CN102881045A - Three-dimensional visualization method of stereographic projection in block theory - Google Patents

Three-dimensional visualization method of stereographic projection in block theory Download PDF

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CN102881045A
CN102881045A CN2012102537638A CN201210253763A CN102881045A CN 102881045 A CN102881045 A CN 102881045A CN 2012102537638 A CN2012102537638 A CN 2012102537638A CN 201210253763 A CN201210253763 A CN 201210253763A CN 102881045 A CN102881045 A CN 102881045A
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structural plane
dimensional
cone
block
stereographic projection
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薛健
李建勇
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University of Chinese Academy of Sciences
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Abstract

The invention discloses a three-dimensional visualization method of stereographic projection in a block theory. The three-dimensional visualization method belongs to the field of discontinuous engineering calculation and visualization of the discontinuous engineering calculation. A basic idea of the three-dimensional visualization method is that two-dimensional stereographic projection is recovered into three-dimensional space for carrying out displayed and interactive operations, and the method mainly comprises the following steps of: obtaining each joint surface equation according to an angle of inclination and a direction of inclination which are input to a joint surface; obtaining an intersecting line of every two joint surfaces, recording all possible sliding directions; analyzing and calculating a sliding direction of each joint cone according to the direction of an external force; building three-dimensional models of all joint cones; analyzing and calculating a sliding mode and a safety factor of each joint cone; drawing a three-dimensional visual model of the stereographic projection according to a result of calculation, and carrying out interactive operations of a mouse in the three-dimensional space. The three-dimensional visualization method of the stereographic projection in the block theory disclosed by the invention has functions that an original obscure analysis progress is easier to understand, and an analysis result is more visual, and therefore, application of a key block theory is promoted in practical engineering.

Description

The three-dimensional visualization method of Block Theory stereographic projection
Technical field
The field is discontinuous engineering calculation and visual under the present invention, relates to the technology such as discontinuous analysis in the Geotechnical Engineering and calculating, computer graphics, visualization in scientific computing.
Background technology
Rock mass is as the direct effect object of the engineerings such as side slope, ground and underground chamber, in very long earth history evolution, to have stood various geologic function, and under the long term of terrestrial stress, section has kept the sign of various permanent strains and the natively plastid of tectonic structure person's movements and expression within it.Therefore, rock mass has certain architectural feature.These architectural features are by containing dissimilar structural plane in the rock mass and distribution and combined state in the space determine.
Structural plane is in the earth history development, what form in rock mass has certain orientation, certain scale, certain form and characteristic, relatively low face, slit and a banded geological interface of mechanical strength, such as level rock, schistosity, joint, weak intercalated layer, crack, and fault belt etc.
Structure claims again block, makes a general reference the rock mass by all kinds of structural plane and free face cut.Under state of nature, these blocks are in static balancing state, in carrying out hand excavation's process or after the excavation moulding, or after rock mass applied new load, because the stress redistribution, some block that is exposed on the free face can lose original static balancing state, along some structural plane slippage, and then cause the unstable failure of engineering rock mass, bring serious threat to construction, directly safety and the progress of impact construction.
The destruction of rock mass can be divided into deformation failure and block unstable failure.Can find out from a large amount of engineering practices, in the rock mass excavation projects such as underground chamber, side slope and ground, the destruction of rock mass shows as the unstable failure of block more, all with the stability of country rock block substantial connection is arranged such as the design of the rocvk classification of underground chamber and surrounding rock supporting; The mechanical strength of rock mass comprises rock block intensity and structural plane intensity, and generally, the existence of structural plane and intensity thereof are being controlled intensity and the stability of rock mass.Actual engineering rock mass, its deformation instability are often because structural plane opens, closure, the changing of the relative positions etc. cause, and the mechanical property of sillar is usually much higher than structural plane, and its distortion is relatively much smaller, if also stablize manyly when not having structural plane.So in the design and construction of the rock mass engineerings such as underground chamber, side slope and ground, the Rock Slide Stability Journal of Sex Research is a very important content.
The purpose of Stability Analysis of Rock Mass is exactly by various means and approach, correctly is familiar with the deformation and failure rule of stressed rock mass, judges the stability situation, predicts the variation in its future, makes effective engineering treatment measures.Its general research process comprises: on the basis of geologic prospect, rock mass physical mechanical property test, by analogies of experience, qualitative analysis on engineering geology etc., stability and unstable failure pattern are done qualitative analysis; Carry out necessary simplification by the rock mass with complexity, as abstract be rigidity, elastoplasticity continuous modification body, adopt Limit equilibrium analysis method, method of finite difference, Finite Element, discrete element method, boundary element method, discontinuous deformation analysis method and the popular method of numerical value etc., carry out rock stability calculating and engineering excavation, supporting analysis, for engineering design proposes scientific and reasonable opinions and suggestions.
