research article analytical investigation for in situ...

Research ArticleAnalytical Investigation for In Situ Stress Measurement withRheological Stress Recovery Method and Its Application

Quansheng Liu12 Jingdong Jiang1 Chengyuan Zhang2 and Yuanguang Zhu2

1School of Civil Engineering Wuhan University Wuhan 430072 China2State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil MechanicsChinese Academy of Sciences Wuhan 430071 China

Correspondence should be addressed to Quansheng Liu liuqswhrsmaccn

Received 10 October 2015 Revised 5 December 2015 Accepted 8 December 2015

Academic Editor Marek Lefik

Copyright copy 2016 Quansheng Liu et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In situ stress is one of the most important parameters in underground engineering Due to the difficulty and weakness ofcurrent stress measurement methods in deep soft rock a new one rheological stress recovery (RSR) method to determine three-dimensional stress tensor is developed It is supposed that rock stresses will recover gradually with time and can be measured byembedding transducers into the borehole In order to explore the relationship between the measured recovery stress and the initialstress analytical solutions are developed for the stress measurement process with RSR method in a viscoelastic surrounding rockThe results showed that themeasured recovery stress would bemore close to the initial stress if the rockmass has a better rheologicalproperty and the property of grouting material should be close to that of rock mass Then the RSR method as well as overcoringtechnique was carried out to measure the in situ stresses in Pingdingshan Number 1 coal mines in Henan Province China Thestress measurement results are basically in the same order and the major principal stresses are approximately in the direction ofNW-SE which correlates well with the stress regime of Pingdingshan zone known from the tectonic movement history

1 Introduction

In situ stress is one of the most important parameters fordesigning stable underground structures and improvingmin-ing methods in deep soft rock Rock stresses originate fromgravity and tectonic forces and can only be inferred by drillinga borehole making a slot and coring the rock [1] A largenumber of stress measuring methods have been developedand a detailed summary of these techniques can be found inAmadei and Stephansson [2] Ljunggren et al [3] Corthesyet al [4] and Ulusay [5]

However with the decrease of shallow coal resourcesin China most of the key collieries have mined deep coalseams [6] the surrounding rocks of which tend to be softand fragmentized There exist limitations and measurementerrors in common methods for stress measurement of softrocks and effective testing is very difficult

Hydraulic fracturing (HF) can only determine the maxi-mal and minimal principle stresses in a plane vertical to theborehole and is limited in highly anisotropic and fractured

rock [7] Although hydraulic tests on preexisting fractures(HTPF) can determine the 3D stress tensor by testing a largenumber of fractures along the borehole [8ndash10] it is notan efficient method due to its assumptions Borehole reliefmethod [11ndash13] would be strongly influenced by the stresspath constitutive law and associated parameters in the inter-pretation of stress measurement [4] Other stress measuringmethods such as borehole breakout [14] and Kaiser effect[15] which estimate rock stresses based on the phenomenonrelevant to stresses have relatively low reliability and are con-troversial as a method to determine in situ stress Anelasticstrain recovery (ASR) method [16ndash18] requires orientatedrock cores and is affected by a lot of factors (eg temperaturevariation dehydration of samples and accurate orientation)[19] Therefore it is important to develop a new method tomeasure in situ stress in deep soft rock

A newmethod for in situ stress measurement in deep softrocks namely rheological stress recovery (RSR) method isproposed in this studyThe advantages of thismethod are thatit is simple inexpensive and 3DThe basic principles testing

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 7059151 12 pageshttpdxdoiorg10115520167059151

2 Mathematical Problems in Engineering

Sensing faces

(a)

Pushrod

Triangle pulley

Goniometer

(b)

Explosion-proofenclosure

Data logger

TDPT

(c)

Figure 1 Test equipment of RSR method (a) TDPTs (b) pushrod and the goniometer (c) explosion-proof data logger

equipment calculation equations and related procedures ofRSR method will be briefly introduced Then the measuringprocess is analyzed by analytical solutions to explore theapplicability and accuracy of this method Finally the RSRmethod as well as overcoring technique was conducted inPingdingshanNumber 1 coalmine tomeasure both the in situstress orientation and magnitude at a depth of 877m

2 An Outline of RSR Method

21 Basic Principles A large number of field monitoring andlaboratory tests [20 21] have shown that rheological proper-ties of soft rocks are very significant under high geostressEven for hard rock mass that is cut by several joints and frac-tures creep deformation can also attain considerable mag-nitude [22] Thus a borehole will shrink gradually to beclosed under high geostress due to the rheological charac-teristic of soft rocks and rock stresses will recover to theinitial stress state with the growth of the time Based onthis stress measurement with RSR method is proposed It issupposed that rock stresses around the pressure transducersthat are embedded in the borehole will recover graduallyand eventually tend to be stable due to the rheologicalcharacteristics of surrounding rocks

22 Main Equipment The equipment used in this methodinvolves pressure transducers push rods with orientationdevice and a data logger shown in Figure 1 A three-dimensional pressure transducer (TDPT) which can mea-sure normal stresses in three directions is developed for insitu stress measurement with RSRmethod (Figure 1(a)) and atest point needs twoTDPTs in different directionsTheTDPTwhich contains three sensing faces (diameter = 58mm) is awaterproof cube structure (side length = 80mm) and suitablefor a pressure up to 30MPa Vibrating wire force transducersare adopted on each sensing face due to the advantages of highaccuracy and repeatability possibility for remote measuringdigitalization of results long service stability [23] and so

forth Eight corners of the TDPT have been cut out for therequirements of miniaturizationThe pushrod is used to sendthe transducers to the test point and the rotation angles ofthe transducer are recorded by the goniometer in order tocalculate the azimuth angle of each sensing face The datalogger is developed through explosion-proof design to meetthe requirement of coal mine shown in Figure 1(c)

23 Testing Procedures The RSR method for measuringthe stress in deep soft rocks comprises the following steps(Figure 2)

(1) A borehole is drilled till the test point in surroundingrocks of a soft rock tunnel

(2) Stress transducers are fixed on a connecting rod andsent to the test point a direction cosine of any twosensing faces in the normal direction is recorded andis not 1 a normal stress measuring device is mountedon each sensing face and connected with a data loggeroutside the borehole through long cables

(3) Grouting is carried out on the drilling hole and theborehole is sealed after being entirely filled

(4) After the grout is solidified pressure values arecontinually read from the data logger and six stressvalues are substituted into the calculation equationsafter the values are stable so as to obtain 3D rockstress at the test point With the adoption of thismethod evolutional stress data of the test point canbe also obtained Moreover the spatial variation andevolution of rock stress state can bemeasured througha series of pressure transducers embedded in differentdepth of the borehole

24 Calculation Equations A spatial coordinate system 119900119909119910119911

is established by taking normal directions of three mutu-ally perpendicular sensing faces as directions of coordinateaxes and 119909

1015840- 1199101015840- and 119911

1015840-axis are normal directions of

Mathematical Problems in Engineering 3

Grout

TDPTsPushrods

Borehole

Tunnel

Data logger

Cables

Figure 2 Sketch of stress measurement process with RSR method

other sensing faces 120590119909 120590119910 120590119911 1205901015840

119909 1205901015840

119910 1205901015840

119911are normal stresses

measured by each sensing face respectively The stress state(120590119909 120590119910 120590119911 120591119909119910 120591119910119911 120591119911119909) of the test point under the coordinate

system 119900119909119910119911 can be calculated through

1205901015840

119909= 1198972

1120590119909+ 1198982

1120590119910+ 1198992

1120590119911+ 211989711198981120591119909119910

+ 211989811198991120591119910119911

+ 211989911198971120591119911119909

1205901015840

119910= 1198972

2120590119909+ 1198982

2120590119910+ 1198992

2120590119911+ 211989721198982120591119909119910

+ 211989821198992120591119910119911

+ 211989921198972120591119910119911

1205901015840

119911= 1198972

3120590119909+ 1198982

3120590119910+ 1198992

3120590119911+ 211989731198983120591119909119910

+ 211989831198993120591119910119911

+ 211989931198973120591119910119911

(1)

where 120591119909119910 120591119910119911 and 120591

119911119909are shear stress components under the

coordinate system 119900119909119910119911 1198971 1198972 and 119897

3 respectively represent

direction cosines between 1199091015840- 1199101015840- and 119911

1015840-axis and 119909-axis1198981 1198982 and 119898

3 respectively represent direction cosines

between 1199091015840- 1199101015840- and 119911

1015840-axis and 119910-axis and 1198991 1198992 and 119899

3

respectively represent direction cosines between 1199091015840- 1199101015840- and

1199111015840-axis and 119911-axis

3 Definition of the Problem

In this paper a two-dimensionalmodel of the stressmeasure-ment process is conducted to determine the recovery stress onthe pressure transducer The transducer which is adhered tothe borehole by elastic grout layer is thought to be hollow andelastic The cross sections of the transducer grout layer andthe borehole are circular and concentric shown in Figure 3The interfaces between the rock and the grout layer andbetween the grout layer and the transducer are assumed to besmooth The surrounding rocks are homogeneous isotropicand linearly viscoelastic and the lateral pressure coefficient is120582

Regarding the above assumptions the problem is con-sidered as a two-dimensional (2D) infinite viscoelastic planesubjected to a biaxial stress which treats a geometricallysimilar problem with tunnel linings in circular tunnels

P

r

r0

r0

r1

r1

r2

p(t)p(t)

120582P

q(t)

q(t)

Rock Grout layer (t gt t0) Transducer (t gt t0)

Figure 3 Illustration of the radii of the grout layer and the trans-ducer

[24 25] The process of stress measurement can be dividedinto two stages During the first stage spanning fromboreholeexcavation until the time at 119905 = 119905

0 pressure of the

surrounding rock is released and there is no pressure on thegrout layer and the transducer The second stage spans fromthe time of the solidification of the grout at 119905 = 119905

0 onwards

The contact pressures between the rock and the grout layerand between the grout layer and the transducer which willvary with time are assumed as 119901(119905) and 119902(119905) respectively

For such a biaxial plane strain condition a cylindricalcoordinate system (119903 120579 119911) is employed and the in situ stressat infinity (119903 = infin) can be written as follows

120590119903=

119875

2

[(1 + 120582) + (1 minus 120582) cos 2120579]

120590120579=

119875

2

[(1 + 120582) minus (1 minus 120582) cos 2120579]

120591119903120579

= minus

119875

2

(1 minus 120582) sin 2120579

(2)

where 120590119903is the radial stress of the rock 120590

120579is the hoop stress of

the rock 120591119903120579is the shear stress of the rock and119875 is the vertical

in situ stressThe in situ stress can be divided into two parts uniform

part and nonuniform part Correspondingly the contactpressures on the interfaces can also be divided into uniformpart and nonuniform part

