CN116911000A - Method for converting rock block corner-to-corner contact based on azimuth angle - Google Patents

Method for converting rock block corner-to-corner contact based on azimuth angle Download PDF

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Publication number
CN116911000A
CN116911000A CN202310799236.5A CN202310799236A CN116911000A CN 116911000 A CN116911000 A CN 116911000A CN 202310799236 A CN202310799236 A CN 202310799236A CN 116911000 A CN116911000 A CN 116911000A
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contact
edge
rock
corner
gamma
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CN116911000B (en
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樊火
何思明
欧阳朝军
陈晓清
苏立君
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Institute of Mountain Hazards and Environment IMHE of CAS
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Institute of Mountain Hazards and Environment IMHE of CAS
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling

Abstract

The invention discloses a method for converting angular contact between rock blocks into angular contact based on azimuth angle, which comprises the following steps of S1, constructing an initial geometric model of discrete rock blocks and setting calculation parameters; s2, determining the angular contact between two rock masses; s3, dividing the corner contact into corner contact of the candidate contact edge homonymy and corner contact of the candidate contact edge variant; s4, dividing plane space by diagonal contact; s5, calculating the instantaneous speed of the contact corner points of two rock masses in the angular contact by adopting a discrete medium numerical method; s6, calculating azimuth angles of instantaneous speeds of two rock mass contact angular points in angular contact; and S7, converting the angular contact to the angular contact based on the azimuth angle of the instantaneous speed. The invention realizes reasonable selection of contact edges, is suitable for wider application scenes, can more accurately predict the motion evolution process of discrete rock blocks, and can be adopted by related scientific research, commercial computer codes and programs.

Description

Method for converting rock block corner-to-corner contact based on azimuth angle
Technical Field
The invention belongs to the technical field of geotechnical engineering and engineering geological numerical simulation, and particularly relates to a method for converting angular contact between rock blocks into angular contact based on azimuth angles.
Background
Along with the prosperity and development of the economy in China, geotechnical engineering occupies a very important position in various civil engineering. Geotechnical engineering is systematic work performed by comprehensively renovating, reforming and utilizing a geotechnical body by using various exploration and test technologies based on soil mechanics, rock mass mechanics and engineering geology. Geotechnical engineering is an important component of civil engineering, and comprises geotechnical engineering investigation, design, test, construction and monitoring, relates to the whole process of engineering construction, and is used for solving the problems of geotechnical and soil engineering, including problems of foundation and foundation, side slope, underground engineering and the like. Has very important significance in various constructions such as houses, municipal administration, energy sources, water conservancy, roads, shipping, mines, national defense and the like.
The motion evolution of the discrete rock has important significance for exploring geotechnical engineering and engineering geology, and at present, in order to explore the motion evolution process of the discrete rock, the motion evolution process of the discrete rock is subjected to numerical simulation, and the contact between the rock can be divided into three types of side-to-side contact, angle-to-angle contact and the like. Wherein angular contact is visually comparable to "tip-to-tip" contact, with instability. To ensure smooth performance of numerical simulation, it is necessary to convert the angular contact into an appropriate angular contact. How to fully consider the motion trend of the corner points in the corner angle contact and reasonably select the most likely contacted edge of the contact corner points in the next calculation step (namely how to reasonably convert the corner angle contact into the corner edge contact) is always a key and a difficult point in the numerical simulation of the motion evolution process of the discrete rock mass.
Since the corner points of the rock are geometrically non-differentiable points or so-called singularities, the contact direction at the corner points cannot be determined. Therefore, in numerical simulation, the corner contact must be changed to the corner contact. The existing shortest invasion distance method and the longest slippage distance method do not fully consider the movement trend of angular points in angular contact, and are sensitive to parameters such as contact spring stiffness, block elastic modulus, calculation time step and the like. That is, for the same geometric rock, the values of these parameters are different, and the two existing methods often give different numerical simulation results, which is obviously unreasonable.
Disclosure of Invention
The invention aims to provide a method for converting angular contact between rock blocks into angular contact based on azimuth angles, aiming at the defects in the prior art, so as to solve the problem of contact normal uncertainty of angular contact in numerical simulation of discrete rock block motion evolution process in the prior art.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method of converting a rock-to-rock angular contact to an angular-to-edge contact based on azimuth angle, comprising the steps of:
s1, constructing an initial geometric model of a discrete rock and setting calculation parameters;
s2, determining angular contact between two rock masses by adopting a distance criterion;
s3, dividing the angular contact into angular contact of the candidate contact edge homonymy and angular contact of the candidate contact edge variant by adopting an angle criterion;
s4, dividing plane space by diagonal contact;
s5, calculating the instantaneous speed of the contact corner points of two rock masses in the angular contact by adopting a discrete medium numerical method;
s6, calculating azimuth angles of instantaneous speeds of two rock mass contact angular points in angular contact;
and S7, converting the angular contact to the angular contact based on the azimuth angle of the instantaneous speed.