Block Theory is a kind of rock mass engineering project method for analyzing stability, is proposed at 20 century 70s by stone root China the earliest.1977, Shi Genhua delivered " the stereographic projection method of Stability Analysis of Rock Mass " literary composition at " Chinese science ", indicate that Block Theory begins to take shape, and subsequently Block Theory is being done strict mathematical justification.1985, " Block Theory and Its Application to Rock Engineering " book that Shi Genhua and R.E.Goodman write was jointly published, and indicates the formal formation of Block Theory system.At present, Block Theory has become a kind of effective ways of the engineering rock mass stability analyses such as underground chamber, side slope and the dam foundation, has obtained studying widely and using in countries in the world and area.
Classical Block Theory at first putative structure face is the plane and runs through whole survey region, draws the concept of semispace, is the common factor of several groups of structural planes and free face semispace depending on block, sets up the block taxonomic hierarchies; Secondly the structural plane of different occurrences carried out translation, set up the mathematical abstractions model of block: cone (Pyramid), and further distinguish block and bore (Block Pyramid), joint cone (Joint Pyramid), the concept of excavation cone (Excavation Pyramid) and space cone (Space Pyramid), and then proposition block " finiteness theorem " (Finiteness Theorem) and block " mobility theorem " (Removability Theorem), if JP is the joint cone, EP is the excavation cone, SP is the space cone, BP is the block cone, then can provide the succinct statement of two theorems:
The finiteness theorem: block is limited, and and if only if
Figure BSA00000752590700021
The mobility theorem: movably and if only if for the projection body And
Figure BSA00000752590700023
These two theorems have given strict mathematical justification by Shi Genhua, therefore be also referred to as the Shi Shi theorem, are the cores of Block Theory.Use on this basis total space stereographic projection and vector meter algorithm to identify fast and effectively and judge the movable block of side slope, tunnel etc.; Then suppose that rigid block movement breaks away from or shearing slip along weak structural plane, under the effect that active force is made a concerted effort, can determine the sliding-modes of respective masses; Angle of internal friction according to structural plane identifies real Key Blocks at last.
Summary of the invention
As previously mentioned, in Practical Project, particularly in the work progress, key-block theory is adopted in the stability analysis of rock block usually, use three-dimensional visualization method to show its analysis result, can make analysis result more directly perceived on the one hand, be easier to understand; In conjunction with two-dimentional stereographic projection, demonstrate same result with several different methods on the other hand, can make the result have more cogency; Simultaneously, by the three-dimension interaction function is provided, can carry out certain interactively test to the three-dimensional visualization result, with check analysis result's reliability.
The three-dimensional visualization of key-block theory mainly comprises to the three-dimensional visualization of stereographic projection with to the three-dimensional visualization of actual block.Stereographic projection originally is to represent three-dimensional plane and straight line (vector) with the circle on the two dimensional surface and point, although indigestion directly perceived.The three-dimensional visualization method that the purpose of this invention is to provide a kind of stereographic projection, its analytic process and result are mapped to three dimensions, in reference sphere, use the mutual relationship between the mode direct representation rock structural face (espespecially joint plane) of three-dimensional picture, satisfy simultaneously mutual requirement, its key is to set up structural plane cone (joint cone espespecially according to given rock mass joint structural plane parameter, hereinafter to be referred as JP) three-dimensional model, and provide its sliding-modes to help judging block stability.The key step of the method is as follows.
Step 1: inclination angle (Dip) and tendency (Dip Direction) according to the input structure face obtain each equation of structural planes;
Step 2: ask per two structural plane intersections, record all possible glide direction;
Step 3: according to the glide direction of each structural plane cone of external force direction analytical calculation;
Step 4: the three-dimensional model of setting up all structural plane cones (JP);
Step 5: sliding-modes and the safety coefficient of each structural plane cone (JP) of analytical calculation;
Step 6: draw the stereographic projection three-dimensional visualization model according to result of calculation, and carry out mouse in three-dimensional interactive operation;
Step 7: also draw towards setting up the Key Blocks three-dimensional model with the position according to top analysis result and free face.