119901 (119905) = 1199010(119905) + 119901

1(119905) cos 2120579

119902 (119905) = 1199020(119905) + 119902

1(119905) cos 2120579

(3)

where 1199010(119905) and 119902

0(119905) are contact stresses under uniform

in situ stress and 1199011(119905) cos 2120579 and 119902

1(119905) cos 2120579 are contact

stresses under nonuniform in situ stressAfter the grout is solidified (119905 gt 119905

0) the boundary condi-

tion for this problem is

119906119903119888(1199030 119905) = 119906

119903(1199030 119905)

119906119903119879

(1199031 119905) = 119906

119903119888(1199031 119905)

(4)

where 119906119903 119906119903119888 and 119906

119903119879are the radial displacements in the

rock the grout layer and the transducer respectively 1199030is


the radius of the borehole and 1199031is the external radius of the

transducer

4 Solution for the Problem

41 The Forms of Solution in Laplace Domain under UniformStress Field According to the correspondence principle theviscoelastic displacement of the rock under uniform in situstress (119875(1+120582)2) at the borehole wall (119903 = 119903

0) can be written

as [24 26]

1199061198750

(1199030 119905) =

1198751199030

4

(1 + 120582) 119869 (119905) (5)

where 119869(119905) is the shear creep compliance andwill be describedin more detail below

The radial displacement of the rock under uniform in situstress after time 119905

0is

Δ1199061198750

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 (6)

where Δ119869 = 119869(119905 + 1199050) minus 119869(119905

0)

After time 1199050 contact pressures exist on the interface

between the rock and the grout layer Then the total radialdisplacement of the rock at the borehole wall (119903 = 119903

0) can be

written as

1199061199030

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 minus

1199010(119905) 1199030

21198660

(7)

where 1198660is the shear modulus of the rock

The Laplace transform of a function 119891(119905) is defined as

119891 (119904) = int

infin

0

119891 (119905) 119890minus119904119905

119889119905 (8)

where 119904 is the transform parameter and the inverse Laplacetransform is expressed by

119871minus1

[119891 (119904)] = 119891 (119905) =

1

2120587119894

int

120573+119894infin

120573minus119894infin

119891 (119904) 119890119904119905119889119905 (9)

The Laplace transform of (7) gives rise to

1199061199030

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 minus

1199010(119904) 1199030

21198660(119904)

(10)

The grout layer is thought to be linear elastic and 119866119888

120583119888are the shear modulus and Poissonrsquos ratio respectively

The radial displacements of the grout layer under contactpressures (119901

0(119905) and 119902

0(119905)) in the Laplace domain at 119903 = 119903

0

and 119903 = 1199031 are

1199061198880

(1199030 119904) =

1199010(119904) 1199030

2119866119888

1198981198880

minus

1199020(119904) 1199030

2119866119888

1198991198880

1199061198880

(1199031 119904) =

1199010(119904) 1199030

2119866119888

1198981015840

1198880minus

1199020(119904) 1199030

2119866119888

1198991015840

1198880

(11)

where

1198981198880

=

1199032

1+ (1 minus 2120583

119888) 1199032

0

1199032

0minus 1199032

1

1198991198880

=

1199032

1(2 minus 2120583

119888)

1199032

0minus 1199032

1

1198981015840

1198880=

1199032

0(2 minus 2120583

119888)

1199032

0minus 1199032

1

1198991015840

1198880=

1199032

0+ (1 minus 2120583

119888) 1199032

1

1199032

0minus 1199032

1

(12)

are constant coefficients of parameters 1199030 1199031 and 120583

119888

The radial displacement of the transducer on the inter-faces between the grout layer and the transducer (119903 = 119903

1) in

Laplace domain is

1199061198790

(1199031 119904) =

1199020(119904) 1199031

2119866119879

1198981198790

(13)

where119866119879 120583119879are the shear elasticmodulus and Poissonrsquos ratio

of the transducer respectively and

1198981198790

=

1199032

2+ (1 minus 2120583

119879) 1199032

1

1199032

1minus 1199032

2

(14)

is a constant coefficient of parameters 1199031 1199032 and 120583

119879

42 The Forms of Solution in Laplace Domain under Nonuni-form Stress Field To simplify the solution of this problemthe Poissonrsquos ratio of the rock 120583

0is assumed to be a constant

and then the total radial displacement of the rock undernonuniform stress field at the borehole wall (119903 = 119903

0) in the

Laplace domain is

1199061199031

(1199030 119904) =

1 minus 120582

4

(3 minus 41205830) 1198751199030Δ119869

minus

1199011(119904) 1199030

61198660(119904)

(5 minus 61205830) cos 2120579

(15)

The Laplace transform of the radial displacement of thegrout layer on the interface (119903 = 119903

0and 119903 = 119903

1) under

nonuniform contact pressures can be written as

1199061198881

(1199030 119904) =

1199011(119904) 1199030

2119866119888

1198981198881cos 2120579 minus

1199021(119904) 1199030

2119866119888

1198991198881cos 2120579

1199061198881

(1199031 119904) =

1199011(119904) 1199031

2119866119888

1198981015840

1198881cos 2120579 minus

1199021(119904) 1199031

2119866119888

1198991015840

1198881cos 2120579

(16)

Define

1198981198881

= 1198911198881

minus 1198911198885119903minus4

0+ 212058311988811989111988831199032

0minus 2 (1 minus 120583

119888) 1198911198887119903minus2

0

1198991198881

= 1198911198882

minus 1198911198886119903minus4

0+ 212058311988811989111988841199032


119888) 1198911198888119903minus2

0

1198981015840

1198881= 1198911198881

minus 1198911198885119903minus4

1+ 212058311988811989111988831199032


119888) 1198911198887119903minus2

1

1198991015840

1198881= 1198911198882

minus 1198911198886119903minus4

1+ 212058311988811989111988841199032


119888) 1198911198888119903minus2

1

1198911198881

=

1199036

0+ 1199034

01199032

1+ 21199032

01199034

1

(1199032

0minus 1199032

1)3

1198911198882

=

21199034

01199032

1+ 1199032

01199034

1+ 1199036

1

(1199032

0minus 1199032

1)3


1198911198883

= minus

1199034

0+ 31199032

01199032

1

3 (1199032

0minus 1199032

1)3

1198911198884

= minus

31199032

01199032

1+ 1199034

1

3 (1199032

0minus 1199032

1)3

1198911198885

=

31199036

01199034

1+ 1199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198886

=

1199036

01199034

1+ 31199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198887

= minus

21199036

01199032

1+ 1199034

01199034

1+ 1199032

01199036

1

(1199032

0minus 1199032

1)3

1198911198888

= minus

1199036

01199032

1+ 1199034

01199034

1+ 21199032

01199036

1

(1199032

0minus 1199032

1)3

(17)

The Laplace transform of the radial displacement of thetransducer on the interface (119903 = 119903

1) under nonuniform

contact pressure is expressed as follows

1199061198791

(1199031 119904) =

1199021(119904) 1199031

2119866119879

1198981198791

cos 2120579 (18)

where

1198981198791

= 1198911198791

minus 1198911198793

119903minus4

1+ 21205831198791198911198792

1199032


119879) 1198911198794

119903minus2

1(19)

with

1198911198791

=

1199036

1+ 1199034

11199032

2+ 21199032

11199034

2

(1199032

1minus 1199032

2)3

1198911198792

= minus

1199034

1+ 31199032

11199032

2

3 (1199032

1minus 1199032

2)3

1198911198793

=

31199036

11199034

2+ 1199034

11199036

2

3 (1199032

1minus 1199032

2)3

1198911198794

= minus

21199036

11199032

2+ 1199034

11199034

2+ 1199032

11199036

2

(1199032

1minus 1199032

2)3

(20)

43 Determination of the Contact Pressures According to theboundary condition (4) the boundary compatibility condi-tions in the Laplace domain are

1199061199030

(1199030 119904) = 119906

1198880(1199030 119904)

1199061199031

(1199030 119904) = 119906

1198881(1199030 119904)

1199061015840

1198880(1199031 119904) = 119906

1198790(1199031 119904)

1199061015840

1198881(1199031 119904) = 119906

1198791(1199031 119904)

(21)

Submitting (10)ndash(18) into (21) the following can be ob-tained

1199010(119904) =

Δ119869

11198660(119904) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) (1198661198791198991015840

1198880+ 1198661198881198981198790

) 119866119888)

sdot

1 + 120582

2

119875

1199020(119904) =

Δ119869

((1198661198791198661198881198991015840

1198880+ 1198662

1198881198981198790

) 1198661198791198661198881198981015840

1198880) (1119866

0(119904)) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) 1198661198791198661198881198981015840

1198880)

sdot

1 + 120582

2

119875

1199011(119904) =

(3 minus 41205830) Δ119869

((5 minus 61205830) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) (1198661198791198991015840

1198881+ 1198661198881198981198791

) 119866119888)

sdot

1 minus 120582

2

119875

1199021(119904) =

(3 minus 41205830) Δ119869

((1198661198791198991015840

1198881+ 1198661198881198981198791

) 1198661198791198981015840

1198881) ((5 minus 6120583

0) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) 1198661198791198661198881198981015840

1198881)

sdot

1 minus 120582

2

119875

(22)

44 Analytical Solution for 3-Parameter Solid Model For thetime-dependent behavior of soft or highly jointed rock massor rock mass with high in situ stress the 3-parameter solidmodelmay be commonly employed as shown in Figure 4 theshear creep compliance is written as

119869 (119905) =

1

1198661

+

1

1198662

(1 minus exp(minus

1198662119905

120578

)) (23)

where1198661 1198662are the shear moduli and 120578 is the viscosity coef-

ficientsThe differential equation of 3-parameter solid model can

be written as

1 + 1198753 = 119876

3120574 + 119876

4 (24)


G1

G2

120578

Figure 4 Sketch of 3-parameter solid model

where

1198753=

120578

1198661+ 1198662

1198763=

11986611198662

1198661+ 1198662

1198764=

1205781198661

1198661+ 1198662

(25)

Then the contact pressure on the transducer can be ob-tained

119902 (119905) = 1199020(119905) + 119902

1(119905) cos 2120579 =

1 + 120582

2

119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198771+ 119866infin1198772

(1 minus exp(minus

1198771+ 11987631198772

11987531198771+ 11987641198772

119905))

+

1 minus 120582

2

(3 minus 41205830) 119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198773+ 119866infin1198774

(1 minus exp(minus

1198773+ 11987631198774

11987531198773+ 11987641198774

119905))

sdot cos 2120579

(26)

where119866infin

= 11986611198662(1198661+1198662) is the long-term shearmodulus

119866ini = 1198661is the initial shear modulus and

1198771=

1198661198791198991015840

1198880+ 1198661198881198981198790

1198661198791198981015840

1198880

1198772=

1198661198791198991015840

1198881+ 1198661198881198981198791

1198661198791198981015840

1198881

5 minus 61205830

3

1198773=

11986611987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880

1198661198791198661198881198981015840

1198880

1198774=

11986611987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881

1198661198791198661198881198981015840

1198881

(27)

