2. The process of material volumetric disintegration with stepwise loading can be predicted on the basis of data obtained with complex loading under constant side pressure conditions. 3. The correlation dependence of ultrasound velocity on residual volumetric disintegration is invariant in relation to both stress-~train state parameter for the material and loading path. LITERATURE CITED i. 2. 3. 4. 5. 6.

7.

8.

A.A. II'yushin, Plasticity [inRussian],Gos. Izd. Tekh.-Teor. Lit., Moscow--Leningrad (1948). A . N . Stavrogin and A. G. Protosenya, Plasticity of Rocks [in Russian], Nedra, Moscow (1979). Y. Chen, X. Yao, and N. Geng, "Stress path, strength, and dilatancy of rocks," Scientia Sinica, 0.3, No. 4 (1980). K. Kovari and A. Tisa, "Multiple failure state and strain controlled triaxial tests," Rock Mech., 7/i, (1975). A . N . Stavrogin and A. G. Protosenya, Strength of Rocks and Stability of Workings at Considerable Depths [in Russian], Nedra, Moscow (1985). A . N . Stavrogin, G. G. Zaretskii-Feoktistov, and G. N. Tanov, "Study of dilation effects in rocks with a complex axlsymmetrical stressed state," Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (1985). A . N . Stavrogin, G. G. Zaretskii-Feoktistov, and G. N. Tanov, "Study of acoustic emission with rock deformation under complex axisymmetrical stressed state conditions," Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 5, (1986). V . N . Nikolaevskii, Mechanics of Porous and Cracked Materials [in Russian], Nedra, Moscow (1984).

DETERMINATION OF SUPPORT PRESSURE IN COAL FACES OF GAS-BEARING COAL SEAMS A. K. Beiikov, G. I. Korshunov, and A. G. Protosenya

Gas found in nature of support MPa coal strength surrounding rocks

UDC 622.831

coal seams has an effect on processes of deformation and the amount and pressure [i, 2]. With an increase in gas support pressure from 40 to 80 decreases by a factor of 1.5, and a similar behavior is also followed for [2].

In order to describe the limiting state of gas-bearing rocks a condition was suggested in [I]

( o . - - % ) 2 + 4 x ~ - - s i n 2p os + o v + ~

(K - m P tg p) ctg p ,

(1)

where o x, Oy, ~xy are stress components, MPa; K and 0 are rock cohesion and internal friction angle, deg; m is the gas component. Apart from the gas factor, moisture content also has a considerable effect on formation of the support pressure zone [2, 3]. Empirical dependences for the change in cohesion factor and internal friction angle on coal moisture content obtained for the conditions of the Vorkuta deposit are known [2]: K, " t,9 - 0,29W~ p - - 4 0 -- 3 W ,

whe,e 2 < Wp < 6,5; where 2 < Wp < 7,0,

(2) (3)

Production Association '~orkutaugol'," Vorkuta. Translated from Fiziko-Tekhnicheskie Problemy Razrabotkl Poleznykh Iskopaemykh, No. 5, pp. 14-20, September-October, 1988. Original article submitted January 21, 1988.

0038-5581/88/2405-0399$12.50

9 1989 Plenum Publishing Corporation

399

x

Fig. I. Diagram of stress distribution in the limiting zone of a thin section of a seam.

where Wp is working moisture of the coal, Z. Carrying out coal face working in a coal seam disrupts equilibrium existing in the inIf stress at the boundary of the coal seam exceeds its supporting capacity, then there is breaking of the boundary region of the coal seam. tact rock mass, as a result of which rocks and the seam surrounding the working deform.

Stress components in the zone of the limiting condition of the boundary region for a coal seam satisfy the plasticity condition 91"

o, - - a~ , - sin p (oz + %) + ~

cos p - -

2~ t--m

P sin p,

(4)

where K is cohesion in a coal seam. We construct stress distribution in the limiting zone of a thin sectlon of a seam which makes it possible to find an approximate solution. In a thin seam stress components change weakly over the height, and therefore it is possible to suggest that they do not depend on coordinate Y. We isolate element dx (Fig. i) in a coal seam and we project the force operating on it on axis OX 2hda,--2T,.~,

(5)

where tangential stress over the seam-rock contact is connected with normal stress Cy by a Coulomb dry friction rule T, -- ~a,,

(6)

where ~ = tanpz is coefficient of friction over the contact with friction angle Pz. Considering relationship (6) the equilibrium equation may be written:

dO=~x ~ov-- O.