Further, step S2 includes:
if two corner points of two rock blocks meet the following conditions:
d＜2d 0
wherein d is the distance between two corner points, d 0 Is a predetermined threshold value;
the two corner points constitute angular contact and a pair of angular contact between two rock pieces has four associated sides, i.e. sides AB, AC, DE and DF on the two rock pieces.
Further, step S3 includes:
if alpha is less than or equal to 180 degrees and beta is more than 180 degrees, wherein alpha is an included angle between the upper edge DE of the rock mass 2 and the upper edge AB of the rock mass 1, beta is an included angle between the upper edge DF of the rock mass 2 and the upper edge AC of the rock mass 1, the edges AB and AC are two candidate contact edges and are on the rock mass 1, and the corner contact is a corner contact of the same body as the candidate contact edge;
if alpha is less than or equal to 180 degrees and beta is less than or equal to 180 degrees, the AB on the rock mass 1 and DF on the rock mass 2 are two candidate contact edges and are respectively arranged on the rock mass 1 and the rock mass 2, and the angular contact is the angular contact of the candidate contact edge variant.
Further, in step S4, planar space division of corner contact between the candidate contact edges and the body includes:
straight lines AB and AC are perpendicular to the upper edge AB and AC of the rock mass 1 respectively, a straight line AF is an angular bisector of an angle C, AB and an angle BAC, and a region covered by the angle BAF is defined as a natural sliding region of the upper edge AB of the rock mass 1; the area covered by the +.FAC is defined as the natural slip area of the AC above the rock mass 1; the area covered by +.cab is defined as the separation of the rock mass 2.
Further, in step S4, the planar space division of the angular contact of the candidate contact edge variant includes:
straight lines AF and AG are respectively perpendicular to the upper edges AB and AC of the rock mass 1, and straight lines AC and AB are respectively reverse extension lines of straight lines CA and BA;
for the corner A on the rock mass 1, the area covered by CAG is defined as a natural sliding area of the AC above the rock mass 2; the area covered by +.gab is defined as the relative sliding region of AB above block 1; the area covered by +.b.ac is defined as the separation of rock mass 2;
for the corner A on the rock mass 2, the area covered by the +.BAC is defined as the front overlapping separation area of the two rock masses; the area covered by B AC is defined as the back overlap separation of the two rock masses.
Further, step S6 includes:
calculating unit vectorsAnd-> and />Included angle a between i and bi ；
Based on the included angle a i and bi Respectively calculating azimuth angles gamma of the instantaneous speeds of the two contact angular points 1 and γ2 ：
When 0 is less than or equal to b i Pi/2 or less, gamma i ＝a i ；
When pi/2 is less than or equal to b i Pi is less than or equal to gamma i ＝2π-a i ；
wherein ,to construct a horizontal right unit vector starting from the contact corner a,/>To construct a unit vector vertically upwards starting from the contact corner a,/>For the moment of speed V starting from the contact point a i (i=1, 2) direction building unit vector.
Further, in step S7, converting the corner contact of the candidate contact edge body to the corner contact includes:
at the instantaneous velocity azimuth angle gamma of the corner a on the rock mass 1 1 To examine the object:
if the azimuth angle gamma 1 Falls under BAF coverIn the range of (1), i.e. falling in the natural sliding region of the upper edge AB of the rock mass 1, the edge AB is selected as the contact edge;
if the azimuth angle gamma 1 The method comprises the steps that when the angle FAC falls in a range covered by the FAC, namely falls in a natural sliding area of the upper side AC of the rock mass 1, the side AC is selected as a contact side;
if the azimuth angle gamma 1 And falls within the range covered by the CAB, namely falls in the separation area, the contact edge is not selected.
