CN102855664A - Three-dimensional modeling method of complicated block body - Google Patents
Three-dimensional modeling method of complicated block body Download PDFInfo
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- CN102855664A CN102855664A CN2012102537445A CN201210253744A CN102855664A CN 102855664 A CN102855664 A CN 102855664A CN 2012102537445 A CN2012102537445 A CN 2012102537445A CN 201210253744 A CN201210253744 A CN 201210253744A CN 102855664 A CN102855664 A CN 102855664A
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Abstract
The invention discloses a three-dimensional modeling method of a complicated block body. The complicated block body is a non-lug body comprising a concave combination air face, the basic idea of the three-dimensional modeling method is that the non-lug body is taken as a combination of a series of lug bodies, and the air face is used for dividing space; sub lug bodies in each sub-region are extracted, and finally a series of sub-lug bodies are combined in a final complicated block body; the three-dimensional modeling method comprises the following main steps of: selecting the air face to divide the block body into two parts on the air face of the non-bug combination, and splitting the parts, wherein if the parts contain no air faces of a concave combination, the parts are lug bodies which can be directed extracted, and if the parts contain the air faces of a concave combination, one air face is selected to repeat the above steps until the residual part does not comprise the air face of the concave combination. The method can finish the modeling of the complicated block body with not revising the classical block body theoretical hypothesis, has a vigorous supplement on the classical block body theory, and has important application value in engineering practice.
Description
Technical field
The field is discontinuous engineering calculation under the present invention, relates to discontinuous analysis and the technology such as calculating, computer graphics and Geometric Modeling in the Geotechnical Engineering.
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 planes 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
The mobility theorem: movably and if only if for the projection body
And
These two theorems have given strict mathematical justification by Shi Genhua, so 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
An important prerequisite hypothesis of classical Block Theory is that structural plane (espespecially joint plane) and free face all are the planes on the unlimited geometric meaning that extends, the block that is obtained by structural plane and free face cutting under this hypotheses only may be the projection body, and in the engineering structure, the situation that free face is the concavity combination also is ubiquitous, the block that consists of in this case generally also is non-projection body (being recessed block), all have so non-projection body such as the arris place of underground chamber inside, nook, porch etc., what have goes back quite dangerous.Therefore, on the basis of classical Block Theory, the block feature in the free face complex combination situation is carried out deep analysis, and design the modeling method of complicated non-projection body, important actual value is arranged concerning rock mass engineering project, the development of Block Theory is also had positive theory significance.
The present invention has namely realized a kind of like this three-dimensional modeling method of complicated block, its basic thought is to be the combination of a series of projection bodies non-projection is stereoscopic, free face by the concavity combination is divided the space, obtain sub-projection body in every sub regions, at last a series of sub-projection body is merged into final complicated block, its key step is as follows:
Step 1: according to input parameter structural texture face and free face equation, the set of initialization plane;
Step 2: if the plane set of being untreated in addition turns step 3, otherwise turn step 6;
Step 3: all free faces in the traversal set if exist the concavity combination to turn step 4, otherwise turn step 5;
Step 4: according to concavity combination free face spatial division is become two semispaces, form respectively two new structural planes, free face set, turn step 2;
Step 5: the set that does not have concavity combination free face is obtained sub-projection body by the method for asking semispace to occur simultaneously and adds the set of sub-block body, turn step 2;
Step 6: all the sub-projection bodies in the set of sub-block body are merged into final complicated block.
The invention has the beneficial effects as follows the modeling that in the situation that need not revise the infinitepiston hypothesis, just can finish complicated block, strong replenishing to classical Block Theory, in engineering practice, has important using value, particularly in the underground cavern excavation process, run into the three-dimensional model that can accurately produce complicated block in the situation of complicated Key Blocks, have important reference value for formulation and the enforcement of the safety practices such as support reinforcement.