Beneficial effect of the present invention is to utilize computer graphics techniques that the stereographic projection analytical approach of classical Block Theory is carried out three-dimensional visualization, the easy to understand so that script analytic process hard to understand becomes, analysis result is vivider directly perceived, thereby promotes the application of key-block theory in Practical Project.
Description of drawings
Fig. 1 is structural plane cone three-dimension modeling schematic diagram;
Fig. 2 is two-dimentional stereographic projection analysis result schematic diagram;
Fig. 3 is checking example stereographic projection three-dimensional visualization result schematic diagram;
Fig. 4 is that checking example label is 1001 JP shape and glide direction thereof;
Fig. 5 is that checking example label is 1001 Key Blocks shape rendering result.
Embodiment
Below in conjunction with accompanying drawing the present invention is described in detail, be to be noted that described embodiment only is intended to be convenient to the understanding of the present invention, and it is not played any restriction effect.
Step 1: inclination angle (Dip) and tendency (Dip Direction) according to the input structure face obtain each structural plane P iEquation A iX+B iY+C iZ=0 (centre of sphere that structural plane is moved to by the reference sphere is initial point) namely records the normal vector of each structural plane
n i＝normalize([A i，B i，C i，0] T) (1)
Step 2: ask per two structural plane P iAnd P iIntersection, it is divided into (vector that the both direction of initial point) is opposite, and record shares this vectorial intersection face numbering, symbolically is e from the centre of sphere IjAnd e Ji(vector direction is by the right-handed system rule), available following formula calculates:
e ij = n i × n j | n i × n j | , e ji = n j × n i | n j × n i | - - - ( 2 )
These vectors will as the rib of JP, also may become the two face sliding direction of a certain JP on the one hand on the other hand;
Step 3: ask all possible JP glide direction, comprise that single face slides and two face sliding, and all glide directions are sorted from small to large by the angle with external force (being generally gravity) direction.Obtained all possible two face sliding direction in step 2, asked the single face glide direction, the vector that a demand goes out on each structural plane with external force direction angle minimum gets final product, that is: s i=normalize (n i* r * n i), wherein r is outer force vector;
Step 4: set up the three-dimensional model of all JP, by the combination of the lower half-space on each structural plane, n structural plane may surround 2 at most nIndividual JP, if the upper half-space (semispace that normal vector points to) of each structural plane is expressed as 0, the lower half-space is expressed as 1, then the combination of the lower half-space can be expressed as from 0 to 2 on all structural planes n-1 binary number.Get each such combination, search drops on the rib (namely satisfying simultaneously the two face sliding vector of all semispace inequations) in all semispaces common factors, these ribs are pressed the seamed edge that the end to end ordering of target structural plane sequence number just becomes this JP three-dimensional model, for example rib e 23e 42e 31e 14Become e after the ordering 23e 31e 14e 42, namely consisted of by structural plane P 2P 3P 1P 4With rib e 23e 31e 14e 42The JP that surrounds, and the profile of JP is represented by structural plane semispace and reference sphere intersection, as shown in Figure 1;
Step 5: sliding-modes and the safety coefficient of analyzing each JP, sliding-modes is made of slidably property and the glide direction of JP, glide direction is determined by dropping in the JP and with the sliding vector of external force direction angle minimum, namely to each JP, only needing that search is sorted may the sliding vector tabulation, and first that finds drops on the glide direction that sliding vector in the JP is this JP.And slidably property is determined jointly by the maximum static friction force of JP external force direction, glide direction and place structural plane thereof (may be two), if external force direction and glide direction angle are greater than 90 degree, represent that then this JP is stable, not slidably, otherwise, angle from numerical analysis, can increase a direction fictitious force opposite with glide direction makes JP keep balance, can try to achieve the numerical value of this fictitious force by equilibrium equation, for directly dropping, be that glide direction is identical with external force direction in JP, fictitious force size f then k=| r|; Slide for single face, the large I of this fictitious force is tried to achieve by following formula:
f k＝|v i×r|+v i·rtanφ i (3)
Safety coefficient is got:
s k = | v i · r tan φ i | | v i × r | - - - ( 4 )
Wherein, φ iBe structural plane P jAngle of friction,
Figure BSA00000752590700042
For two face sliding, then have:
f k＝|r·e ij|-N itanφ i-N jtanφ j (5)
Safety coefficient is got:
s k = | N i tan φ i + N j tan φ j | | r · e ij | - - - ( 6 )
Wherein: N i = - ( r × v j ) · ( v i × v j ) ( v i × v j ) · ( v i × v j ) , N j = ( r × v i ) · ( v i × v j ) ( v i × v j ) · ( v i × v j )
If try to achieve f by above-mentioned formula kValue is for negative, represents that then maximum static friction force enough offsets external force, and the JP security is higher, is difficult for sliding, if its value represents then that for just maximum static friction force is not enough to offset external force, the corresponding block of this JP is Key Blocks, needs the enforcement supporting measure;