(7)

Full-scale observations for the nature of gas pressure distribution in the boundary region of a coal seam indicates that it is variable and increases to a specific value at a distance from the working perimeter, and then it decreases to a value ~H. On the basis of experimental data [4] for gas pressure distribution in the zone near the face of a coal seam it is possible to suggest that the rule for gas pressure distribution is known. Without loss of generality it is assumed that gas pressure in the coal seam can be approximated by means of an expression

P (x) = P. (~ - ~ alxi,

(8)

where a i is the approximation factor. Full-scale observations for seam deformation indicate that strength of the rock mass in the side of a seam working is variable. The region of the seam near the perimeter is most broken, it is in the post-limit condition, and strength increases with distance from the

400

working perimeter.

In order to take account of loss of strength in the zone of the seam

near the perimeter cohesion in i t w i l l

be considered v a r i a b l e , changing by the r u l e N

-----~,

K(z)-

(9)

(a-- =/

where d and bj are approximation factors. We construct an approximate solution in the limiting region for which we solve set of Eqs. (4) and (7) taking account of relationships (8) and (9):

(lO) where ~

-$-~,

A' (Z) -,, 2k (:~)cosp i--m

(11)

2msin p p, (z). i--m

The solution of Eq. (I0) has the form

ay-- CeS" +

I

-

-

(t2)

"~sin p i A' (-9 e-":dz, 0

where C is an arbitrary constant. Stress component o x is expressed in terms of Oy, which follows from Eq. 4 I -- sinp

O,= ~ 6 y - -

A (z)

Arbitrary constant C can be determined from boundary condition Ox[x= 0 - 0. A (0) C ~= i _i,sin

where

A o = A (0) =

Ao P -- I -- sin p'

c~ p

(13)

I +sinp"

Then

(14)

-~j -- ma o sin p .

Stress components in the limiting zone of the coal seam edge are written

a~

~ "

jl--sxap

(16)

0

In calculating stress in the limiting zone it is normally assumed that cohesion in the coal seam is constant. We write stress components for this case assuming that gas pressure can be approximated by expression (8). Then stress components in the limiting zone are written:

.,.o

where

,r,@,,=>

+T

+...+

,,<.,<.>

P. (x) = ~" alxl.

(17) (18)

Considering the change in strength characteristics, in practical calculations in a number of cases we limit ourselves to constant values of cohesion and gas pressure. With constant values of K and P Eq. (17) is considerably simplified and it is written:

401

2 (k cos p mP sin p) '( J - - m) ( 1 - - sin p) , t - -

Oe--

"~t'+'!"% "

(19)

l-*mp

It was assumed above that gas pressure (8) in the limiting zone of the roof of a coal seam is known. Besides this, in practical calculations approxlmationfactors are not always known. Therefore, we find gas pressure distribution on the basis of using mechanics equations for two-phase materials [5]. We consider a regime of steady-state filtration. equation for the gas component is written:

a~ _ i,(I -,,,) W. aZ

'

With plane-parallel gas movement the

0;

(20)

a

a (p~,,,w.) ,,. O,

( 21 )

az

where P2 is gas density, N/m3; p is dynamic viscosity, Nsec/m=; u is a coefficient proportional to penetrability; W x is average gas movement, m/sec. To a first approximation rock characteristics P2, u, a, and m w i l l b e stant. Then the solution of system (20) with boundary conditions:

PI...