Paying attention to the analytical expression derived forthe contact pressure on the transducer (119902(119905)) for 3-parametersolid model instead it can be found that the stable contactpressure on the transducer (119902(infin)) is dependent mainly onthe mechanical properties of the rock mass the solidificationtime of the grout (119905

0) and the shear moduli of the grout

layer as shown in (26) With the decrease of the long-term shear modulus of the rock the contact pressure on the

0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900

t0 = 0

t0 = 10ht0 = 20ht0 = 50h

t0 = 100ht0 = 200ht0 = 500h

Figure 5 The ratio of the contact pressure (119902(119905)) on the transducerto the in situ stress calculated at 120579 = 0

∘ for various solidificationtimes

transducer increases In order to expound the effects of thegrout solidification time (119905

0) the shear moduli of the grout

and the properties of the rock mass on the contact pressures(119902(119905)) parametric investigations have been presented here

Regarding the geometrical properties of this problem wehave 119903

0= 65mm 119903

1= 55mm 119903

2= 50mm 119875 = 1MPa and

120582 = 12 The values of the mechanical properties are 119866119888

=

4GPa 120583119888= 035 119866

119879= 80GPa and 120583

119879= 025 According to

the experiment tests and back analysis [20 25] the followingvalues can be assumed 119866

1= 2576MPa 119866

2= 1903MPa 120578 =

31671198905MPasdoth and 1205830

= 035 for 3-parameter solid modelFor the sake of explanation the ratio of the contact pressureto the in situ stress will be presented in Figures 5 6 and 7

The solidification time of the grout is assumed to be sevenvalues 0 10 h 20 h 50 h 100 h 200 h and 500 h The generaltrend is that the contact pressures increase gradually andreach stability after a period of time

In Figure 5 it can be found that the contact pressureson the transducer develop to be stable over time When thesolidification time increases the ratio of the stable contactpressure to the in situ stress decreases from 60 to 0 Thusit can be concluded that the less solidification time will bebeneficial for the recovery of the contact pressure on thetransducer

45 Influence of the ShearModulus of the GroutMaterial Theshear modulus of the transducer is a fixed value of 80GPaNine values of the modulus of the grout material (119866

119888) are

selected and the transducer-groutmodulus ratios are 1 1 2 15 1 10 1 25 1 50 1 100 1 200 1 and 500 1 respectivelyThe influence of the shear modulus of the grout material isanalyzed for a solidification time of 119905

0= 10 h

In Figure 6 the results of the ratio of the contact pressures(119902(119905)) on the transducer to the in situ stress calculated at


0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900

Gc GT = 1 1Gc GT = 1 10Gc GT = 1 100Gc GT = 1 2Gc GT = 1 25

Gc GT = 1 200Gc GT = 1 5Gc GT = 1 50Gc GT = 1 500

(a)

0 100 200 300 400 500

025

030

035

040

045

050

055

060

Ratio

of s

tabl

e rec

over

y str

ess t

o in

situ

stre

ss

GTGc

(b)

Figure 6 Results for different shear moduli of the grout material (a) ratio of the contact pressure (119902(119905)) to in situ stress (b) ratio of stablerecovery stress to in situ stress

120579 = 0∘ with different shear moduli of the grout material are

plotted It can be found that the contact pressure increasesgradually and reaches stability after a period of time andthe ratio of the stable recovery pressure on the transducerto the in situ stress first increases and then decreases withthe increase of transducer-grout modulus ratio as shownin Figure 6 When the transducer-grout modulus ratio isbetween 20 1 and 50 1 the stable recovery pressure on thetransducer reaches the maximum value (about 60 of thein situ stress) From these figures it emerges that suitablegroutmaterial is important for transducers to achieve optimalstresses The type of the grout material should be determinedafter the mix proportion test before field application Thegrout material used in the field test should have goodmechanical properties and are made into samples to measurethemechanical parameters in the lab Moreover it is essentialto carry out calibration tests for the transducer using differentgrouting materials before its field application

46 Influence of the Properties of the Rock Mass To illustratethe influence of the properties of the rock mass on therecovery stresses measured by the transducer an example ispresented herein The properties of the grouting material areassumed to be the same with that of rock masses The shearmodulus 119866

1is fixed and 119866

2are assumed to be six different

values and the ratio of the initial modulus 119866ini to the long-termmodulus 119866

infinis 12 15 2 3 5 11 21 and 51 accordingly

The results have been shown in Figure 7In Figure 7(a) it can be found that the recovery stresses

measured by the transducer increase gradually and reachstability after a period of time From Figure 7(b) withthe reduction of the long-term modulus 119866

infin that is the

increase of themodulus ratio1198660119866infin the final recovery stress

increasesWhen themodulus ratio is greater than 10 the finalrecovery stress gradually turns to be stable and is above 90of the initial stress From the figures it emerges that if the rockmass has a better rheological property the recovery stressmeasured by the transducer is more close to the initial stressMoreover in practical measurement the final recovery ratiocan be obtained from the initial long-term modulus ratio1198660119866infinwhich can be calculated through creep experiment of

rockmasses according to the curves in Figure 7(b) and the insitu stress can be evaluated from the final recovery ratio andthe practical measured recovery stresses

5 Field Test

The in situ stressmeasurements were carried out in Pingding-shan Number 1 coal mine situated in Henan Provincenorthern China as shown in Figure 8 The Pingdingshancoalfield is about 38 km long EndashW and 20 km wide NndashS and the coal-bearing sediments are mostly of Permianage mainly comprising sandstone sandy mudstone andcarbonaceous shale besides coals which are overlain by theTertiary andQuaternary deposits [27]The general structuralconfiguration of Pingdingshan coal mine is a series of NWfolds in which the major one is Likou syncline It is a broadand gentle fold appearing as a brush structure converging tothe southeast and diverging to the northwest There are someother secondary folds in this area for example Guozhuanganticline Niuzhuang syncline and Zhugemiao anticline inthe south of Likou syncline and Baishigou anticline Ling-wushan syncline and Xiangxia fault in the north of Likousyncline


0 200 400 600 800 100000

02

04

06

08

10

t (h)

q(t

)1205900

G1G2 = 1 5G1G2 = 4 1G1G2 = 1 2G1G2 = 10 1

G1G2 = 1 1G1G2 = 20 1G1G2 = 2 1G1G2 = 50 1

(a)

0 10 20 30 40 5001

02

03

04

05

06

07

08

09

10

Fina

l rec

over

y str

ess r

atio

GiniGinfin

(b)

Figure 7 Results for different rock properties (a) ratio of the contact pressure (119902(119905)) to in situ stress (b) ratio of stable recovery stress to insitu stress

Table 1 In situ stress magnitudes by overcoring technique using different elastic parameters at the horizontal borehole

Parameter 1205901

1205902

1205903

119864 (GPa) ] Magnitude (MPa) Azimuth (∘) Dip (∘) Magnitude (MPa) Azimuth (∘) Dip (∘) Magnitude (MPa) Azimuth (∘) Dip (∘)5 031 2292 14556 445 1829 33199 8553 1501 23559 0508 031 3445 14315 507 2720 34827 8440 2266 23336 237

The test site of Pingdingshan Number 1 coal mine islocated at a track-dip tunnel with a vertical buried depthof about 877m the lithology of which is dark gray sandymudstone The in situ stress measurements were carried outin both horizontal and vertical boreholes with 30m in depthand 130mm in diameter The sketch of borehole layout isshown in Figure 9 The horizontal borehole was inclined tothe horizontal plane at 10∘ Before the application of theRSR method overcoring technique was carried out in thehorizontal borehole according to the ISTM standard [28]After overcoring the rock core including the hollow inclusiongaugewas calibrated in the calibration instrument In order toobtain themechanical parametersmore accurately rock coresdrilled from the testing borehole were prepared into standardspecimens with 50mm in diameter and 100mm in lengthThe elastic parameters were determined by several specimensfrom uniaxial compression experiment in lab Then theTDPTs were installed at the overcoring position accordingto the testing procedures of RSR method The appropriategrouting materials were selected after a mix design in the labto make the property of grouting materials close to that ofrock masses

6 Results and Discussion

The overcoring test was first finished in horizontal boreholeat Number 1 coal mine and the curves of microstrain values

versus the overcoring depth were given in Figure 10 Basedon the test of elastic parameters of rock mass the elasticmodulus varies in a range (5GPasim8GPa) and the calculatedin situ stresses using different elastic modulus are shown inTable 1 It can be found that themagnitudes of three principalstress components increase as elastic modulus 119864 increaseswhereas their azimuth and dip angles are maintained nearlythe same Ge and Hou [29] have found that when Poissonrsquosratio ] is constant the magnitudes of three principal stresseswill increase (or decrease) with the increase (or decrease) of119864 Therefore the principal stress magnitudes of overcoringtechnique vary in a range

The monitor of the recovery stresses using TDPTsand temperature changes in both horizontal and verticalboreholes at Pingdingshan Number 1 coal mine has beenrecorded for a period of about 500 days It should be notedthat the calibration coefficients of each sensing face weredetermined by calibration test using the actual groutingmaterial and the influence of the environmental temperatureon the transducer is analyzed and compensated For thesake of brief only the results of horizontal borehole inPingdingshan Number 1 coal mine are shown in Figure 11It is clear that the recovery stress measured by all sensingfaces in different directions increases gradually to be stablealthough the rate of stress recovery decreases with timeAccording to the analytical results of the relationship between


Syncline

N

Anticline

Normal fault

Reverse fault

Coal mine

Likou syncline

Niuzhuang syncline

Baishigou anticline

Guozhuang anticline

Xiangxia fault

Lingwushan syncline

Guodishan

normal fault

Xiaxian

fault

No 9

No 5

No 7No 2

No 8

No 1

No 10

No 12

No 4

No 6No 11

No 3

Beijing

Test area

Pingdingshan city

150

(km)

Figure 8 Schematic map of the Pingdingshan coal mine [27]

Roadway

Horizontal borehole

Vert

ical

bor

ehol

e

10∘

Depth = 30m diameter = 130mm

Dep

th=30

m d

iam

eter=130

mm

Figure 9 Sketch of the borehole layout

the final recovery stress and initial stress and the ratio ofthe initial modulus to the long-term modulus (119866ini119866infin asymp