Step 6:JP three-dimensional visualization result adopts the OpenGL graphics engine to draw, to adapt to cross-platform demand, and three-dimension interaction operation is finished by mouse or other pointing apparatus (such as touch-screen etc.), require simultaneously mutual feedback consistent with experience directly perceived, here relate to two need problems to be processed, one is that this point is finished by the drafting under the OpenGL preference pattern to the choosing of the three-dimensional graphic object in the drawing result; Another is the motion that the motion of mouse or two-dimentional pointing apparatus is converted to Drawing Object selected in the three dimensions, because the motion of mouse can only provide the coordinate information of two dimension, can't directly recover three-dimensional coordinate, need the adding of other supplementarys just can finish conversion, here we can obtain the 3rd the coordinate components z=0 that mouse moves with the mobile restriction of mouse on the xoy plane of screen coordinate system (being plane, display screen place), move in the object coordinate system after the tri-vector when being converted to mouse, also need it is projected on the glide direction of JP, so that JP can only move along its glide direction, thereby make interactive operation have more practical significance.Above-mentioned two dimensional motion can be finished by the calculating of following formula to the conversion of three-dimensional motion:
v＝((M -1V -1P -1u)·s)s (7)
Wherein, M, V, P are respectively model transferring, view transformation and the projective transformation matrix of graphics engine, and u is the motion-vector of mouse under normalized device coordinate system (NDC), and s is the glide direction vector of JP;
Step 7: the analysis result according to step 5 is sought the JP that may become Key Blocks, analyze the structural plane that consists of this JP and add whether free face consists of Key Blocks, its method is: according to the position of structural plane and free face and towards, a semispace can be determined in each plane, utilize the set operation method in computational geometry Point Set space, ask the common factor of these semispaces, if occur simultaneously for empty, then do not consist of block, otherwise the formation block obtains simultaneously with the three-dimensional model of this block of B reps (B-rep) expression and carries out color applying drawing with the method for graphics.
By above-mentioned steps, can realize the three-dimensional visualization that stereographic projection is analyzed, we program with C++ and to have realized above-mentioned method for visualizing, with validity and the practicality of checking institute of the present invention extracting method on a computing machine.The below provides an example, form 1 is the input data of checking example, wherein, inclination angle, tendency determine that the plane is towards (normal vector direction), the planimetric position is by a bit providing on the plane, its two-dimentional stereographic projection analysis result as shown in Figure 2, adopt three-dimensional visualization result such as Fig. 3, Fig. 4, shown in Figure 5 of the inventive method gained, wherein, Fig. 3 is whole visual result, Fig. 4 is JP shape and the glide direction visualization result thereof of label 1001, and Fig. 5 is the Key Blocks model rendering result of label 1001.
The structural plane of form 1 checking example, free face input data
Figure BSA00000752590700051
The above; only be the embodiment among the present invention; but protection scope of the present invention is not limited to this; anyly be familiar with the people of this technology in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should be encompassed in of the present invention comprising within the scope, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (3)

1. the three-dimensional visualization method of a Block Theory stereographic projection, it is characterized in that utilizing computer graphics techniques that two-dimension analysis process and the result of Block Theory stereographic projection showed at three dimensions, and provide the function of three-dimension interaction, make analytic process and result have dynamic effect, be conducive to understanding and application to Block Theory, it comprises the steps:
Step 1: inclination angle and tendency according to the input structure face obtain each equation of structural planes, and structural plane is moved to the centre of sphere by reference sphere, record the normal vector of each structural plane;
Step 2: ask per two structural plane intersections, as the rib of structural plane cone and possible two face sliding direction;
Step 3: ask all possible structural plane cone glide direction, comprise that single face slides and two face sliding, and all glide directions are sorted from small to large by the angle with external force direction;
Step 4: the three-dimensional model of setting up all structural plane cones;
Step 5: sliding-modes and the safety coefficient of each structural plane cone of analytical calculation, sliding-modes is made of slidably property and the glide direction of structural plane cone, and glide direction is determined by dropping in the structural plane cone and with the sliding vector of external force direction angle minimum;
Step 6: draw the stereographic projection three-dimensional visualization model according to result of calculation, and carry out mouse in three-dimensional interactive operation.
