: volume weight gamma of mine slope slide, inclination angle alpha of structural surface, cohesion c of structural surface and friction angle of structural surface
4. The method for calculating the optimal excavation slope rate of the mine side slope according to claim 1, characterized in that: the stress analysis of the mine side slope slide body is specifically as follows: gravity G acting on the centroid of the mine slope slide body, and shear force F acting on the mine slope slide body structural surfaceSAnd normal force FNIn which F isSTurning in the counterclockwise direction negative, FNThe pressure is positive.
5. The method for calculating the optimal excavation slope rate of the mine side slope according to claim 1, characterized in that: the establishment of the stable safety objective function and the excavation economy objective function of the mine side slope specifically comprises the following steps:
firstly, establishing a stable safety objective function of a mine side slope
Taking the stability safety coefficient of the mine slope as a stability safety objective function, seeking the maximum value of the stability safety coefficient of the mine slope, and establishing the stability safety objective function as follows:
Maximize:K
in the formula: maximize means "max"; k is the mine slope stability safety coefficient;
establishing an excavation economy objective function of the mine side slope
Taking the excavation benefit, which is the product of the price of the unit volume of the excavation slope sliding body and the excavation volume, as an excavation economic objective function, seeking the maximum value of the excavation benefit, and establishing the objective function of the excavation economic as follows:
Maximize:J
in the formula: maximize means "max"; j is mine side slope excavation benefit, and when a side slope sliding body with unit width is taken for calculation:
in the formula: k is a radical of1The unit volume selling price of the mine side slope sliding body is H, the height of the mine side slope, theta, the excavation slope rate of the mine side slope and beta, the natural slope rate of the mine side slope.
6. The method for calculating the optimal excavation slope rate of the mine side slope according to claim 1, characterized in that: the constraint conditions for establishing the limit balance of the mine slope landslide body are as follows:
the constraint conditions of the limit balance of the mine slope landslide body comprise: the balance equation constraint condition of the mine slope landslide body and the yield condition of the structural plane;
balance equation constraint conditions of mine slope landslide:
the balance equation of the mine slope sliding body in the horizontal direction is established as follows:
FS cosα-FN sinα＝0
the balance equation in the vertical direction of the mine slope sliding body is established as follows:
G+FS sinα+FN cosα＝0
wherein:
g is the gravity acting on the mine slope slide centroid, FSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; h is the height of the mine side slope1The distance from the bottom end of the structural plane to the x axis is used, and theta is the excavation slope rate of the mine side slope; gamma is the volume weight of the mine slope sliding body;
secondly, the yield condition of the mine side slope slide body structure surface is as follows:
in the formula: k is the mine slope stability safety coefficient; c.
respectively the cohesion and friction angle of the structural surface; l is the length of the structural plane.
7. The method for calculating the optimal excavation slope rate of the mine side slope according to claim 1, characterized in that: the establishment of the multi-objective optimization nonlinear mathematical programming model for the mine slope stability safety and the excavation economy is as follows:
the method comprises the following steps of establishing a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy, which takes mine slope stability safety factors and excavation benefits as dual objective function and simultaneously meets constraint conditions of mine slope slide mass balance equations and yield conditions of structural surfaces, as follows:
in the formula: k is the mine slope stability safety coefficient; j, mine side slope excavation benefit; fSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; g is the gravity acting on the centroid of the mine slope slide body; c.
respectively the cohesion and friction angle of the structural surface; l is the length of the structural plane; k is a radical of1The unit volume selling price of the mine slope slide body is obtained; h is the height of the mine side slope; theta is the excavation slope rate of the mine side slope; beta is the natural slope rate of the mine side slope.
8. The method for calculating the optimal excavation slope rate of the mine side slope according to claim 1, characterized in that: solving a multi-objective optimization nonlinear mathematical programming model of mine slope stability safety and excavation economy to obtain stability safety factor, excavation benefit and optimal excavation slope rate when the stability safety and the excavation economy are optimal, specifically:
solving a nonlinear mathematical programming model with optimal stability and safety by adopting a penalty function method, wherein the nonlinear mathematical programming model with optimal stability and safety is as follows:
in the formula:
for excavation stabilizingThe slope stability safety coefficient when the comprehensiveness is optimal; fSShear forces acting on structural surfaces, in which FSNegative in counterclockwise rotation; fNIs a normal force acting on a structural surface, wherein FNThe pressure is taken as positive; alpha is a positive included angle between the structural plane and the x axis, and alpha rotates in the counterclockwise direction to be positive; g is the gravity acting on the centroid of the mine slope slide body; c.
respectively the cohesion and friction angle of the structural surface; l is the length of the structural plane; k is a radical of1The unit volume selling price of the mine slope slide body is obtained; h is the height of the mine side slope; j. the design is a square1The side slope excavation benefit is achieved when the excavation stability and safety are optimal; thetaKExcavating slope rate for the side slope with optimal excavation stability and safety; beta is the natural slope rate of the mine side slope;
solving the nonlinear mathematical programming model with the optimal excavation economy by adopting a penalty function method, wherein the nonlinear mathematical programming model with the optimal excavation economy is as follows:
in the formula:
the side slope excavation benefit is achieved when the excavation economy is optimal; k1The safety coefficient is stabilized for the side slope when the excavation economy is optimal; thetaJExcavating slope rate for the side slope with optimal excavating economy;
and thirdly, constructing an objective function with optimal stability, safety and excavation economy as follows:
in the formula: z is an objective function when the stability safety and the excavation economy are optimal;
the method is used for realizing the slope excavation benefit when the stability safety and the excavation economy are optimal;
the slope stability safety factor is the slope stability safety factor when the stability safety and the excavation economy are both optimal;
solving the nonlinear mathematical programming model of the mine slope excavation economy and the stable safety by adopting a penalty function method, wherein the nonlinear mathematical programming model of the mine slope excavation economy and the stable safety is as follows:
in the formula: thetaoptThe optimal excavation slope rate is achieved when the stability, the safety and the excavation economy are optimal.
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