18) from experimental tests the final recovery ratio can bedetermined (about 045) Then the initial stresses verticalto each sensing face can be calculated and inserted into the

calculation formulation (1) to obtain the stress tensor in localcoordinate system and the principal stress components inglobal coordinate system can be calculated using coordinatetransformation The results of the magnitude azimuth anddip angle of three principal stresses in both horizontal andvertical boreholes in Pingdingshan Number 1 coal mine arelisted in Table 2 All the test results show that the orientationof the maximum principal stress 120590

1and the minimum stress

1205903is approximately in the horizontal plane and that of the

intermediate principal stress is nearly verticalFrom Tables 1 and 2 it can be found that the princi-

pal stress magnitudes of overcoring vary in a range whenselecting different elastic parameters and the results of RSRmethod are within this range The orientations of principalstresses by both overcoring technique and RSR method aredrawn in the stereographic projection shown in Figure 11Thedominant orientations of the maximum principal stress arealmost the same for both the overcoring technique and RSRmethod Pingdingshan region has experienced three obvioustectonic movements in the geologic history the Indosinianmovement during theTriassic period theYanshanmovementduring the Mesozoic period and the Himalayan movementduring the Neozoic period Accordingly the direction of themajor principle stress in this region has shifted from NE-SW


Table 2 In situ stress magnitudes by RSR method at the horizontal and vertical boreholes

Boreholeposition

1205901

1205902

1205903

Magnitude (MPa) Azimuth (∘) Dip (∘) Magnitude (MPa) Azimuth (∘) Dip (∘) Magnitude (MPa) Azimuth (∘) Dip (∘)Horizontal 2821 14887 378 2050 30664 8592 1780 5877 154Vertical 3056 1096 1511 2142 4583 7484 1994 1929 117

0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e

Overcoring depth (cm)

Channel 1 Channel 7Channel 2 Channel 8Channel 3 Channel 9Channel 4 Channel 10Channel 5 Channel 11Channel 6 Channel 12

minus1000

Figure 10 Stress relief curves during the overcoring of horizontalborehole at Number 1 coal mine

to NW-SE then to approximately EW [30] Figure 12 showsthat the major principle stress directions of testing pointsare mostly NW-SE and agree with those in the second andthird tectonicmovements which reveals that the in situ stressfield at present is caused primarily by the latter two tectonicmovements Therefore it can be said that the result from theRSR method is reliable and the new method for in situ stressmeasurement can be used to measure rock stresses

Through the practical application of the overcoring tech-nique and RSR method for in situ stress measurement inPingdingshan Number 1 coal mine it can be found that theRSR method may be a maneuverable and effective techniquein deep soft rock The accuracy of elastic parameters has agreat influence on the calculated results of stress magnitudesand orientations for overcoring technique However theexact elastic parameters of rockmass seemnot very necessaryfor RSRmethod with respect to conventional methods In theRSRmethod the stress values in different orientations can bemeasured by the pressure transducer directly and can be usedto calculate the stress tensor The accuracy of stress valuesis dependent on the calibration factor of the transducer thatcan be obtained from calibration test Based on the results ofcurrent research [31] the variation of the elastic modulus ofsurrounding material has little influence on the calibrationfactor when the elastic modulus ratio of the transducer to

0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)

Figure 11 Stress recovery process in the horizontal borehole ofPingdingshan Number 1 coal mine

the surrounding material is large enough Therefore the truerock stresses can be inferred by the rough elastic parametersThe measuring errors of RSR method caused by the elasticparameters are less than that of the conventional methods

For the RSR method the main requirement of rock massis good in rheological property Moreover the greater thedepth of testing site the better as the in situ stress at greaterdepth is generally bigger In addition the grouting qualityis very important for the RSR method and the groutingshould be accomplished as soon as possible after drilling thehole The different lateral pressure coefficient may have aninfluence on the stress values measured by the transducerwhich is caused by the difference between the transducer andsurroundingmaterialThrough the model test and numericalsimulation it has been found that the measured stresses werelinear to the loading stresses for the hydrostatic stress loadingand the measured stresses were linear to both the loadingstresses in the same direction and the differential stressesof the other two directions for the nonhydrostatic stressloading [32] The actual stress values on each sensing facecan be deduced by the combination of calibration coefficientsand the measured stress values although the lateral pressurecoefficient 120582 is unknown

The transducers that the RSRmethod uses can be embed-ded not only in the initial stress area to obtain themagnitudesof original stress but also in the excavation damage zone tomonitor the stress state variation It has been found that the


N

Max mid and min principal stresses of horizontal borehole by RSRMax mid and min principal stresses of vertical borehole by RSR

Max mid and min principal stresses of E = 5GPa by overcoringMax mid and min principal stresses of E = 8GPa by overcoring

Figure 12 Orientations of principal stresses by both overcoring technique and RSR method

stressmeter that is installed in a specimen under loadwill pickup the absolute ambient stress in the host when observed overa period of time concurrently it responded immediately toan increase of stress generated in the host after the time of itsinsertion [33]

The RSR method is used to measure the in situ stressbased on the rheological behavior of rock the longer themonitoring time is therefore the more precise the resultsbecome However further research is needed to see how tocalculate the stress state of one point through monitoring ina short time for engineering applications

7 Conclusions

For the measurement of the stress in deep soft rock a RSRmethod to determine the orientations and magnitudes of 3Din situ stress is proposed as well as its test equipment andprocess and analytical solutions were derived to analyze thecharacteristics of this method Then the RSR method aswell as overcoring technique was conducted in PingdingshanNumber 1 coal mine to measure both the in situ stressorientation and magnitude at a depth of 877m The resultsare summarized as follows

If the rock mass has a better rheological property therecovery stress measured by the transducer is more close tothe initial stress Moreover the grouting quality should beensured that the properties of grouting materials should beclose to that of rock masses in actual operation

These results tested by RSR method and overcoringtechnique are basically in the same order which validatesthat the RSR method is a useful method for deep soft rockmasses The major principal stresses are approximately in

the direction of NW-SE which correlates well with thestress regime of Pingdingshan zone known from the tectonicmovement history

The RSR method can be used to obtain more reliabledata when stress relief method cannot be applied in soft orhighly jointed rock masses under great depth Therefore itcan be said that the RSRmethodmay bewell suitable formorecomplicated geological conditions However more studiesare required to see how to calculate the stress state of onepoint through monitoring in a short time for engineeringapplications

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Basic Research Pro-gram of China (ldquo973rdquo Program) (Grant no 2014CB046904)and theNationalNatural Science Foundation ofChina (Grantnos 41130742 and 11302242)

References

[1] A Zang and O Stephansson Stress Field of the Earthrsquos CrustSpringer Science amp Business Media 2009

[2] B Amadei and O Stephansson Rock Stress and Its Measure-ment Springer Dordrecht The Netherlands 1997

[3] C Ljunggren Y Chang T Janson and R Christiansson ldquoAnoverview of rock stress measurement methodsrdquo International


Journal of Rock Mechanics and Mining Sciences vol 40 no 7-8pp 975ndash989 2003

[4] R Corthesy M H Leite D E Gill and B Gaudin ldquoStressmeasurements in soft rocksrdquo Engineering Geology vol 69 no3-4 pp 381ndash397 2003

[5] R Ulusay The ISRM Suggested Methods for Rock Characteriza-tion Testing and Monitoring 2007ndash2014 Springer 2015

[6] C Liu ldquoDistribution laws of in-situ stress in deep undergroundcoal minesrdquo Procedia Engineering vol 26 pp 909ndash917 2011

[7] J Rutqvist C-F Tsang andO Stephansson ldquoUncertainty in themaximum principal stress estimated from hydraulic fracturingmeasurements due to the presence of the induced fracturerdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 37 no 1-2 pp 107ndash120 2000

[8] C Ljunggren and G Raillard ldquoRock stress measurements bymeans of hydraulic tests on pre-existing fractures at Gideatest site Swedenrdquo International Journal of Rock Mechanics andMining Sciences amp Geomechanics Abstracts vol 24 no 6 pp339ndash345 1987

[9] B C Haimson and F H Cornet ldquoISRM suggested methodsfor rock stress estimation Part 3 Hydraulic fracturing (HF)andor hydraulic testing of pre-existing fractures (HTPF)rdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 40 no 7-8 pp 1011ndash1020 2003

[10] M H Talebi S Heidari M Moosavi and M Rahimi ldquoIn situstress measurements of two hydropower projects in Iran byhydraulic fracturing methodrdquo Arabian Journal of Geosciencesvol 8 no 9 pp 7073ndash7085 2015

[11] M L Wu Y Q Zhang C T Liao et al ldquoPreliminary results ofin-situ stress measurements along the Longmenshan fault zoneafter theWenchuanM

11990480 earthquakerdquoActa Geologica Sinicamdash

English Edition vol 83 no 4 pp 746ndash753 2009[12] B Amadei Rock Anisotropy and the Theory of Stress Measure-

ments Springer 1983[13] P Thompson R Corthesy and M Leite ldquoRock stress measure-

ments at great depth using the modified doorstopper gaugerdquo inProceedings of the International Symposium Rock Stress JapanK Sugawara and Y Obara Eds pp 59ndash64 AA Balkema 1997

[14] G Della Vecchia A Pandolfi G Musso and G Capasso ldquoAnanalytical expression for the determination of in situ stress statefrom borehole data accounting for breakout sizerdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 66 pp 64ndash68 2014

[15] M Seto D K Nag and V S Vutukuri ldquoIn-situ rock stress mea-surement from rock cores using the acoustic emission methodand deformation rate analysisrdquo Geotechnical and GeologicalEngineering vol 17 no 3-4 pp 241ndash266 1999

[16] L Gao W Lin D Sun and H Wang ldquoExperimental anelas-tic strain recovery compliance of three typical rocksrdquo RockMechanics and Rock Engineering vol 47 no 6 pp 1987ndash19952014

[17] K Matsuki and K Takeuchi ldquoThree-dimensional in situ stressdetermination by anelastic strain recovery of a rock corerdquoInternational Journal of Rock Mechanics and Mining Sciences ampGeomechanics Abstracts vol 30 no 7 pp 1019ndash1022 1993

[18] D Sun W Lin J Cui et al ldquoThree-dimensional in situ stressdetermination by anelastic strain recovery and its applicationat the Wenchuan Earthquake Fault Scientific Drilling Hole-1(WFSD-1)rdquo Science China Earth Sciences vol 57 no 6 pp 1212ndash1220 2014

[19] L Teufel ldquoDetermination of in situ stress from partial anelasticstrain recovery measurements of oriented cores from deepboreholesrdquo in Proceedings of the 34th US Rock MechanicsSymposium on Short Course Modern In Situ Stress MeasurementMethods pp 27ndash30 June 1993

[20] Z Guan Y Jiang and Y Tanabashi ldquoRheological parameterestimation for the prediction of long-term deformations inconventional tunnellingrdquo Tunnelling and Underground SpaceTechnology vol 24 no 3 pp 250ndash259 2009