-

P.,

assumed to be con-

PI.-, - P,

is the following expression P = P,

P . -- PI Z

i

"

(22)

Stress components in the limiting region of the coal seam edge in this case are written: 2 (k cos P--mPasuP) ~

2" sm P(Pa-- Pt)

(23)

Determination of support pressure parameters around a coal face working are connected with consideration of elastoplastic problems for the stress--strains state of the coal seam. In considering stresses in the elastic region of the seam it is possible by limiting ourselves to analysis of stresses and strains in a thin seam to reduce the problem to solving an integral equation. Currently solution of this equation can only be obtained numerically in a computer. In practice another approach is more widespread when the rule for stress distribution in the elastic region is previously prescribed. Experimental data and theoretical calculations are used in order to select the form of the rule. This approach is contained in [i, 3, 4, etc. ]. On the basis of these works distribution of stresses o v normal to the seam can be approximated by the relationship

[

"I

av--YH t + ( K o - l ) e-'~,

(24)

where b is half the linear dimension of the worked-out space, m; K 0 is stress concentration factor. The size of the limiting condition znoe C and value of coefficient K0 are determined from the stress Oy continuity condition with x - C and equality to zero of the projection of the vector for all of the additional forces on axis OY (Fig. 2)

Qo+O,-Q2+Q3,

(25)

where Q0 is rock mass component, and values of QI, Q2 and Q~ are calculated by the equations:

402

r

Q, - ?Ha - - S o,,dz;

(2 6 )

Q i.

Q, = [

o,dx

yH

--

(C --

a);

(27)

a

Q,

: ~. (or - - ?H) dz.

( 28 )

c

We find components QI, Q2, Q, of Eq. (25). The component of additional forces in the elastic region is calculated by the equation

Q, = ,~ {?Hfi + (Ko - - t)e -z/b] -- ?fir} dz == ?H (K o -- t ) e -~/b.

(29)

e

Components Qz and Q2 in the limiting region with stresses (16) have the form

Q, = ?Ha-- ~ 11-"4~8t-p) (eBa_ i) --

(,) e - ~ dz dz;

e~ 0

i --sinp

!--e,np a

( 30 )

0

(31)

0

The component of mass for hanging rock Q0 can be found by the following equations: for workings in which caving of the rock stratum has not occurred

(32)

Qo = yH---~, where s is width of the working, m;

for coal face workings with complete rock stratum subsidence into the worked-out space component Q0 depends on the working regime of the main roof and it can be approximately determined as the weight of rock bounded by the caving lines Btg~

Qo = ? B ' ~ v + where s deg.

2

'

(33)

is roof caving increment for the main roof, m; ~ is rock stratum caving angle,

As results of full-scale observations show [6], the value of rock caving angle varies from 15 to 25 ~ . The value of a is found from the equation

?H =

,a~

)

' A o ~-

(34)

A' (z) e-~' dz . 0

Concentration factor K0 for stresses Oy can be determined from the continuity condition for them at the interface of plastic and elastic materials x = C

Koft

+ e ~/b ~?H (t -- sin p)

/ |Ao + k

*

)}

(35)

a

Dimensions of the zone for limiting strains C in the boundary zone of the coal seam are found by Eq. (25) by introducing into it constants Qz, Q2, and Qs

403

~r

Fig. 2.

Diagram of support pressure distribution coal seam.

Q0-

Ao(~--,) i~ iA'(,).-~. __ A.(tP~--'') ~----,[Y~a z a x = ~1--,inp)

~(i-smp)

$

e

c

J V--"'~ p dz d.x - - yHC 4 ! C Kn p Ao +

a

Relationship solution can only

0

x

-- J

in a

o

(36)

\

A" (z) e - ~ d z ) - - ~Hb. o

( 3 6 ) i s an i n t e g r a l equation relating be f o u n d by u s i n g a c o m p u t e r .

t o unknown v a l u e

C, a n d i t s

For practical calculations in relationship (8) to a first approximation it to limit ourselves to a first degree polynomial (22). We w r i t e t h e r e l a t i o n s h i p lating support pressure parameters with a change in gas pressure in the limiting seam a c c o r d i n g t o r u l e ( 2 2 ) . We f i n d

numerical

is possible for calcuzone of the

c o m p o n e n t s Q1 a n d Q2

Q, - vHa [ ~ ( | -2- m (e~a - t) [ ) ( l --sinp) (g r

2(~_eJ~)

[

Q2 - ~ ( I - m) ( 1 --sin p) (g cos ,o -

m (P. -- Pl) sin p ]

r a P . s i n p) +

raP. sin p) +

~l

~

{P. -- Pt) sin p

] 4- (l--m)(1--sinp)~t'

m(Po--Pt)sin p

?~.;c--a~(P.--P:tsinp]

~

t I - m) ( I -- sin p) ~

- - yH (c - - a).