Further, in step S7, converting the corner contact of the candidate contact edge variant to the corner-edge contact includes:
case I:
γ 1 e.sub.CAG, azimuth angle gamma 1 A natural slip zone of AC falling above the rock mass 1;
if gamma is 2 E < BAC >, selecting an edge AC;
if gamma is 2 E, F, selecting an edge AC;
if gamma is 2 E < FAB, and
∠A 2 AB＜∠CAA 1 selecting an edge AB;
∠A 2 AB＞∠CAA 1 selecting an edge AC;
∠A 2 AB＝∠CAA 1 then selecting the side AB and the side AC at the same time;
case II:
γ 1 e.g. azimuth angle gamma 1 A relative sliding area falling on the upper side AB of the rock mass 1;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 e.c.AF, and
∠BAA 1 ＞∠A 2 AC, then select edge AB;
∠BAA 1 ＜∠A 2 AC, selecting an edge AC;
∠BAA 1 ＝∠A 2 AC, selecting the side AB and the side AC at the same time;
case III:
γ 1 e.c.AB, i.e. azimuth angle gamma 1 The separation zone falling on the rock mass 2 is not in the IV zone nor the V zone;
if gamma is 2 E < BAC >, separating two corner points, and not selecting a contact edge;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, F, selecting an edge AC;
case IV
γ 1 Angle BAC, azimuth angle gamma 1 The two rock blocks fall on the front overlapped separation area;
if gamma is 2 ∈∠A 1 AC, separating two corner points, and not selecting a contact edge;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, F, selecting an edge AC;
if gamma is 2 ∈∠BAA 1 And (2) and
∠BAA 2 ＜∠A 1 AC, then select edge AB;
∠BAA 2 ＞∠A 1 AC, selecting an edge AC;
∠BAA 2 ＝∠A 1 AC, selecting the side AB and the side AC at the same time;
case V
γ 1 e.sup.b.sup.AC, i.e. azimuth angle gamma 1 The two rock blocks fall on the back overlapping separation area;
if gamma is 2 ∈∠BAA 1 The two corner points are separated, and the contact edge is not selected;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, F, selecting an edge AC;
if gamma is 2 ∈∠A 1 AC, and
∠A 1 AB＞∠CAA 2 selecting an edge AB;
∠A 1 AB＜∠CAA 2 selecting an edge AC;
∠A 1 AB＝∠CAA 2 at the same timeSelecting an edge AB and an edge AC;
wherein ,A1 and A2 Point a on rock mass 1 and rock mass 2, respectively.
The azimuth angle-based method for converting rock block corner-to-corner contact into corner-to-corner contact has the following beneficial effects:
the invention adopts an angle criterion to divide the angle contact into two types of 'candidate contact edge homonymy' and 'candidate contact edge variant'. Dividing the plane space of the first type into a natural sliding area (I area) of AB above the rock mass 1, a natural sliding area (II area) of AC above the rock mass 1 and a separation area (III area) of the rock mass 2; the plane space of the second class is divided into five areas, namely a natural sliding area (I area) of an edge AB, a natural sliding area (II area) of an edge AC, a separation area (III area) of a rock block 2, a front overlapping separation area (IV area) of two rock blocks, and a back overlapping separation area (V area) of two rock blocks; and further, the motion trend of the contact angular points is considered, the most probable contact edge of the contact angular points of the next calculation step is reasonably selected, and the angular contact is converted into angular edge contact. The invention realizes reasonable selection of the contact edge, reduces the sensitivity of parameters such as the rigidity of the contact spring, the elastic modulus of the block body, the calculation time step length and the like, is suitable for wider application scenes, can more accurately predict the motion evolution process of discrete rock blocks, and can be adopted by related scientific researches, commercial computer codes and programs.
Drawings
FIG. 1 is a schematic view of a distance criterion for angular contact in the present invention;
FIG. 2 is a view of a "candidate contact edge homobody" angular contact distinguished by an angular criterion in accordance with the present invention;
FIG. 3 is a view of a "candidate contact edge variant" angular contact distinguished by an angular criterion in accordance with the present invention;
FIG. 4 illustrates three sections of the "candidate contact edge homobody" angular contact plane space in accordance with the present invention;
FIG. 5 is a view of five sections of the "candidate contact edge variant" angular contact plane space of the present invention;
FIG. 6 is a geometric model of a translation test example provided in embodiment 2 of the present invention;
FIG. 7 shows the calculation result of the translation test example provided in embodiment 2 of the present invention;
FIG. 8 is a geometric model of a rotation test example provided in example 3 of the present invention;
FIG. 9 is a calculation result of a rotation test example provided in embodiment 3 of the present invention;
FIG. 10 is a geometric model of a time-step impact test example provided in embodiment 4 of the present invention;
fig. 11 shows the calculation result of the time-step impact test example provided in embodiment 4 of the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
In embodiment 1, the present embodiment provides a method for converting angular contact between rock blocks into angular contact based on azimuth angle, and the present embodiment fully uses geometric information and motion information of angular contact to select a contact edge most likely to be contacted by a next calculation step for angular points in angular contact, thereby implementing reasonable conversion from angular contact to angular contact, so as to enable numerical simulation to accurately predict motion evolution process of discrete rock blocks as much as possible, and the method specifically includes the following steps:
s1, constructing an initial geometric model of a discrete rock mass and setting calculation parameters;
this step may use commercial or open source preprocessing software (e.g., autoCAD, freeCAD, etc.) to build an initial geometric model of the discrete rock mass while giving the computational parameters.