[21] S Wassmann and B Stockhert ldquoRheology of the plateinterfacemdashdissolution precipitation creep in high pressuremetamorphic rocksrdquo Tectonophysics vol 608 pp 1ndash29 2013

[22] D F Malan ldquoTime-dependent behaviour of deep level tabularexcavations in hard rockrdquo Rock Mechanics and Rock Engineer-ing vol 32 no 2 pp 123ndash155 1999

[23] DM StefanescuHandbook of Force Transducers Principles andComponents Springer Science amp Business Media 2011

[24] A Fahimifar F M Tehrani A Hedayat and A VakilzadehldquoAnalytical solution for the excavation of circular tunnels ina visco-elastic Burgerrsquos material under hydrostatic stress fieldrdquoTunnelling andUnderground Space Technology vol 25 no 4 pp297ndash304 2010

[25] H N Wang Y Li Q Ni S Utili M J Jiang and F LiuldquoAnalytical solutions for the construction of deeply buriedcircular tunnels with two liners in rheological rockrdquo RockMechanics and Rock Engineering vol 46 no 6 pp 1481ndash14982013

[26] R E Goodman Introduction to Rock Mechanics Wiley NewYork NY USA 1989

[27] H Li ldquoMajor and minor structural features of a bedding shearzone along a coal seam and related gas outburst Pingdingshancoalfield Northern Chinardquo International Journal of Coal Geol-ogy vol 47 no 2 pp 101ndash113 2001

[28] J Sjoberg R Christiansson and J A Hudson ldquoISRM sug-gested methods for rock stress estimationmdashpart 2 overcoringmethodsrdquo International Journal of Rock Mechanics and MiningSciences vol 40 no 7-8 pp 999ndash1010 2003

[29] X R Ge and M X Hou ldquoPrinciple of in-situ 3D rock stressmeasurement with borehole wall stress relief method and itspreliminary applications to determination of in-situ rock stressorientation and magnitude in Jinping hydropower stationrdquoScience China Technological Sciences vol 55 no 4 pp 939ndash9492012

[30] Y Wang H Jing K Chen and L Wei ldquoStudy of distribu-tion regularities and regional division of in-situ stresses forPingdingshan Mining areardquo Chinese Journal of Rock Mechanicsand Engineering vol 33 no 1 pp 2620ndash2627 2014

[31] R Collins K Lee G Lilly and R Westmann ldquoMechanics ofpressure cellsrdquo Experimental Mechanics vol 12 no 11 pp 514ndash519 1972

[32] Y ZhuQ Liu J Jiang YHuang andY Pan ldquoMeasuring perfor-mance of three-dimensional pressure sensor in cement mortarblockrdquo Chinese Journal of Rock Mechanics and Engineering vol34 pp 1877ndash1885 2015

[33] D Skilton ldquoBehaviour of rigid inclusion stressmeters in vis-coelastic rockrdquo International Journal of Rock Mechanics andMining SciencesampGeomechanics Abstracts vol 8 no 4 pp 283ndash289 1971

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Sensing faces

(a)

Pushrod

Triangle pulley

Goniometer

(b)

Explosion-proofenclosure

Data logger

TDPT

(c)

Figure 1 Test equipment of RSR method (a) TDPTs (b) pushrod and the goniometer (c) explosion-proof data logger

equipment calculation equations and related procedures ofRSR method will be briefly introduced Then the measuringprocess is analyzed by analytical solutions to explore theapplicability and accuracy of this method Finally the RSRmethod as well as overcoring technique was conducted inPingdingshanNumber 1 coalmine tomeasure both the in situstress orientation and magnitude at a depth of 877m

2 An Outline of RSR Method

21 Basic Principles A large number of field monitoring andlaboratory tests [20 21] have shown that rheological proper-ties of soft rocks are very significant under high geostressEven for hard rock mass that is cut by several joints and frac-tures creep deformation can also attain considerable mag-nitude [22] Thus a borehole will shrink gradually to beclosed under high geostress due to the rheological charac-teristic of soft rocks and rock stresses will recover to theinitial stress state with the growth of the time Based onthis stress measurement with RSR method is proposed It issupposed that rock stresses around the pressure transducersthat are embedded in the borehole will recover graduallyand eventually tend to be stable due to the rheologicalcharacteristics of surrounding rocks

22 Main Equipment The equipment used in this methodinvolves pressure transducers push rods with orientationdevice and a data logger shown in Figure 1 A three-dimensional pressure transducer (TDPT) which can mea-sure normal stresses in three directions is developed for insitu stress measurement with RSRmethod (Figure 1(a)) and atest point needs twoTDPTs in different directionsTheTDPTwhich contains three sensing faces (diameter = 58mm) is awaterproof cube structure (side length = 80mm) and suitablefor a pressure up to 30MPa Vibrating wire force transducersare adopted on each sensing face due to the advantages of highaccuracy and repeatability possibility for remote measuringdigitalization of results long service stability [23] and so

forth Eight corners of the TDPT have been cut out for therequirements of miniaturizationThe pushrod is used to sendthe transducers to the test point and the rotation angles ofthe transducer are recorded by the goniometer in order tocalculate the azimuth angle of each sensing face The datalogger is developed through explosion-proof design to meetthe requirement of coal mine shown in Figure 1(c)

23 Testing Procedures The RSR method for measuringthe stress in deep soft rocks comprises the following steps(Figure 2)

(1) A borehole is drilled till the test point in surroundingrocks of a soft rock tunnel

(2) Stress transducers are fixed on a connecting rod andsent to the test point a direction cosine of any twosensing faces in the normal direction is recorded andis not 1 a normal stress measuring device is mountedon each sensing face and connected with a data loggeroutside the borehole through long cables

(3) Grouting is carried out on the drilling hole and theborehole is sealed after being entirely filled

(4) After the grout is solidified pressure values arecontinually read from the data logger and six stressvalues are substituted into the calculation equationsafter the values are stable so as to obtain 3D rockstress at the test point With the adoption of thismethod evolutional stress data of the test point canbe also obtained Moreover the spatial variation andevolution of rock stress state can bemeasured througha series of pressure transducers embedded in differentdepth of the borehole

24 Calculation Equations A spatial coordinate system 119900119909119910119911

is established by taking normal directions of three mutu-ally perpendicular sensing faces as directions of coordinateaxes and 119909

1015840- 1199101015840- and 119911

1015840-axis are normal directions of


Grout

TDPTsPushrods

Borehole

Tunnel

Data logger

Cables



119909 1205901015840

119910 1205901015840




1205901015840

119909= 1198972

1120590119909+ 1198982

1120590119910+ 1198992

1120590119911+ 211989711198981120591119909119910

+ 211989811198991120591119910119911

+ 211989911198971120591119911119909

1205901015840

119910= 1198972

2120590119909+ 1198982

2120590119910+ 1198992

2120590119911+ 211989721198982120591119909119910

+ 211989821198992120591119910119911

+ 211989921198972120591119910119911

1205901015840

119911= 1198972

3120590119909+ 1198982

3120590119910+ 1198992

3120590119911+ 211989731198983120591119909119910

+ 211989831198993120591119910119911

+ 211989931198973120591119910119911

(1)

where 120591119909119910 120591119910119911 and 120591





1015840-axis and 119909-axis1198981 1198982 and 119898


between 1199091015840- 1199101015840- and 119911


3


1199111015840-axis and 119911-axis




P

r

r0

r0

r1

r1

r2

p(t)p(t)

120582P

q(t)

q(t)




0 pressure of the


0 onwards



120590119903=

119875

2

[(1 + 120582) + (1 minus 120582) cos 2120579]

120590120579=

119875

2

[(1 + 120582) minus (1 minus 120582) cos 2120579]

120591119903120579

= minus

119875

2

(1 minus 120582) sin 2120579

(2)






119901 (119905) = 1199010(119905) + 119901

1(119905) cos 2120579

119902 (119905) = 1199020(119905) + 119902

1(119905) cos 2120579

(3)

where 1199010(119905) and 119902



1(119905) cos 2120579 are contact




119906119903119888(1199030 119905) = 119906

119903(1199030 119905)

119906119903119879

(1199031 119905) = 119906

119903119888(1199031 119905)

(4)

where 119906119903 119906119903119888 and 119906





transducer



0) can be written

as [24 26]

1199061198750

(1199030 119905) =

1198751199030

4

(1 + 120582) 119869 (119905) (5)



0is

Δ1199061198750

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 (6)

where Δ119869 = 119869(119905 + 1199050) minus 119869(119905

0)



0) can be

written as

1199061199030

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 minus

1199010(119905) 1199030

21198660

(7)



119891 (119904) = int

infin

0

119891 (119905) 119890minus119904119905

119889119905 (8)


119871minus1

[119891 (119904)] = 119891 (119905) =

1

2120587119894

int

120573+119894infin


119891 (119904) 119890119904119905119889119905 (9)


1199061199030

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 minus

1199010(119904) 1199030

21198660(119904)

(10)




0(119905) and 119902


0

and 119903 = 1199031 are

1199061198880

(1199030 119904) =

1199010(119904) 1199030

2119866119888

1198981198880

minus

1199020(119904) 1199030

2119866119888

1198991198880

1199061198880

(1199031 119904) =

1199010(119904) 1199030

2119866119888

1198981015840

1198880minus

1199020(119904) 1199030

2119866119888

1198991015840

1198880

(11)

where

1198981198880

=

1199032

1+ (1 minus 2120583

119888) 1199032

0

1199032

0minus 1199032

1

1198991198880

=

1199032

1(2 minus 2120583

119888)

1199032

0minus 1199032

1

1198981015840

1198880=

1199032

0(2 minus 2120583

119888)

1199032

0minus 1199032

1

1198991015840

1198880=

1199032

0+ (1 minus 2120583

119888) 1199032

1

1199032

0minus 1199032

1

(12)


119888


1) in

Laplace domain is

1199061198790

(1199031 119904) =

1199020(119904) 1199031

2119866119879

1198981198790

(13)



1198981198790

=

1199032

2+ (1 minus 2120583

119879) 1199032

1

1199032

1minus 1199032

2

(14)


119879




0) in the

Laplace domain is

1199061199031

(1199030 119904) =

1 minus 120582

4

(3 minus 41205830) 1198751199030Δ119869

minus

1199011(119904) 1199030

61198660(119904)

(5 minus 61205830) cos 2120579

(15)


0and 119903 = 119903

1) under


1199061198881

(1199030 119904) =

1199011(119904) 1199030

2119866119888

1198981198881cos 2120579 minus

1199021(119904) 1199030

2119866119888

1198991198881cos 2120579

1199061198881

(1199031 119904) =

1199011(119904) 1199031

2119866119888

1198981015840

1198881cos 2120579 minus

1199021(119904) 1199031

2119866119888

1198991015840

1198881cos 2120579

(16)

