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The condition of directed every which way tunnels in transversally-isotropic environment with not continuous coupling of inclined layers elastic-creeping

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The condition of directed every which way tunnels in transversally-isotropic environment with not continuous coupling of inclined layers elastic-creeping


Horizontal underground cavities, in the form of diagonal developments depending on a direction of their longitudinal axis concerning a line of spread of inclined layers subdivided into three groups: the drift-cavities passed along line of layers spread, the cross-cuts-developments put transversally of layers spread and diagonal cavities-developments, intermediate between drifts and cross-cuts.

The intense and deformed condition of these horizontal cavities except for a mutual arrangement, depth location, and form of cross section depends also from elastic and creeping properties of an environmental mountain massif.

The research of law of distribution elastic-creeping voltage and moving near to cavities of any depth location and forms of section in dependence also from non-uniform - cracked structures is not only theoretical interest, but also direct practical meaning.

Directed every which way underground cavities superficial location in heavy trans trope a file depending on degree discontinuity flaw coupling of small inclined layers at an angle φ when longitudinal axes of cavities make any corner ψ with a line of plane spread of the isotropy coinciding with a plane of cracks. We will designate through Н depth location developments with distance between their centers L.

Equation of the generalized Guk’s law anisotropic massif with cavities at generalized flat deformation concerning Cartesian system of Oxyz coordinates (see fig.1) enters the name as

hello_html_6cd00c71.gif; (1)

wherehello_html_m716356bc.gif, hello_html_m2251e8c1.gif,

hello_html_m4b2ded4d.gif- factors of deformations determined by the formulas [1]:

hello_html_43c030a2.gif

hello_html_m46a92de1.gif

hello_html_m1897aead.gif (2)

hello_html_m3e338b47.gif


hello_html_m69e91031.pnghello_html_372cde16.png


hello_html_m6b32b729.png

Figure 1. The settlement scheme of studying of an anisotropic massif tension

а)Spatial kind; b) the generalized flat kind; c)a plane with periodic system of cracks


hello_html_1d3c383b.gif

hello_html_m196fc73d.gif

hello_html_1b53fbda.gif

hello_html_m5f71dcd5.gif

hello_html_3bc2bd6e.gif


In these formulas hello_html_m3e291131.gif - effective elastic constants trans trope massif equivalent on rigidity to an anisotropic massif with cracks, which depend from elastic constants of the last hello_html_m20e073fb.gif and cracks geometry hello_html_m64c3530c.gif. [2-4].

By means of Z.S.Erzhanov’s rocks creep theory and a method of final elements in the conditions of the generalized flat deformation laws of creeping pressure distribution and moving near pair diagonal cavities in powerful creeping trans trope massif are investigated.

Time processes (at t> 0) near to underground cavities are caused by display of properties of creep of surrounding rocks. For their research, involving main principles of the Z.S.Erzhanov’s creep rocks theory (2) resulted elastic constants hello_html_61975a89.gifand factors of Puasson hello_html_626ae09b.gif are replaced with temporary operator hello_html_m75be64b5.gif

hello_html_m3f497dcc.gifhello_html_1c8a7f12.gif, (3)

hello_html_m4e4d13d7.gifhello_html_m48973ef5.gif

hello_html_m370d04ee.gif, hello_html_5a21a619.gif - nucleus of a heredity.

As have shown laboratory researches [5] creeping parameters anisotropic of mountain breeds a little bit change in different directions.

Therefore in job temporary operators hello_html_m75be64b5.gifare set as

hello_html_625e335c.gif, hello_html_56c9dcc4.gif.


Then creeping parameters of mountain breeds at commutative nucleus creeping are determined by the formulas hello_html_m9886f10.gif hello_html_22caa868.gif;

hello_html_m141f68a1.gifcreeping parameters of mountain breeds, hello_html_m75f30077.gif time.

At account of the intense condition of diagonal cavities in conditions isotropic display of properties of trans trope mountain breeds creeping the meanings of temporary modules for t=120 and t=600 are used, [2].

In a heavy untouched massif the distribution of the basic voltage is represented by Dinnikov and with factors of lateral pressurehello_html_m25c07bf7.gif by being functions of elastic constant environment and corners φ, ψ.

By virtue of complexity of the task strict decision about the intense condition diagonal cavities in a heavy massif in conditions mountain breeds creeping, in this work is involved numerical methods of the analysis of a Method of Final Elements with isoparametric settlement elements at generalized of flat deformation.

The researched settlement area with cavities automatically is broken on isoparametric elements with help of the program FEM_3D in Delphi object-oriented environment. On each unit the vertical force from weights works.