Step 7: the analysis result according to step 5 is sought the structural plane cone that may become Key Blocks, analyzes the structural plane that consists of this structural plane cone and adds whether free face consists of Key Blocks, if the formation Key Blocks is then set up its three-dimensional model and drawn.
2. three-dimensional visualization method according to claim 1 is characterized in that structural plane cone three-dimensional model is set up as follows in the step 4: by the combination of the lower half-space on each structural plane, n structural plane may surround 2 at most nIndividual structural plane cone is expressed as 0 with the upper half-space of each structural plane (semispace that normal vector points to), and the lower half-space is expressed as 1, and then the combination of the lower half-space can be expressed as from 0 to 2 on all structural planes n-1 binary number; Get each such combination, search drops on the rib (namely satisfying simultaneously the two face sliding vector of all semispace inequations) in all semispaces common factors, and these ribs are pressed the seamed edge that the end to end ordering of target structural plane sequence number just becomes this structural plane cone three-dimensional model; To ask friendship namely to obtain the three-dimensional model of structural plane cone by infinite cone and reference sphere that these seamed edges consist of.
3. three-dimensional visualization method according to claim 1, it is characterized in that the Key Blocks model in the step 7 sets up as follows: according to the position of structural plane and free face and towards, a semispace can be determined in each plane, utilize the set operation method in computational geometry Point Set space, ask the common factor of these semispaces, if occur simultaneously for empty, then do not consist of block, otherwise the formation block obtains simultaneously with the three-dimensional model of this block of B reps (B-rep) expression and carries out color applying drawing with the method for graphics.
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CN103728437A (en) * 2014-01-20 2014-04-16 中水北方勘测设计研究有限责任公司 Forecasting method applied to underground cavern rock burst failure mode
CN106846476A (en) * 2017-02-10 2017-06-13 中国电建集团成都勘测设计研究院有限公司 Rock block stability fast appraisement method based on three-dimensional live and stereographic projection
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CN107945272A (en) * 2017-11-09 2018-04-20 长江三峡勘测研究院有限公司（武汉） A kind of searching method of the rock mass discontinuity based on high definition drilling colour TV
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CN113032952A (en) * 2021-01-07 2021-06-25 北京华根仕数据技术有限公司 Visualization method for calculating stability of joint cone and block
CN117475119A (en) * 2023-10-31 2024-01-30 上海木圣网络科技有限公司 Geological structure bare eye projection system, method, equipment and readable medium

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CN103728437A (en) * 2014-01-20 2014-04-16 中水北方勘测设计研究有限责任公司 Forecasting method applied to underground cavern rock burst failure mode
CN103728437B (en) * 2014-01-20 2015-04-01 中水北方勘测设计研究有限责任公司 Forecasting method applied to underground cavern rock burst failure mode
CN106846476A (en) * 2017-02-10 2017-06-13 中国电建集团成都勘测设计研究院有限公司 Rock block stability fast appraisement method based on three-dimensional live and stereographic projection
CN106846476B (en) * 2017-02-10 2020-07-07 中国电建集团成都勘测设计研究院有限公司 Rock block stability rapid evaluation method based on three-dimensional live-action and red-horizontal projection
CN107194997A (en) * 2017-05-15 2017-09-22 中国科学院大学 A kind of three-dimensional visualization method of Block Theory equilibrium region figure
CN107194997B (en) * 2017-05-15 2020-07-07 中国科学院大学 Three-dimensional visualization method for block theory balance area map
CN107945272A (en) * 2017-11-09 2018-04-20 长江三峡勘测研究院有限公司（武汉） A kind of searching method of the rock mass discontinuity based on high definition drilling colour TV
CN107945272B (en) * 2017-11-09 2021-10-08 长江三峡勘测研究院有限公司（武汉） Rock mass structural plane searching method based on high-definition drilling color television
CN109001420A (en) * 2018-05-21 2018-12-14 深圳市工勘岩土集团有限公司 The method of the analysis geological disaster of tectonic stress circle or slope stability
CN113032952A (en) * 2021-01-07 2021-06-25 北京华根仕数据技术有限公司 Visualization method for calculating stability of joint cone and block
CN113032952B (en) * 2021-01-07 2023-11-14 北京华根仕数据技术有限公司 Visualization method for calculating joint cone and block stability
CN117475119A (en) * 2023-10-31 2024-01-30 上海木圣网络科技有限公司 Geological structure bare eye projection system, method, equipment and readable medium

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