Define

1198981198881

= 1198911198881

minus 1198911198885119903minus4

0+ 212058311988811989111988831199032


119888) 1198911198887119903minus2

0

1198991198881

= 1198911198882

minus 1198911198886119903minus4

0+ 212058311988811989111988841199032


119888) 1198911198888119903minus2

0

1198981015840

1198881= 1198911198881

minus 1198911198885119903minus4

1+ 212058311988811989111988831199032


119888) 1198911198887119903minus2

1

1198991015840

1198881= 1198911198882

minus 1198911198886119903minus4

1+ 212058311988811989111988841199032


119888) 1198911198888119903minus2

1

1198911198881

=

1199036

0+ 1199034

01199032

1+ 21199032

01199034

1

(1199032

0minus 1199032

1)3

1198911198882

=

21199034

01199032

1+ 1199032

01199034

1+ 1199036

1

(1199032

0minus 1199032

1)3


1198911198883

= minus

1199034

0+ 31199032

01199032

1

3 (1199032

0minus 1199032

1)3

1198911198884

= minus

31199032

01199032

1+ 1199034

1

3 (1199032

0minus 1199032

1)3

1198911198885

=

31199036

01199034

1+ 1199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198886

=

1199036

01199034

1+ 31199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198887

= minus

21199036

01199032

1+ 1199034

01199034

1+ 1199032

01199036

1

(1199032

0minus 1199032

1)3

1198911198888

= minus

1199036

01199032

1+ 1199034

01199034

1+ 21199032

01199036

1

(1199032

0minus 1199032

1)3

(17)


1) under nonuniform


1199061198791

(1199031 119904) =

1199021(119904) 1199031

2119866119879

1198981198791

cos 2120579 (18)

where

1198981198791

= 1198911198791

minus 1198911198793

119903minus4

1+ 21205831198791198911198792

1199032


119879) 1198911198794

119903minus2

1(19)

with

1198911198791

=

1199036

1+ 1199034

11199032

2+ 21199032

11199034

2

(1199032

1minus 1199032

2)3

1198911198792

= minus

1199034

1+ 31199032

11199032

2

3 (1199032

1minus 1199032

2)3

1198911198793

=

31199036

11199034

2+ 1199034

11199036

2

3 (1199032

1minus 1199032

2)3

1198911198794

= minus

21199036

11199032

2+ 1199034

11199034

2+ 1199032

11199036

2

(1199032

1minus 1199032

2)3

(20)


1199061199030

(1199030 119904) = 119906

1198880(1199030 119904)

1199061199031

(1199030 119904) = 119906

1198881(1199030 119904)

1199061015840

1198880(1199031 119904) = 119906

1198790(1199031 119904)

1199061015840

1198881(1199031 119904) = 119906

1198791(1199031 119904)

(21)


1199010(119904) =

Δ119869

11198660(119904) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) (1198661198791198991015840

1198880+ 1198661198881198981198790

) 119866119888)

sdot

1 + 120582

2

119875

1199020(119904) =

Δ119869

((1198661198791198661198881198991015840

1198880+ 1198662

1198881198981198790

) 1198661198791198661198881198981015840

1198880) (1119866

0(119904)) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) 1198661198791198661198881198981015840

1198880)

sdot

1 + 120582

2

119875

1199011(119904) =

(3 minus 41205830) Δ119869

((5 minus 61205830) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) (1198661198791198991015840

1198881+ 1198661198881198981198791

) 119866119888)

sdot

1 minus 120582

2

119875

1199021(119904) =

(3 minus 41205830) Δ119869

((1198661198791198991015840

1198881+ 1198661198881198981198791

) 1198661198791198981015840

1198881) ((5 minus 6120583

0) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) 1198661198791198661198881198981015840

1198881)

sdot

1 minus 120582

2

119875

(22)


119869 (119905) =

1

1198661

+

1

1198662

(1 minus exp(minus

1198662119905

120578

)) (23)



be written as

1 + 1198753 = 119876

3120574 + 119876

4 (24)


G1

G2

120578


where

1198753=

120578

1198661+ 1198662

1198763=

11986611198662

1198661+ 1198662

1198764=

1205781198661

1198661+ 1198662

(25)


119902 (119905) = 1199020(119905) + 119902

1(119905) cos 2120579 =

1 + 120582

2

119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198771+ 119866infin1198772

(1 minus exp(minus

1198771+ 11987631198772

11987531198771+ 11987641198772

119905))

+

1 minus 120582

2

(3 minus 41205830) 119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198773+ 119866infin1198774

(1 minus exp(minus

1198773+ 11987631198774

11987531198773+ 11987641198774

119905))

sdot cos 2120579

(26)

where119866infin



1198771=

1198661198791198991015840

1198880+ 1198661198881198981198790

1198661198791198981015840

1198880

1198772=

1198661198791198991015840

1198881+ 1198661198881198981198791

1198661198791198981015840

1198881

5 minus 61205830

3

1198773=

11986611987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880

1198661198791198661198881198981015840

1198880

1198774=

11986611987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881

1198661198791198661198881198981015840

1198881

(27)




0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900

t0 = 0

t0 = 10ht0 = 20ht0 = 50h

t0 = 100ht0 = 200ht0 = 500h







0= 65mm 119903

1= 55mm 119903

2= 50mm 119875 = 1MPa and


=

4GPa 120583119888= 035 119866

119879= 80GPa and 120583



1= 2576MPa 119866

2= 1903MPa 120578 =

31671198905MPasdoth and 1205830





119888) are


0= 10 h



0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900



(a)

0 100 200 300 400 500

025

030

035

040

045

050

055

060

Ratio

of s

tabl

e rec

over

y str

ess t

o in

situ

stre

ss

GTGc

(b)











infin that is the




5 Field Test



0 200 400 600 800 100000

02

04

06

08

10

t (h)

q(t

)1205900

G1G2 = 1 5G1G2 = 4 1G1G2 = 1 2G1G2 = 10 1

G1G2 = 1 1G1G2 = 20 1G1G2 = 2 1G1G2 = 50 1

(a)

0 10 20 30 40 5001

02

03

04

05

06

07

08

09

10

Fina

l rec

over

y str

ess r

atio

GiniGinfin

(b)



Parameter 1205901

1205902

1205903








Syncline

N

Anticline

Normal fault

Reverse fault

Coal mine

Likou syncline

Niuzhuang syncline

Baishigou anticline

Guozhuang anticline

Xiangxia fault

Lingwushan syncline

Guodishan

normal fault

Xiaxian

fault

No 9

No 5

No 7No 2

No 8

No 1

No 10

No 12

No 4

No 6No 11

No 3

Beijing

Test area

Pingdingshan city

150

(km)


Roadway

Horizontal borehole

Vert

ical

bor

ehol

e

10∘


Dep

th=30

m d

iam

eter=130

mm











Boreholeposition

1205901

1205902

1205903


0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e



minus1000




0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)






N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Grout

TDPTsPushrods

Borehole

Tunnel

Data logger

Cables



119909 1205901015840

119910 1205901015840




1205901015840

119909= 1198972

1120590119909+ 1198982

1120590119910+ 1198992

1120590119911+ 211989711198981120591119909119910

+ 211989811198991120591119910119911

+ 211989911198971120591119911119909

1205901015840

119910= 1198972

2120590119909+ 1198982

2120590119910+ 1198992

2120590119911+ 211989721198982120591119909119910

+ 211989821198992120591119910119911

+ 211989921198972120591119910119911

1205901015840

119911= 1198972

3120590119909+ 1198982

3120590119910+ 1198992

3120590119911+ 211989731198983120591119909119910

+ 211989831198993120591119910119911

+ 211989931198973120591119910119911

(1)

where 120591119909119910 120591119910119911 and 120591





1015840-axis and 119909-axis1198981 1198982 and 119898


between 1199091015840- 1199101015840- and 119911


3


1199111015840-axis and 119911-axis




P

r

r0

r0

r1

r1

r2

p(t)p(t)

120582P

q(t)

q(t)




0 pressure of the


0 onwards



120590119903=

119875

2

[(1 + 120582) + (1 minus 120582) cos 2120579]

120590120579=

119875

2

[(1 + 120582) minus (1 minus 120582) cos 2120579]

120591119903120579

= minus

119875

2

(1 minus 120582) sin 2120579

(2)






119901 (119905) = 1199010(119905) + 119901

1(119905) cos 2120579

119902 (119905) = 1199020(119905) + 119902

1(119905) cos 2120579

(3)

where 1199010(119905) and 119902



1(119905) cos 2120579 are contact




119906119903119888(1199030 119905) = 119906

119903(1199030 119905)

119906119903119879

(1199031 119905) = 119906

119903119888(1199031 119905)

(4)

where 119906119903 119906119903119888 and 119906





transducer



0) can be written

as [24 26]

1199061198750

(1199030 119905) =

1198751199030

4

(1 + 120582) 119869 (119905) (5)



0is

Δ1199061198750

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 (6)

where Δ119869 = 119869(119905 + 1199050) minus 119869(119905

0)



0) can be

written as

1199061199030

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 minus

1199010(119905) 1199030

21198660

(7)



119891 (119904) = int

infin

0

119891 (119905) 119890minus119904119905

119889119905 (8)


119871minus1

[119891 (119904)] = 119891 (119905) =

1

2120587119894

int

120573+119894infin


119891 (119904) 119890119904119905119889119905 (9)


1199061199030

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 minus

1199010(119904) 1199030

21198660(119904)

(10)




0(119905) and 119902


0

and 119903 = 1199031 are

1199061198880

(1199030 119904) =

1199010(119904) 1199030

2119866119888

1198981198880

minus

1199020(119904) 1199030

2119866119888

1198991198880

1199061198880

(1199031 119904) =

1199010(119904) 1199030

2119866119888

1198981015840

1198880minus

1199020(119904) 1199030

2119866119888

1198991015840

1198880

(11)

where

1198981198880

=

1199032

1+ (1 minus 2120583

119888) 1199032

0

1199032

0minus 1199032

1

1198991198880

=

1199032

1(2 minus 2120583

119888)

1199032

0minus 1199032

1

1198981015840

1198880=

1199032

0(2 minus 2120583

119888)

1199032

0minus 1199032

1

1198991015840

1198880=

1199032

0+ (1 minus 2120583

119888) 1199032

1

1199032

0minus 1199032

1

(12)


119888


1) in

Laplace domain is

1199061198790

(1199031 119904) =

1199020(119904) 1199031

2119866119879

1198981198790

(13)



1198981198790

=

1199032

2+ (1 minus 2120583

119879) 1199032

1

1199032

1minus 1199032

2

(14)


119879




0) in the

Laplace domain is

1199061199031

(1199030 119904) =

1 minus 120582

4

(3 minus 41205830) 1198751199030Δ119869

minus

1199011(119904) 1199030

61198660(119904)