(37)

(38)

Values of a and Ko are determined from the relationships "fH=

2 (~ cos p -- raP. s i n p) 2 m s i n p ( e . - - Pl) ( l - - m) (l -- sin p) eSa4- {l -- m) {l -- sin p) [~/ (#a__|),

K o - I + e~" [2 (x cos .o- rap. ,in p) e~ + LTH ( l - - m~ (l - - s i n p)

2,,, ,i,, p (p~ - ~,~

(39)

]

y H ~1 - - m ) { 1 - - s i n p) [~l ( e ~ - -

t) --

t .

(40)

The size of the limiting deformation zone in the boundary region of the coal seam is determined from the equation 2[(l+b~}el~__l] [.... Qo 4- ~lH (c 4- b) f= [~(l_m)~l_sinp)L~SCOsp--mP. sinp) 4- rn(P.--P:)sinp]~t The s i z e a)

of the zone for for workings

limiting

is

found from the equations:

in which caving has not occurred

vH( + 404

deformations

2m(c'['b)(Pa--Pt)sinP(I--m)(t--sinp)[3t( 4 1 )

2[('§ b")e~--1} (~ COS O -- repay sinp); + b) 4-'fHC f= [~(l_m)(l_sinp ) .

(42)

b)

for coal face workings with caving of the main roof V H ~cav ~ H ~

+b) + T H C =

~(i2 [(t ~--,l]_m)(l+ b~} sinp)9 {~ c~p-- mPav sin p).

(43)

As an example we introduce calculation of support pressure parameters for the burstprone seem of the Moshchnyi pit "Yur-Shor" of the Production Association 'Workutaugos Starting data are: coal ultimate strength Oco = 16 RPa; value of coal cohesion and internal friction angle are determined by the relationship (2)-(3); H - 670 m; Pay = 3.55 RPa; 2h - 3.8 m; ~ - 18~ &car = 12 m; Pl = 29~ the proportion of the gas component in the coal seem according to results of experimental studies [4] is taken as m = 0.2. Results of calculations for the distance from the coal face operations to the maximum support pressure C, values of stress concentration factor K0 and the values of maximum stresses Q2 carried out by (43), (40), (38), are 9.3, 1.17, and 47 MPa respectively. Comparison of these values with full-scale measurements of rock pressure parameters carried out by the authors and other researchers [3] in the "Yur-Shor" mine have shown good agreement, which was within the limits 80-90%. Thus, the calculation procedure suggested taking account of gas pressure in a seem and coal moisture content can be used with a sufficient degree of reliability for determining support pressure parameters in coal faces in solving practical problems of mining production. LITERATURE CITED i. 2.

3. 4. 5. 6.

A . N . Stavrogin and A. G. Protosenya, Strength of Rocks and Stability of Working at Considerable Depths [in Russian], Nedra, Moscow (1985). O . V . Kovalev and Yu. I. Kalimov, "Improvement of the effficiency of hydraulic squeezing as a method for combating sudden outbursts," in: Technology for Mining and Enrichment of Coal in the Pechorsk Basin [in Russian], Nedra, Moscow (1971). L.M. Gusel'nikov and P. A. Reipol'skii, Change in the Stressed State of a Rock Mass with Hydraulic Treatment [in Russian], Nedra, Moscow (1977). V . V . Khodot, Sudden Outbursts of Coal and Gas [in Russian], Izd. GNTI, Moscow (1961). V . N . Nikolaevskii, K. S. Basniev, A. T. Gorbunova, et al., Mechanics of Impregnated Porous Materials [in Russian], Nedra, Moscow (1970). I.M. Petukhov et al., Protective Seems [in Russian], Nedra, Leningrad (1972).

405