Description of drawings
Fig. 1 is the process flow diagram of complicated block three-dimensional modeling method;
Fig. 2 is free face concavity combination synoptic diagram;
Fig. 3 is free face convex combination synoptic diagram;
Fig. 4 is the example Block Model synoptic diagram of verification algorithm;
Fig. 5 is the line frame graph that algorithm calculates the gained model;
Fig. 6 is the rendering effect figure that algorithm calculates the gained model.
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.
The present invention is from above-mentioned basic thought, based on recurrence and the pattern progressively found the solution, Design and implementation the efficient algorithm of non-protruding Key Blocks identification and modeling.Free face for the concavity combination, choose a free face block is divided into two parts, then must be the projection body if cut apart the free face that gained part no longer comprises the concavity combination, but direct solution, if still comprise the free face of concavity combination, then therefrom choose a free face and repeat aforesaid operations, until remaining part no longer comprises the free face of concavity combination.Its embodiment specifically, comprises the steps: shown in Fig. 1 complicated block three-dimensional modeling method process flow diagram
Step 1: inclination angle (Dip), tendency (Dip Direction) and position according to input structure face and free face obtain each structural plane J
iWith free face F
iEquation, wherein for consisting of block, structural plane has two kinds of possibilities (there is rock on the two sides) towards (normal vector direction), and free face is towards according to actual conditions being (towards the rock back side) fixed, two groups of plane equations are formed a set, and write down each plane attribute and possible towards, this set is added among the formation Q;
Step 2: if formation Q is then execution in step 6 of sky, otherwise take out a set execution in step 3 from formation Q head
Step 3: all free faces in the traversal set, judge whether to exist the combination of free face concavity, determination methods is whether the intersection of seeing two crossing free faces spends less than 180 at the dihedral angle that free face upper half-space (being a normal vector space pointed) side becomes, if less than then being concavity combination (as shown in Figure 1), otherwise be convex combination (as shown in Figure 2), if find a concavity to make up then execution in step 4, otherwise execution in step 5.
Step 4: from consisting of two free face F of concavity combination
1And F
2In appoint and to get a free face, for example get F
1, by plane F
1Be two semispaces with spatial division, thus original structural plane and free face be divided into two set A and B, set A comprises all structural planes and free face F
1, set B comprises all structural planes and free face F
1', F
2, F wherein
1' be F
1Oppositely the plane (is about to F
1Normal vector counter-rotating), such F in set B
1' and F
2Must be the convex combination, i.e. the combination of concavity in set A and set B number average subtracts 1, then set A and B is all added formation Q, turns step 2.
Step 5: all free faces are convex combination in the set, and it only may produce the projection body with the structural plane cutting, and each structural plane is towards there being two kinds of possibilities when consisting of block, and then n structural plane just has 2
nPlant combination, for every kind of such combination, add all free faces, each plane adds it towards determining a semispace, asks all semispaces to occur simultaneously, be empty set if occur simultaneously, illustrate that then this kind combination does not produce block, if do not produced block for empty set then shows, and this block is a sub-block of final block, the sub-block body that produces is added among the block set K, turn step 2.
Step 6: all sub-block bodies that block is gathered among the K are asked union, and its result is final desired complicated block.
In said method, because step 4 has guaranteed that the combination of free face concavity only subtracts and do not increase in the plane set of new generation, finally all free face concavity combinations all will be eliminated, and it is limited that therefore whole algorithm is carried out step number, can not produce infinite loop.
We program with C++ and to have realized above-mentioned algorithm on a computing machine, with checking algorithm complexity that the present invention is carried and practicality.The below provides an example and verifies, form 1 is the instance data of input, wherein, inclination angle, tendency determine that the plane is towards (normal vector direction), for structural plane, reverse possibility is also arranged, and for free face its towards by the inclination angle, tendency is unique determines that the planimetric position is by a bit providing on the plane.According to measured result, this structural plane, free face constitute complicated block as shown in Figure 3, and this type of block generally is positioned at the underground chamber infall.