All component of moving are represented as function from coordinates x, z of cross section of cavities.

The basic system of the algebraic equations about 3N concerning moving components with N of units, with which help the investigated area is broken into elements, is decided by an iterative method Gauss–Seidel method with factor of top relaxation hello_html_f46aa22.gif Previously program complex is tested on the decisions of known test tasks.

The multivariate accounts on calculation of voltage components near to cavities of vaulted cross section are carried out at different parameters: depths of location corners φ, ψ and degree of coupling of layers, which is defined through the periods of crackshello_html_m7262f053.gif.

The attention on law of distribution a vertical voltage on the crosspiece - pillar between cavities and on components moving and five components a voltage in points of contours pulled together drift is especially removed (ψ=0).

The table 1 contains voltage meanings and vertical moving in points of contours of cavities (see fig.2). The numbering of cavities contours points numbers is shown in this figure.

The table 1. Meanings elastic - creeping vertical moving and pressure in points gangue contours of cavities in a massif with not continuous coupling of layers at

t=120 and t=600 hello_html_m7f77d9fe.gif =6

The left cavity

t=120

t=600

 w/a=6.0

hello_html_7a3d1e78.gif

hello_html_m379ae1fc.gif

hello_html_m6b4d9e24.gif

hello_html_2a013062.gif

hello_html_7a3d1e78.gif

hello_html_m379ae1fc.gif

hello_html_m6b4d9e24.gif

hello_html_2a013062.gif

1

0,045

-0,610

0,001

0,000

0,071

-0,943

0,001

0,000

2

0,053

-0,588

0,001

0,001

0,082

-0,908

0,001

0,000

3

0,043

-0,514

0,000

0,001

0,067

-0,795

0,000

0,001

4

0,012

-0,420

0,000

0,001

0,018

-0,649

0,000

0,001

5

-0,013

-0,348

0,000

0,000

-0,020

-0,538

0,000

0,000

6

0,003

-0,251

0,001

0,001

0,005

-0,388

0,001

0,001

7

0,000

-0,113

0,001

0,000

0,001

-0,174

0,001

0,000

8

0,002

-0,248

0,001

0,001

0,002

-0,384

0,001

0,001

9

0,037

-0,348

0,000

0,000

0,058

-0,538

0,000

0,000

10

0,037

-0,409

-0,001

0,001

0,058

-0,632

-0,001

0,001

11

0,031

-0,499

0,000

0,001

0,048

-0,772

0,000

0,001

12

0,036

-0,575

0,001

0,000

0,055

-0,890

0,001

0,000

The right cavity

t=120

t=600

w/a=6.0

hello_html_7a3d1e78.gif

hello_html_m379ae1fc.gif

hello_html_m6b4d9e24.gif

hello_html_2a013062.gif

hello_html_7a3d1e78.gif

hello_html_m379ae1fc.gif

hello_html_m6b4d9e24.gif

hello_html_2a013062.gif

1

0,075

-0,591

0,002

0,000

0,116

-0,914

0,002

0,000

2

0,087

-0,582

0,002

0,001

0,134

-0,900

0,002

0,001

3

0,087

-0,526

0,000

0,001

0,134

-0,814

0,000

0,000

4

0,080

-0,443

0,000

0,000

0,124

-0,685

0,000

0,000

5

0,061

-0,373

0,000

0,000

0,094

-0,577

0,000

0,000

6

0,005

-0,267

0,000

0,000

0,007

-0,413

0,000

0,000

7

-0,008

-0,114

0,000

0,000

-0,013

-0,177

0,001

0,000

8

-0,003

-0,243

-0,001

0,001

-0,005

-0,375

0,000

0,001

9

-0,024

-0,336

0,000

-0,001

-0,036

-0,520

0,000

-0,001

10

-0,009

-0,396

-0,001

-0,001

-0,014

-0,613

-0,001

-0,001

11

0,023

-0,482

-0,001

-0,001

0,036

-0,746

-0,001

-0,001

12

0,052

-0,555

0,000

0,000

0,081

-0,858

0,000

0,000


hello_html_1841ab64.png

Figure 2. Circuits of an arrangement of numbering of cavities contours


The analysis of the settlement data shows about increase of vertical moving with reduction of parameter hello_html_m7f77d9fe.gif. The dependence of vertical pressure from hello_html_m7f77d9fe.gif is essential, and influence of a corner of an cracks planes inclination on sizes of pressure and moving is significant; their distribution on contours of cavities is asymmetrical; on gangue contours of cavities on the part of hanging sides the increase moving is observed, than on the part of laying sides and such tendency in meanings of moving grows with reduction of distance of the cavities centres.