Step S2, referring to FIG. 1, searching for angular contact between two rock masses by adopting a distance criterion, wherein the method specifically comprises the following steps:
if two corner points of two rock blocks meet the following conditions:
d＜2d 0
wherein d is the distance between two corner points, d 0 Is a predetermined threshold value;
the two corner points constitute angular contact and a pair of angular contact between two rock pieces has four associated sides, i.e. sides AB, AC, DE and DF on the two rock pieces.
Step S3, referring to fig. 2 and 3, using an angle criterion, dividing the angular contact into an angular contact of the candidate contact edge homonymy and an angular contact of the candidate contact edge variant, which specifically includes:
let alpha be the angle between DE on the rock mass 2 and AB on the rock mass 1, and beta be the angle between DF on the rock mass 2 and AC on the rock mass 1;
if alpha is less than or equal to 180 degrees and beta is more than 180 degrees, the sides AB and AC are two candidate contact sides and are on the rock mass 1, and the corner contact is the corner contact of the candidate contact sides;
if alpha is less than or equal to 180 degrees and beta is less than or equal to 180 degrees, the AB on the rock mass 1 and DF on the rock mass 2 are two candidate contact edges and are respectively arranged on the rock mass 1 and the rock mass 2, and the angular contact is the angular contact of the candidate contact edge variant.
S4, carrying out plane space division on diagonal contact;
referring to fig. 4, planar spatial partitioning of angular contact of candidate contact edges with a body, comprising:
straight lines AB and AC are perpendicular to the upper edges AB and AC of the rock mass 1, respectively, and straight line AF is the bisector of +.c×ab, and straight line AF is also the bisector of +.bac.
The area covered by the +.BAF is defined as the natural sliding area (zone I) of AB above the rock mass 1;
the area covered by the +.FAC is defined as the natural slip zone (zone II) of the AC above the rock mass 1;
the area covered by the +.cab is defined as the separation zone of the rock mass 2 (zone III);
referring to fig. 5, planar spatial partitioning of angular contacts of candidate contact edge variants, comprising:
straight lines AF and AG are respectively perpendicular to the upper edges AB and AC of the rock mass 1, and straight lines AC and AB are respectively reverse extension lines of straight lines CA and BA;
for the corner A on the rock mass 1, the area covered by CAG is defined as the natural sliding area (I area) of the AC above the rock mass 2; the area covered by +.gab is defined as the relative sliding region (region II) of AB above block 1; the area covered by +.b.ac is defined as the separation area of rock mass 2 (area III).
Similarly, for the corner a on the rock mass 2, three corresponding regions may also be defined. The area covered by ++BAC is defined as the frontal overlap separation (V-zone) of the two rocks; the area covered by B AC is defined as the back overlap separation (V-zone) of the two rock masses.
S5, calculating the instantaneous speed of the contact corner points of two rock masses in the angular contact by adopting a discrete medium numerical method;
the instant velocity V of contact corner points on rock mass 1 and rock mass 2 in angular contact is calculated by a numerical calculation method based on discrete medium, such as Discrete Element Method (DEM) or Discontinuous Deformation Analysis (DDA), respectively 1 and V2 The superscripts "1", "2" indicate rock mass 1 and rock mass 2, respectively.
Step S6, calculating azimuth angles of instantaneous speeds of two rock mass contact angular points in angular contact, wherein the method specifically comprises the following steps:
calculating unit vectorsAnd-> and />Included angle a between i and bi ；
Based on the included angle a i and bi Square for calculating instantaneous speed of two contact angular pointsAngle of position gamma 1 and γ2 ：
When 0 is less than or equal to b i Pi/2 or less, gamma i ＝a i ；
When pi/2 is less than or equal to b i Pi is less than or equal to gamma i ＝2π-a i ；
wherein ,to construct a horizontal right unit vector starting from the contact corner a,/>To construct a unit vector vertically upwards starting from the contact corner a,/>For the moment of speed V starting from the contact point a i (i=1, 2) direction building unit vectors; "." is dot product; /> and />Respectively the modulus of the corresponding vector, because they are unit vectors
S7, converting the angular contact to the angular contact based on the azimuth angle of the instantaneous speed;
converting the corner-to-corner contact of the candidate contact edge with the body to the corner-to-edge contact, comprising:
at the instantaneous velocity azimuth angle gamma of the corner a on the rock mass 1 1 To examine the object (if the corner a on the rock 1 is stationary, the azimuth angle γ is measured at the instantaneous velocity of the corner a on the rock 2 2 As the object of investigation):
if the azimuth angle gamma 1 The method comprises the steps that when the rock falls within the range covered by the BAF, namely falls in a natural sliding area (I area) of the AB on the rock mass 1, the AB is selected as a contact side;
if the azimuth angle gamma 1 Falls under the coverage of FACIn the range, namely a natural sliding area (II area) falling on the upper side AC of the rock mass 1, selecting the side AC as a contact side;
if the azimuth angle gamma 1 If the contact edge falls within the range covered by the CAB, namely falls in a separation area (area III), the contact edge is not selected, which implies that the two contact corner points have a separation trend.