The structural plane of form 1 checking example, free face input data
Should organize data and input above-mentioned algorithm, can obtain Fig. 4 and result shown in Figure 5, theoretical model signal and actual conditions, the as can be known correctness of this algorithm of contrast Fig. 3.
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 modeling method of a complicated block, it is characterized in that non-protruding complicated block is considered as the combination of a series of projection bodies, by concavity combination free face recurrence being carried out in the space divides, progressively solve the sub-projection body that all consist of complicated block, synthesize at last required complicated block three-dimensional model, its process may further comprise the steps:
Step 1: inclination angle, tendency and position according to input structure face and free face obtain each structural plane J
iWith free face F
jEquation forms a set with two groups of plane equations, and write down each plane attribute and possible towards, this set is added among the formation Q;
Step 2: if formation Q is then execution in step 6 of sky, otherwise take out a plane set execution in step 3 from formation Q head;
Step 3: all free faces in the traversal set, judge whether to exist the combination of free face concavity, determination methods is whether the dihedral angle that becomes of semispace one side that the intersection of seeing two crossing free faces points at the free face normal vector is less than 180 degree, if less than then being the concavity combination, otherwise be the convex combination, if find a concavity to make up then execution in step 4, otherwise execution in step 5;
Step 4: according to concavity combination free face spatial division is become two semispaces, in two semispaces, form respectively among two new structural planes, free face set and the adding formation Q, turn step 2;
Step 5: the set that does not have concavity combination free face is asked sub-projection body and added sub-block body set K, turn step 2;
Step 6: all the sub-block bodies among the sub-block body set K are asked union, and its result is final desired complicated block.
2. three-dimensional modeling method according to claim 1 is characterized in that the specific implementation method of step 4 is: from consisting of two free face F of concavity combination
1And F
2In appoint and to get a free face, for example get F
1, by plane F
1Be two semispaces with spatial division, thus original structural plane and free face be divided into two set A and B, set A comprises all structural planes and free face F
1, set B comprises all structural planes and free face F
1', F
2, F wherein
1' be F
1Oppositely the plane (is about to F
1Normal vector counter-rotating), such F in set B
1' and F
2Must be the convex combination, i.e. the combination of concavity in set A and set B number average subtracts 1.
3. three-dimensional modeling method according to claim 1 is characterized in that the specific implementation method of step 5 is: for each structural plane towards two kinds that exist may, n structural plane provides 2
nPlant various combination, for every kind of such combination, add all free faces, each plane adds that it towards determining a semispace, seeks common ground to all semispaces, is empty set if occur simultaneously, illustrate that then this kind combination does not produce block, if do not produced block for empty set then shows, and this block is a sub-block of final block, and the sub-block body that produces is added among the block set K.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN106971425A (en) * | 2017-03-14 | 2017-07-21 | 天津大学 | Rock block group's fine modeling and recognition methods based on polyhedron network model |
| 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 |
| CN109215124A (en) * | 2018-09-25 | 2019-01-15 | 中国科学院武汉岩土力学研究所 | The construction method of underground engineering 3D grid model under a kind of complex geological condition |
-
2012
- 2012-07-23 CN CN2012102537445A patent/CN102855664A/en active Pending
Non-Patent Citations (1)
| Title |
|---|
| JIANYONG LI等: "《Block theory on the complex combinations of free planes》", 《COMPUTERS AND GEOTECHNICS》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN106971425A (en) * | 2017-03-14 | 2017-07-21 | 天津大学 | Rock block group's fine modeling and recognition methods based on polyhedron network model |
| 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 |
| CN109215124A (en) * | 2018-09-25 | 2019-01-15 | 中国科学院武汉岩土力学研究所 | The construction method of underground engineering 3D grid model under a kind of complex geological condition |
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Application publication date: 20130102 |