THE LITERATURE:


1. Zh.S.Erzhanov, Sh.M.Aitaliev, Zh.К.Маsаnоv Stability of horizontal developments in slantwise-flaky massif. Alma-Ata, "Science" Каz SSR, 1971.- 160p.

2. Zh.S.Erzhanov, Sh.M.Aitaliev, Zh.К.Маssаnоv Seismological-stress condition of underground structures in anisotropic layered massif. Alma-Ata, "Science" КазССР, 1980.- 212p.

3.Маssаnоv Zh.К., Omarov А.D., Маhмеtоvа N.М. Static and seismological-stress of transport underground structures in anisotropic vectorially nonlinear massif. – Alma-Ata: Bastau, 2002.-244p.

4. Аitаliеv SH.М., Маssаnоv ZH.К. Account of mountain pressure in directed every which way horizontal developments. // Mountain pressure in capital and preparatory developments. Novosibirsk: 1973. - with 21-26.

5. Sаrsемbаеv А.А., Siniyaev А.Y., Маtvееvа V.P., Кudаshоv Е.F. About definition of elastic and temporary deformations on layered samples // In кн.: " Researches on the mechanics of mountain breeds ". Alma-Ata, "Science" .-1965.-C.45-50.



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Краткое описание документа:

The condition of directed every which way tunnels in transversally-isotropic  environment with not continuous coupling of inclined layers elastic-creeping

 

Horizontal underground cavities, in the form of diagonal developments depending on a direction of their longitudinal axis concerning a line of spread of inclined layers  subdivided into three groups: the drift-cavities passed along  line of layers spread, the cross-cuts-developments put transversally of layers spread and diagonal cavities-developments, intermediate between drifts and cross-cuts.

The intense and deformed condition of these horizontal cavities except for a mutual arrangement, depth location, and form of cross section depends also from elastic and creeping properties of an environmental mountain massif.

The research of law of distribution elastic-creeping voltage and moving near to cavities of any depth location and forms of section in dependence also from non-uniform - cracked structures is not only theoretical interest, but also direct practical meaning.

Directed every which way underground cavities superficial location in heavy trans trope a file depending on degree discontinuity flaw  coupling of small inclined layers at an angle φ when longitudinal axes of cavities make any corner ψ with a line of plane spread of the isotropy coinciding with a plane of cracks. We will designate through Н depth location developments with distance between their centers L.

Equation of the generalized Guk’s law anisotropic massif with cavities at generalized flat deformation concerning Cartesian system of Oxyz coordinates (see fig.1) enters the name as

;                                                                       (1)

where, ,                     

- factors of deformations determined by the formulas[1]:

                      (2)

 

            

 

Figure 1. The settlement scheme of studying of an anisotropic massif tension 

а)Spatial kind; b) the generalized flat kind; c)a plane with periodic system of cracks

 

 

In these formulas  - effective elastic constants trans trope massif equivalent on rigidity to an anisotropic massif with cracks, which depend from elastic constants of the last  and cracks geometry . [2-4].

By means of Z.S.Erzhanov’s rocks creep theory and a method of final elements in the conditions of the generalized flat deformation laws of creeping pressure distribution and moving near pair diagonal cavities in powerful creeping trans trope massif are investigated.

Time processes (at t> 0) near to underground cavities are caused by display of properties of creep of surrounding rocks. For their research, involving main principles of the Z.S.Erzhanov’s creep rocks theory (2) resulted elastic constants and factors of Puasson  are replaced with temporary operator

    ,           (3)

                            

,  -  nucleus of a heredity.

As have shown laboratory researches [5] creeping parameters anisotropic of mountain breeds a little bit change in different directions.

Therefore in job temporary operators are set as

, .

 

Then creeping parameters of mountain breeds at commutative nucleus creeping are determined by the formulas    ;                

 creeping parameters of mountain breeds,  time.        

At account of the intense condition of diagonal cavities in conditions isotropic display of properties of trans trope mountain breeds creeping the meanings of temporary modules for t=120 and t=600 are used, [2].             

In a heavy untouched massif the distribution of the basic voltage is represented by Dinnikovand with factors of lateral pressure by being functions of elastic constant environment and cornersφ, ψ.

By virtue of complexity of the task strict decision about the intense condition diagonal cavities in a heavy massif in conditions mountain breeds creeping, in this work is involved numerical methods of the analysis of a Method of Final Elements with isoparametric settlement elements at generalized of flat deformation. 

The researched settlement area with cavities automatically is broken on isoparametric elements with help of the program FEM_3D in Delphi object-oriented environment. On each unit the vertical force from weights works.