Converting corner-to-corner contact of a candidate contact-edge variant to corner-to-edge contact, comprising:
A 1 and A2 Representing point a on rock mass 1 and rock mass 2, respectively;
case I:
γ 1 e.sub.CAG, azimuth angle gamma 1 A natural slip zone of AC falling above the rock mass 1;
if gamma is 2 E < BAC >, selecting an edge AC;
if gamma is 2 E, F, selecting an edge AC;
if gamma is 2 E < FAB, and
∠A 2 AB＜∠CAA 1 selecting an edge AB;
∠A 2 AB＞∠CAA 1 selecting an edge AC;
∠A 2 AB＝∠CAA 1 then selecting the side AB and the side AC at the same time;
case II:
γ 1 e.g. azimuth angle gamma 1 A relative sliding area falling on the upper side AB of the rock mass 1;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 e.c.AF, and
∠BAA 1 ＞∠A 2 AC, then select edge AB;
∠BAA 1 ＜∠A 2 AC, selecting an edge AC;
∠BAA 1 ＝∠A 2 AC, selecting the side AB and the side AC at the same time;
case III:
γ 1 e.c.AB, i.e. azimuth angle gamma 1 The separation zone (zone III) falling on the rock mass 2, which is neither zone IV nor zone V;
if gamma is 2 E < BAC >, separating two corner points, and not selecting a contact edge;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, F, selecting an edge AC;
case IV
γ 1 Angle BAC, azimuth angle gamma 1 The two rock blocks fall on the front overlapped separation area (IV area);
if gamma is 2 ∈∠A 1 AC, separating two corner points, and not selecting a contact edge;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, F, selecting an edge AC;
if gamma is 2 ∈∠BAA 1 And (2) and
∠BAA 2 ＜∠A 1 AC, then select edge AB;
∠BAA 2 ＞∠A 1 AC, selecting an edge AC;
∠BAA 2 ＝∠A 1 AC, selecting the side AB and the side AC at the same time;
case V
γ 1 e.sup.b.sup.AC, i.e. azimuth angle gamma 1 The back overlapping separation area (V area) of the two rock masses;
if gamma is 2 ∈∠BAA 1 The two corner points are separated, and the contact edge is not selected;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, F, selecting an edge AC;
if gamma is 2 ∈∠A 1 AC, and
∠A 1 AB＞∠CAA 2 selecting an edge AB;
∠A 1 AB＜∠CAA 2 selecting an edge AC;
∠A 1 AB＝∠CAA 2 then select side AB and side A simultaneouslyC。
Example 2
The embodiment carries out a translation test calculation by the method in the embodiment 1, which specifically comprises the following steps:
step A1, referring to FIG. 6, an initial geometric model of the discrete rock system is established, as shown in FIG. 6, and calculated parameters are adopted as follows:
density of 2300.00kg/m 3 Young's modulus of 20GPa and Poisson's ratio of 0.30; the contact spring rate was 1000GPa, irrespective of the bulk force and friction. The maximum allowable step displacement rate is 0.01 and the time step is 0.01s. Given an initial speed: u= -W v V=0 where W v Is adjustable in size;
the example consists of two rock masses, 7 fixed points are arranged on a large rock mass, the dotted line is a geometric symmetry axis, and the vector U (U, v) represents the initial speed of a given small rock mass;
a2, a pair of angular contact is known between two rock blocks according to a distance criterion;
step A3, the angular contact is known as the angular contact of the candidate contact edge homonymy according to an angle criterion: the corner point A is a contact point, and the edge AB and the edge AC are two candidate contact edges;
step A4, for the corner contact of the 'candidate contact edge homobody': the planar space can be divided into a natural sliding region (I region) of the side AB of the large rock mass; a natural sliding zone (zone II) of the edge AC of the large rock mass; a separation zone (zone III) of small rock mass;
step A5 to step A7, refer to fig. 7, wherein fig. 7 (a) and (b) are results obtained by the conventional method, and fig. 7 (c) is a result (the solid line is the movement trace of the point) obtained by the present invention.