(5 minus 61205830) cos 2120579

(15)


0and 119903 = 119903

1) under


1199061198881

(1199030 119904) =

1199011(119904) 1199030

2119866119888

1198981198881cos 2120579 minus

1199021(119904) 1199030

2119866119888

1198991198881cos 2120579

1199061198881

(1199031 119904) =

1199011(119904) 1199031

2119866119888

1198981015840

1198881cos 2120579 minus

1199021(119904) 1199031

2119866119888

1198991015840

1198881cos 2120579

(16)

Define

1198981198881

= 1198911198881

minus 1198911198885119903minus4

0+ 212058311988811989111988831199032


119888) 1198911198887119903minus2

0

1198991198881

= 1198911198882

minus 1198911198886119903minus4

0+ 212058311988811989111988841199032


119888) 1198911198888119903minus2

0

1198981015840

1198881= 1198911198881

minus 1198911198885119903minus4

1+ 212058311988811989111988831199032


119888) 1198911198887119903minus2

1

1198991015840

1198881= 1198911198882

minus 1198911198886119903minus4

1+ 212058311988811989111988841199032


119888) 1198911198888119903minus2

1

1198911198881

=

1199036

0+ 1199034

01199032

1+ 21199032

01199034

1

(1199032

0minus 1199032

1)3

1198911198882

=

21199034

01199032

1+ 1199032

01199034

1+ 1199036

1

(1199032

0minus 1199032

1)3


1198911198883

= minus

1199034

0+ 31199032

01199032

1

3 (1199032

0minus 1199032

1)3

1198911198884

= minus

31199032

01199032

1+ 1199034

1

3 (1199032

0minus 1199032

1)3

1198911198885

=

31199036

01199034

1+ 1199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198886

=

1199036

01199034

1+ 31199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198887

= minus

21199036

01199032

1+ 1199034

01199034

1+ 1199032

01199036

1

(1199032

0minus 1199032

1)3

1198911198888

= minus

1199036

01199032

1+ 1199034

01199034

1+ 21199032

01199036

1

(1199032

0minus 1199032

1)3

(17)


1) under nonuniform


1199061198791

(1199031 119904) =

1199021(119904) 1199031

2119866119879

1198981198791

cos 2120579 (18)

where

1198981198791

= 1198911198791

minus 1198911198793

119903minus4

1+ 21205831198791198911198792

1199032


119879) 1198911198794

119903minus2

1(19)

with

1198911198791

=

1199036

1+ 1199034

11199032

2+ 21199032

11199034

2

(1199032

1minus 1199032

2)3

1198911198792

= minus

1199034

1+ 31199032

11199032

2

3 (1199032

1minus 1199032

2)3

1198911198793

=

31199036

11199034

2+ 1199034

11199036

2

3 (1199032

1minus 1199032

2)3

1198911198794

= minus

21199036

11199032

2+ 1199034

11199034

2+ 1199032

11199036

2

(1199032

1minus 1199032

2)3

(20)


1199061199030

(1199030 119904) = 119906

1198880(1199030 119904)

1199061199031

(1199030 119904) = 119906

1198881(1199030 119904)

1199061015840

1198880(1199031 119904) = 119906

1198790(1199031 119904)

1199061015840

1198881(1199031 119904) = 119906

1198791(1199031 119904)

(21)


1199010(119904) =

Δ119869

11198660(119904) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) (1198661198791198991015840

1198880+ 1198661198881198981198790

) 119866119888)

sdot

1 + 120582

2

119875

1199020(119904) =

Δ119869

((1198661198791198661198881198991015840

1198880+ 1198662

1198881198981198790

) 1198661198791198661198881198981015840

1198880) (1119866

0(119904)) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) 1198661198791198661198881198981015840

1198880)

sdot

1 + 120582

2

119875

1199011(119904) =

(3 minus 41205830) Δ119869

((5 minus 61205830) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) (1198661198791198991015840

1198881+ 1198661198881198981198791

) 119866119888)

sdot

1 minus 120582

2

119875

1199021(119904) =

(3 minus 41205830) Δ119869

((1198661198791198991015840

1198881+ 1198661198881198981198791

) 1198661198791198981015840

1198881) ((5 minus 6120583

0) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) 1198661198791198661198881198981015840

1198881)

sdot

1 minus 120582

2

119875

(22)


119869 (119905) =

1

1198661

+

1

1198662

(1 minus exp(minus

1198662119905

120578

)) (23)



be written as

1 + 1198753 = 119876

3120574 + 119876

4 (24)


G1

G2

120578


where

1198753=

120578

1198661+ 1198662

1198763=

11986611198662

1198661+ 1198662

1198764=

1205781198661

1198661+ 1198662

(25)


119902 (119905) = 1199020(119905) + 119902

1(119905) cos 2120579 =

1 + 120582

2

119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198771+ 119866infin1198772

(1 minus exp(minus

1198771+ 11987631198772

11987531198771+ 11987641198772

119905))

+

1 minus 120582

2

(3 minus 41205830) 119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198773+ 119866infin1198774

(1 minus exp(minus

1198773+ 11987631198774

11987531198773+ 11987641198774

119905))

sdot cos 2120579

(26)

where119866infin



1198771=

1198661198791198991015840

1198880+ 1198661198881198981198790

1198661198791198981015840

1198880

1198772=

1198661198791198991015840

1198881+ 1198661198881198981198791

1198661198791198981015840

1198881

5 minus 61205830

3

1198773=

11986611987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880

1198661198791198661198881198981015840

1198880

1198774=

11986611987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881

1198661198791198661198881198981015840

1198881

(27)




0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900

t0 = 0

t0 = 10ht0 = 20ht0 = 50h

t0 = 100ht0 = 200ht0 = 500h







0= 65mm 119903

1= 55mm 119903

2= 50mm 119875 = 1MPa and


=

4GPa 120583119888= 035 119866

119879= 80GPa and 120583



1= 2576MPa 119866

2= 1903MPa 120578 =

31671198905MPasdoth and 1205830





119888) are


0= 10 h



0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900



(a)

0 100 200 300 400 500

025

030

035

040

045

050

055

060

Ratio

of s

tabl

e rec

over

y str

ess t

o in

situ

stre

ss

GTGc

(b)











infin that is the




5 Field Test



0 200 400 600 800 100000

02

04

06

08

10

t (h)

q(t

)1205900

G1G2 = 1 5G1G2 = 4 1G1G2 = 1 2G1G2 = 10 1

G1G2 = 1 1G1G2 = 20 1G1G2 = 2 1G1G2 = 50 1

(a)

0 10 20 30 40 5001

02

03

04

05

06

07

08

09

10

Fina

l rec

over

y str

ess r

atio

GiniGinfin

(b)



Parameter 1205901

1205902

1205903








Syncline

N

Anticline

Normal fault

Reverse fault

Coal mine

Likou syncline

Niuzhuang syncline

Baishigou anticline

Guozhuang anticline

Xiangxia fault

Lingwushan syncline

Guodishan

normal fault

Xiaxian

fault

No 9

No 5

No 7No 2

No 8

No 1

No 10

No 12

No 4

No 6No 11

No 3

Beijing

Test area

Pingdingshan city

150

(km)


Roadway

Horizontal borehole

Vert

ical

bor

ehol

e

10∘


Dep

th=30

m d

iam

eter=130

mm











Boreholeposition

1205901

1205902

1205903


0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e



minus1000




0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)






N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











transducer



0) can be written

as [24 26]

1199061198750

(1199030 119905) =

1198751199030

4

(1 + 120582) 119869 (119905) (5)



0is

Δ1199061198750

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 (6)

where Δ119869 = 119869(119905 + 1199050) minus 119869(119905

0)



0) can be

written as

1199061199030

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 minus

1199010(119905) 1199030

21198660

(7)



119891 (119904) = int

infin

0

119891 (119905) 119890minus119904119905

119889119905 (8)


119871minus1

[119891 (119904)] = 119891 (119905) =

1

2120587119894

int

120573+119894infin


119891 (119904) 119890119904119905119889119905 (9)


1199061199030

(1199030 119905) =

1 + 120582

4

1198751199030Δ119869 minus

1199010(119904) 1199030

21198660(119904)

(10)




0(119905) and 119902


0

and 119903 = 1199031 are

1199061198880

(1199030 119904) =

1199010(119904) 1199030

2119866119888

1198981198880

minus

1199020(119904) 1199030

2119866119888

1198991198880

1199061198880

(1199031 119904) =

1199010(119904) 1199030

2119866119888

1198981015840

1198880minus

1199020(119904) 1199030

2119866119888

1198991015840

1198880

(11)

where

1198981198880

=

1199032

1+ (1 minus 2120583

119888) 1199032

0

1199032

0minus 1199032

1

1198991198880

=

1199032

1(2 minus 2120583

119888)

1199032

0minus 1199032

1

1198981015840

1198880=

1199032

0(2 minus 2120583

119888)

1199032

0minus 1199032

1

1198991015840

1198880=

1199032

0+ (1 minus 2120583

119888) 1199032

1

1199032

0minus 1199032

1

(12)


119888


1) in

Laplace domain is

1199061198790

(1199031 119904) =

1199020(119904) 1199031

2119866119879

1198981198790

(13)



1198981198790

=

1199032

2+ (1 minus 2120583

119879) 1199032

1

1199032

1minus 1199032

2

(14)


119879




0) in the

Laplace domain is

1199061199031

(1199030 119904) =

1 minus 120582

4

(3 minus 41205830) 1198751199030Δ119869

minus

1199011(119904) 1199030

61198660(119904)

(5 minus 61205830) cos 2120579

(15)


0and 119903 = 119903

1) under


1199061198881

(1199030 119904) =

1199011(119904) 1199030

2119866119888

1198981198881cos 2120579 minus

1199021(119904) 1199030

2119866119888

1198991198881cos 2120579

1199061198881

(1199031 119904) =

1199011(119904) 1199031

2119866119888

1198981015840

1198881cos 2120579 minus

1199021(119904) 1199031

2119866119888

1198991015840

1198881cos 2120579

(16)