All component of moving are represented as function from coordinates x, z of cross section of cavities.

The basic system of the algebraic equations about 3N concerning moving components  with N of units, with which help the investigated area is broken into elements, is decided by an iterative method Gauss–Seidel method with factor of top relaxation  Previously program complex is tested on the decisions of known test tasks.

The multivariate accounts on calculation of voltage components near to cavities of vaulted cross section are carried out at different parameters: depths of location cornersφ, ψ and degree of coupling of layers, which is defined through the periods of cracks.

The attention on law of distribution a vertical voltage on the crosspiece - pillar between cavities and on components moving and five components a voltage in points of contours pulled together drift is especially removed (ψ=0).

The table 1 contains voltage meanings and vertical moving in points of contours of cavities (see fig.2). The numbering of cavities contours points numbers is shown in this figure.

The table 1. Meanings elastic - creeping vertical moving and pressure in points gangue contours of cavities in a massif with not continuous coupling of layers at

t=120 and t=600  =6

The left cavity      

t=120

t=600

 w/a=6.0

1

0,045

-0,610

0,001

0,000

0,071

-0,943

0,001

0,000

2

0,053

-0,588

0,001

0,001

0,082

-0,908

0,001

0,000

3

0,043

-0,514

0,000

0,001

0,067

-0,795

0,000

0,001

4

0,012

-0,420

0,000

0,001

0,018

-0,649

0,000

0,001

5

-0,013

-0,348

0,000

0,000

-0,020

-0,538

0,000

0,000

6

0,003

-0,251

0,001

0,001

0,005

-0,388

0,001

0,001

7

0,000

-0,113

0,001

0,000

0,001

-0,174

0,001

0,000

8

0,002

-0,248

0,001

0,001

0,002

-0,384

0,001

0,001

9

0,037

-0,348

0,000

0,000

0,058

-0,538

0,000

0,000

10

0,037

-0,409

-0,001

0,001

0,058

-0,632

-0,001

0,001

11

0,031

-0,499

0,000

0,001

0,048

-0,772

0,000

0,001

12

0,036

-0,575

0,001

0,000

0,055

-0,890

0,001

0,000

The right cavity    

t=120

t=600

w/a=6.0

1

0,075

-0,591

0,002

0,000

0,116

-0,914

0,002

0,000

2

0,087

-0,582

0,002

0,001

0,134

-0,900

0,002

0,001

3

0,087

-0,526

0,000

0,001

0,134

-0,814

0,000

0,000

4

0,080

-0,443

0,000

0,000

0,124

-0,685

0,000

0,000

5

0,061

-0,373

0,000

0,000

0,094

-0,577

0,000

0,000

6

0,005

-0,267

0,000

0,000

0,007

-0,413

0,000

0,000

7

-0,008

-0,114

0,000

0,000

-0,013

-0,177

0,001

0,000

8

-0,003

-0,243

-0,001

0,001

-0,005

-0,375

0,000

0,001

9

-0,024

-0,336

0,000

-0,001

-0,036

-0,520

0,000

-0,001

10

-0,009

-0,396

-0,001

-0,001

-0,014

-0,613

-0,001

-0,001

11

0,023

-0,482

-0,001

-0,001

0,036

-0,746

-0,001

-0,001

12

0,052

-0,555

0,000

0,000

0,081

-0,858

0,000

0,000

                     

 

Figure 2. Circuits of an arrangement of numbering of cavities contours 

 

The analysis of the settlement data shows about increase of vertical moving with reduction of parameter . The dependence of vertical pressure from  is essential, and influence of a corner of an cracks planes inclination on sizes of pressure and moving is significant; their distribution on contours of cavities is asymmetrical; on gangue contours of cavities on the part of hanging sides the increase moving is observed, than on the part of laying sides and such tendency in meanings of moving grows with reduction of distance of the cavities centres.

 

 

THE LITERATURE:

 

1. Zh.S.Erzhanov, Sh.M.Aitaliev, Zh.К.Маsаnоv Stability of horizontal developments in slantwise-flaky massif. Alma-Ata, "Science" Каz SSR, 1971.- 160p.

2. Zh.S.Erzhanov, Sh.M.Aitaliev, Zh.К.Маssаnоv Seismological-stress condition of underground structures in anisotropic layered massif. Alma-Ata, "Science" КазССР, 1980.- 212p.

3.Маssаnоv Zh.К., Omarov А.D., Маhмеtоvа N.М. Static and seismological-stress of transport underground structures in anisotropic vectorially nonlinear massif. – Alma-Ata: Bastau, 2002.-244p.

4. Аitаliеv SH.М., Маssаnо

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