As shown in fig. 7, for a given initial speed (u= -W v V=0), if W v >0, the nub should translate to the left. For existing processes, e.g. given W v If not large enough, the corner a receives the reaction force of the edge AB and the motion trail of the corner a is not opposite (see fig. 7 (a) and (b)); this is because the prior art method pre-selects the edge AB of the steeper large rock mass as the initial contact edge, e.g. W v ≥50.00m/s(W v Large enough), the existing method can obtain positiveAnd (5) confirming results. On the other hand, for the method proposed by the present invention, even W v As small as W v The test of this example, which is =0.000005 m/s, always gives the correct results (see fig. 7 (c)), shows that the proposed method is more sensitive to the small translational movement trend of the rock mass than the prior art method.
Example 3
The present embodiment performs a rotation test calculation by the method in embodiment 1, which specifically includes the following steps:
step B1, referring to FIG. 8, an initial geometric model of a discrete rock system is constructed, wherein a lower rock is fixed and the dotted line is the geometric symmetry axis. The calculation parameters are as follows: density of 1.00kg/m 3 Young's modulus of 5MPa and Poisson's ratio of 0.30; the contact spring rate is 200MN/m and does not take into account bulk forces and friction; the maximum allowable step displacement rate is 0.001, and the time step is 0.001s; vector F is the point load acting on the edge AB of the upper rock mass and its component is fixed at F x ≡0，F y ≡-10.00N；d L Representing the distance between the action line of F and the symmetry axis when F is positioned on the left side of the symmetry axis; d, d R Representing the distance between the action line of F and the symmetry axis when F is positioned on the right side of the symmetry axis;
wherein ,dL The larger the upper rock mass, the more obvious the tendency to left-hand; conversely, d R The larger the upper rock mass, the more obvious the tendency to right-hand;
step B2, a pair of angular contact is known between two rock masses according to a distance criterion;
step B3, the angular contact is known as the angular contact of the candidate contact edge homonymy according to an angle rule: the corner point C is a contact point, and the edge CD and the edge CE are two candidate contact edges;
step B4, for the corner contact of the 'candidate contact edge homobody': the planar space may be divided into a natural sliding region (region I) of the edge CD of the lower rock mass; a natural sliding zone (zone II) of the edge CE of the lower rock mass; a separation zone (zone III) of the upper rock mass;
the results of steps B5 to B7 are shown in fig. 9, wherein fig. 9 (a) and (B) are the results obtained by the conventional method, and fig. 9 (c) and (d) are the results obtained by the present invention (the solid line is the movement trace of the point). As shown in fig. 9For the existing method, if 0.000005<d L ＝d R <0.202m, the contact edge chosen being always CE, no matter whether F is located to the left or to the right of the symmetry axis, up to d L ＝d R Not less than 0.202m, and selecting the corresponding correct contact edge; for the method of the present invention, d is only L ＝d R More than or equal to 0.000001m, the correct contact edge can be selected. The test shows that: compared with the prior art, the method provided by the invention is sensitive to the movement trend of the block body for the rotation of the rock block driven by the point load, so that a more accurate movement process simulation result can be obtained;
example 4
This embodiment performs a time step impact test example in the manner of embodiment 1, which specifically includes the steps of:
step C1, referring to FIG. 10, an initial geometric model of a discrete rock mass system is constructed, wherein a dotted line is a geometric symmetry axis, and the angle BAC is an acute angle of 70 degrees; the calculation parameters used are as follows:
density of 2300.00kg/m 3 Young's modulus of 3GPa and Poisson's ratio of 0.30; the rigidity of the contact spring is 90GPa, and the volume force and friction are not considered; f (F) 1 and F2 For point load acting at the centroid of two blocks and F 1x ＝6373kN，F 1y ＝-9053kN，F 2x ＝-6373kN，F 2y =9053 kN. The maximum allowable step displacement rate is 0.001, and the time step is variable. Due to F 1 and F2 Are all parallel to the edge AB, so if the corner a can get rid of the contact spring in time, it will slide along the edge AB;
step C2, a pair of angular contact is known between two rock masses according to a distance criterion;
step C3, the angular contact is known as the angular contact of the candidate contact edge variant according to an angle criterion: the corner point A is a contact point, and the edge AB of the left rock block and the edge AC of the right rock block are two candidate contact edges;
step C4, for the corner contact of the candidate contact edge variant: the plane space can be divided into five areas, namely a natural sliding area (I area), a relative sliding area (II area), a separation area (III area), a front overlapping separation area (V area) and a back overlapping separation area (V area);
step C5 to step 7, the results obtained are shown in fig. 11, where fig. 11 (a) and (b) are the results obtained by the existing method, and the results obtained by the present invention (the solid line is the motion track of the point), as can be seen from the graph, the maximum allowable step displacement rate is 0.001, and for the existing method, when the time step Δt= 0.00001,0.00002,0.00003,0.00005,0.0001,0.0002,0.0005 and 0.0006s, the corner a slides along the edge AB; but when Δt=0.0007 >0.0006s, the two overlapping corner points will press against each other for a period of time and both blocks will rotate to different extents (obviously incorrect). For the proposed method, when Δt= 0.00001,0.00005,0.0001,0.0002,0.0005,0.001,0.005,0.008 and 0.01s, the motion trajectory of the corner a is always correct, i.e. always slides along the edge AB; this example test shows that the proposed method largely overcomes the time step sensitivity of the existing methods.
Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, it should not be construed as limiting the scope of protection of the present patent. Various modifications and variations which may be made by those skilled in the art without the creative effort are within the scope of the patent described in the claims.

Claims (8)

1. A method for converting angular contact between rock masses into angular-to-side contact based on azimuth angle, comprising the steps of:
s1, constructing an initial geometric model of a discrete rock and setting calculation parameters;
s2, determining angular contact between two rock masses by adopting a distance criterion;
s3, dividing the angular contact into angular contact of the candidate contact edge homonymy and angular contact of the candidate contact edge variant by adopting an angle criterion;
s4, dividing plane space by diagonal contact;
s5, calculating the instantaneous speed of the contact corner points of two rock masses in the angular contact by adopting a discrete medium numerical method;
s6, calculating azimuth angles of instantaneous speeds of two rock mass contact angular points in angular contact;
and S7, converting the angular contact to the angular contact based on the azimuth angle of the instantaneous speed.
2. The azimuth based method of converting rock-to-rock corner-to-corner contacts of claim 1, wherein step S2 comprises:
if two corner points of two rock blocks meet the following conditions:
d＜2d 0
wherein d is the distance between two corner points, d 0 Is a predetermined threshold value;
the two corner points constitute angular contact and a pair of angular contact between two rock pieces has four associated sides, i.e. sides AB, AC, DE and DF on the two rock pieces.
3. The azimuth based method of converting rock-to-rock corner-to-corner contacts of claim 2, wherein step S3 comprises:
if alpha is less than or equal to 180 degrees and beta is more than 180 degrees, wherein alpha is an included angle between the upper edge DE of the rock mass 2 and the upper edge AB of the rock mass 1, beta is an included angle between the upper edge DF of the rock mass 2 and the upper edge AC of the rock mass 1, the edges AB and AC are two candidate contact edges and are on the rock mass 1, and the corner contact is a corner contact of the same body as the candidate contact edge;
if alpha is less than or equal to 180 degrees and beta is less than or equal to 180 degrees, the AB on the rock mass 1 and DF on the rock mass 2 are two candidate contact edges and are respectively arranged on the rock mass 1 and the rock mass 2, and the angular contact is the angular contact of the candidate contact edge variant.
4. The method for converting rock-to-rock corner contacts into corner-to-edge contacts based on azimuth according to claim 3, wherein said planar spatial division of candidate contact-to-edge corner contacts in step S4 comprises:
straight lines AB and AC are perpendicular to the upper edge AB and AC of the rock mass 1 respectively, a straight line AF is an angular bisector of an angle C, AB and an angle BAC, and a region covered by the angle BAF is defined as a natural sliding region of the upper edge AB of the rock mass 1; the area covered by the +.FAC is defined as the natural slip area of the AC above the rock mass 1; the area covered by +.cab is defined as the separation of the rock mass 2.
5. The method for converting rock-to-rock angular contact into angular-to-edge contact based on azimuth according to claim 3, wherein said planar spatial division of angular-to-edge contact of candidate contact-edge variants in step S4 comprises:
straight lines AF and AG are respectively perpendicular to the upper edges AB and AC of the rock mass 1, and straight lines AC and AB are respectively reverse extension lines of straight lines CA and BA;
for the corner A on the rock mass 1, the area covered by CAG is defined as a natural sliding area of the AC above the rock mass 2; the area covered by +.gab is defined as the relative sliding region of AB above block 1; the area covered by +.b.ac is defined as the separation of rock mass 2;
for the corner A on the rock mass 2, the area covered by the +.BAC is defined as the front overlapping separation area of the two rock masses; the area covered by B AC is defined as the back overlap separation of the two rock masses.
6. A method of converting rock-to-rock corner contacts into corner-to-edge contacts based on azimuth angle according to claim 3, wherein said step S6 comprises:
calculating unit vectorsAnd-> and />Included angle a between i and bi ；
Based on the included angle a i and bi Respectively calculating azimuth angles gamma of the instantaneous speeds of the two contact angular points 1 and γ2 ：
When 0 is less than or equal to b i Pi/2 or less, gamma i ＝a i ；
When pi/2 is less than or equal to b i Pi is less than or equal to gamma i ＝2π-a i ；
wherein ,to construct a horizontal right unit vector starting from the contact corner a,/>To construct a unit vector vertically upwards starting from the contact corner a,/>For the moment of speed V starting from the contact point a i (i=1, 2) direction building unit vector.
7. The method for converting rock-to-rock corner contacts into corner-to-edge contacts based on azimuth according to claim 4, wherein said step S7 of converting the corner contacts of the candidate contact-edge co-body into corner-to-edge contacts comprises:
at the instantaneous velocity azimuth angle gamma of the corner a on the rock mass 1 1 To examine the object:
if the azimuth angle gamma 1 Falls within the range covered by BAF, i.e. falls in the natural sliding area of AB on the rock mass 1, then selecting AB as contact side;
if the azimuth angle gamma 1 The method comprises the steps that when the angle FAC falls in a range covered by the FAC, namely falls in a natural sliding area of the upper side AC of the rock mass 1, the side AC is selected as a contact side;
if squareAngle of position gamma 1 And falls within the range covered by the CAB, namely falls in the separation area, the contact edge is not selected.
8. The method of converting rock-to-rock corner contacts to corner-to-edge contacts based on azimuth of claim 5, wherein converting the corner-to-corner contacts of the candidate contact-to-edge variants in step S7 comprises:
case I:
γ 1 e.sub.CAG, azimuth angle gamma 1 A natural slip zone of AC falling above the rock mass 1;
if gamma is 2 E < BAC >, selecting an edge AC;
if gamma is 2 E, F, selecting an edge AC;
if gamma is 2 E < FAB, and
∠A 2 AB＜∠CAA 1 selecting an edge AB;
∠A 2 AB＞∠CAA 1 selecting an edge AC;
∠A 2 AB＝∠CAA 1 then selecting the side AB and the side AC at the same time;
case II:
γ 1 e.g. azimuth angle gamma 1 A relative sliding area falling on the upper side AB of the rock mass 1;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 e.c.AF, and
∠BAA 1 ＞∠A 2 AC, then select edge AB;
∠BAA 1 ＜∠A 2 AC, selecting an edge AC;
∠BAA 1 ＝∠A 2 AC, selecting the side AB and the side AC at the same time;
case III:
γ 1 e.c.AB, i.e. azimuth angle gamma 1 The separation zone falling on the rock mass 2 is not in the IV zone nor the V zone;
if gamma is 2 ∈∠BAC*，The two corner points are separated, and the contact edge is not selected;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, F, selecting an edge AC;
case IV
γ 1 Angle BAC, azimuth angle gamma 1 The two rock blocks fall on the front overlapped separation area; if gamma is 2 ∈∠A 1 AC, separating two corner points, and not selecting a contact edge;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, F, selecting an edge AC;
if gamma is 2 ∈∠BAA 1 And (2) and
∠BAA 2 ＜∠A 1 AC, then select edge AB;
∠BAA 2 ＞∠A 1 AC, selecting an edge AC;
∠BAA 2 ＝∠A 1 AC, selecting the side AB and the side AC at the same time;
case V
γ 1 e.sup.b.sup.AC, i.e. azimuth angle gamma 1 The two rock blocks fall on the back overlapping separation area; if gamma is 2 ∈∠BAA 1 The two corner points are separated, and the contact edge is not selected;
if gamma is 2 E, selecting an edge AB;
if gamma is 2 E, F, selecting an edge AC;
if gamma is 2 ∈∠A 1 AC, and
∠A 1 AB＞∠CAA 2 selecting an edge AB;
∠A 1 AB＜∠CAA 2 selecting an edge AC;
∠A 1 AB＝∠CAA 2 then selecting the side AB and the side AC at the same time;
wherein ,A1 and A2 Point a on rock mass 1 and rock mass 2, respectively.
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