Define

1198981198881

= 1198911198881

minus 1198911198885119903minus4

0+ 212058311988811989111988831199032


119888) 1198911198887119903minus2

0

1198991198881

= 1198911198882

minus 1198911198886119903minus4

0+ 212058311988811989111988841199032


119888) 1198911198888119903minus2

0

1198981015840

1198881= 1198911198881

minus 1198911198885119903minus4

1+ 212058311988811989111988831199032


119888) 1198911198887119903minus2

1

1198991015840

1198881= 1198911198882

minus 1198911198886119903minus4

1+ 212058311988811989111988841199032


119888) 1198911198888119903minus2

1

1198911198881

=

1199036

0+ 1199034

01199032

1+ 21199032

01199034

1

(1199032

0minus 1199032

1)3

1198911198882

=

21199034

01199032

1+ 1199032

01199034

1+ 1199036

1

(1199032

0minus 1199032

1)3


1198911198883

= minus

1199034

0+ 31199032

01199032

1

3 (1199032

0minus 1199032

1)3

1198911198884

= minus

31199032

01199032

1+ 1199034

1

3 (1199032

0minus 1199032

1)3

1198911198885

=

31199036

01199034

1+ 1199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198886

=

1199036

01199034

1+ 31199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198887

= minus

21199036

01199032

1+ 1199034

01199034

1+ 1199032

01199036

1

(1199032

0minus 1199032

1)3

1198911198888

= minus

1199036

01199032

1+ 1199034

01199034

1+ 21199032

01199036

1

(1199032

0minus 1199032

1)3

(17)


1) under nonuniform


1199061198791

(1199031 119904) =

1199021(119904) 1199031

2119866119879

1198981198791

cos 2120579 (18)

where

1198981198791

= 1198911198791

minus 1198911198793

119903minus4

1+ 21205831198791198911198792

1199032


119879) 1198911198794

119903minus2

1(19)

with

1198911198791

=

1199036

1+ 1199034

11199032

2+ 21199032

11199034

2

(1199032

1minus 1199032

2)3

1198911198792

= minus

1199034

1+ 31199032

11199032

2

3 (1199032

1minus 1199032

2)3

1198911198793

=

31199036

11199034

2+ 1199034

11199036

2

3 (1199032

1minus 1199032

2)3

1198911198794

= minus

21199036

11199032

2+ 1199034

11199034

2+ 1199032

11199036

2

(1199032

1minus 1199032

2)3

(20)


1199061199030

(1199030 119904) = 119906

1198880(1199030 119904)

1199061199031

(1199030 119904) = 119906

1198881(1199030 119904)

1199061015840

1198880(1199031 119904) = 119906

1198790(1199031 119904)

1199061015840

1198881(1199031 119904) = 119906

1198791(1199031 119904)

(21)


1199010(119904) =

Δ119869

11198660(119904) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) (1198661198791198991015840

1198880+ 1198661198881198981198790

) 119866119888)

sdot

1 + 120582

2

119875

1199020(119904) =

Δ119869

((1198661198791198661198881198991015840

1198880+ 1198662

1198881198981198790

) 1198661198791198661198881198981015840

1198880) (1119866

0(119904)) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) 1198661198791198661198881198981015840

1198880)

sdot

1 + 120582

2

119875

1199011(119904) =

(3 minus 41205830) Δ119869

((5 minus 61205830) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) (1198661198791198991015840

1198881+ 1198661198881198981198791

) 119866119888)

sdot

1 minus 120582

2

119875

1199021(119904) =

(3 minus 41205830) Δ119869

((1198661198791198991015840

1198881+ 1198661198881198981198791

) 1198661198791198981015840

1198881) ((5 minus 6120583

0) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) 1198661198791198661198881198981015840

1198881)

sdot

1 minus 120582

2

119875

(22)


119869 (119905) =

1

1198661

+

1

1198662

(1 minus exp(minus

1198662119905

120578

)) (23)



be written as

1 + 1198753 = 119876

3120574 + 119876

4 (24)


G1

G2

120578


where

1198753=

120578

1198661+ 1198662

1198763=

11986611198662

1198661+ 1198662

1198764=

1205781198661

1198661+ 1198662

(25)


119902 (119905) = 1199020(119905) + 119902

1(119905) cos 2120579 =

1 + 120582

2

119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198771+ 119866infin1198772

(1 minus exp(minus

1198771+ 11987631198772

11987531198771+ 11987641198772

119905))

+

1 minus 120582

2

(3 minus 41205830) 119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198773+ 119866infin1198774

(1 minus exp(minus

1198773+ 11987631198774

11987531198773+ 11987641198774

119905))

sdot cos 2120579

(26)

where119866infin



1198771=

1198661198791198991015840

1198880+ 1198661198881198981198790

1198661198791198981015840

1198880

1198772=

1198661198791198991015840

1198881+ 1198661198881198981198791

1198661198791198981015840

1198881

5 minus 61205830

3

1198773=

11986611987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880

1198661198791198661198881198981015840

1198880

1198774=

11986611987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881

1198661198791198661198881198981015840

1198881

(27)




0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900

t0 = 0

t0 = 10ht0 = 20ht0 = 50h

t0 = 100ht0 = 200ht0 = 500h







0= 65mm 119903

1= 55mm 119903

2= 50mm 119875 = 1MPa and


=

4GPa 120583119888= 035 119866

119879= 80GPa and 120583



1= 2576MPa 119866

2= 1903MPa 120578 =

31671198905MPasdoth and 1205830





119888) are


0= 10 h



0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900



(a)

0 100 200 300 400 500

025

030

035

040

045

050

055

060

Ratio

of s

tabl

e rec

over

y str

ess t

o in

situ

stre

ss

GTGc

(b)











infin that is the




5 Field Test



0 200 400 600 800 100000

02

04

06

08

10

t (h)

q(t

)1205900

G1G2 = 1 5G1G2 = 4 1G1G2 = 1 2G1G2 = 10 1

G1G2 = 1 1G1G2 = 20 1G1G2 = 2 1G1G2 = 50 1

(a)

0 10 20 30 40 5001

02

03

04

05

06

07

08

09

10

Fina

l rec

over

y str

ess r

atio

GiniGinfin

(b)



Parameter 1205901

1205902

1205903








Syncline

N

Anticline

Normal fault

Reverse fault

Coal mine

Likou syncline

Niuzhuang syncline

Baishigou anticline

Guozhuang anticline

Xiangxia fault

Lingwushan syncline

Guodishan

normal fault

Xiaxian

fault

No 9

No 5

No 7No 2

No 8

No 1

No 10

No 12

No 4

No 6No 11

No 3

Beijing

Test area

Pingdingshan city

150

(km)


Roadway

Horizontal borehole

Vert

ical

bor

ehol

e

10∘


Dep

th=30

m d

iam

eter=130

mm











Boreholeposition

1205901

1205902

1205903


0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e



minus1000




0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)






N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1198911198883

= minus

1199034

0+ 31199032

01199032

1

3 (1199032

0minus 1199032

1)3

1198911198884

= minus

31199032

01199032

1+ 1199034

1

3 (1199032

0minus 1199032

1)3

1198911198885

=

31199036

01199034

1+ 1199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198886

=

1199036

01199034

1+ 31199034

01199036

1

3 (1199032

0minus 1199032

1)3

1198911198887

= minus

21199036

01199032

1+ 1199034

01199034

1+ 1199032

01199036

1

(1199032

0minus 1199032

1)3

1198911198888

= minus

1199036

01199032

1+ 1199034

01199034

1+ 21199032

01199036

1

(1199032

0minus 1199032

1)3

(17)


1) under nonuniform


1199061198791

(1199031 119904) =

1199021(119904) 1199031

2119866119879

1198981198791

cos 2120579 (18)

where

1198981198791

= 1198911198791

minus 1198911198793

119903minus4

1+ 21205831198791198911198792

1199032


119879) 1198911198794

119903minus2

1(19)

with

1198911198791

=

1199036

1+ 1199034

11199032

2+ 21199032

11199034

2

(1199032

1minus 1199032

2)3

1198911198792

= minus

1199034

1+ 31199032

11199032

2

3 (1199032

1minus 1199032

2)3

1198911198793

=

31199036

11199034

2+ 1199034

11199036

2

3 (1199032

1minus 1199032

2)3

1198911198794

= minus

21199036

11199032

2+ 1199034

11199034

2+ 1199032

11199036

2

(1199032

1minus 1199032

2)3

(20)


1199061199030

(1199030 119904) = 119906

1198880(1199030 119904)

1199061199031

(1199030 119904) = 119906

1198881(1199030 119904)

1199061015840

1198880(1199031 119904) = 119906

1198790(1199031 119904)

1199061015840

1198881(1199031 119904) = 119906

1198791(1199031 119904)

(21)


1199010(119904) =

Δ119869

11198660(119904) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) (1198661198791198991015840

1198880+ 1198661198881198981198790

) 119866119888)

sdot

1 + 120582

2

119875

1199020(119904) =

Δ119869

((1198661198791198661198881198991015840

1198880+ 1198662

1198881198981198790

) 1198661198791198661198881198981015840

1198880) (1119866

0(119904)) + ((119866

11987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880) 1198661198791198661198881198981015840

1198880)

sdot

1 + 120582

2

119875

1199011(119904) =

(3 minus 41205830) Δ119869

((5 minus 61205830) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) (1198661198791198991015840

1198881+ 1198661198881198981198791

) 119866119888)

sdot

1 minus 120582

2

119875

1199021(119904) =

(3 minus 41205830) Δ119869

((1198661198791198991015840

1198881+ 1198661198881198981198791

) 1198661198791198981015840

1198881) ((5 minus 6120583

0) 3) (1119866

0(119904)) + ((119866

11987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881) 1198661198791198661198881198981015840

1198881)

sdot

1 minus 120582

2

119875

(22)


119869 (119905) =

1

1198661

+

1

1198662

(1 minus exp(minus

1198662119905

120578

)) (23)



be written as

1 + 1198753 = 119876

3120574 + 119876

4 (24)


G1

G2

120578


where

1198753=

120578

1198661+ 1198662

1198763=

11986611198662

1198661+ 1198662

1198764=

1205781198661

1198661+ 1198662

(25)


119902 (119905) = 1199020(119905) + 119902

1(119905) cos 2120579 =

1 + 120582

2

119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198771+ 119866infin1198772

(1 minus exp(minus

1198771+ 11987631198772

11987531198771+ 11987641198772

119905))

+

1 minus 120582

2

(3 minus 41205830) 119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198773+ 119866infin1198774

(1 minus exp(minus

1198773+ 11987631198774

11987531198773+ 11987641198774

119905))

sdot cos 2120579

(26)

where119866infin



1198771=

1198661198791198991015840

1198880+ 1198661198881198981198790

1198661198791198981015840

1198880

1198772=

1198661198791198991015840

1198881+ 1198661198881198981198791

1198661198791198981015840

1198881

5 minus 61205830

3

1198773=

11986611987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880

1198661198791198661198881198981015840

1198880

1198774=

11986611987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881

1198661198791198661198881198981015840

1198881

(27)




0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900

t0 = 0

t0 = 10ht0 = 20ht0 = 50h

t0 = 100ht0 = 200ht0 = 500h







0= 65mm 119903

1= 55mm 119903

2= 50mm 119875 = 1MPa and


=

4GPa 120583119888= 035 119866

119879= 80GPa and 120583



1= 2576MPa 119866

2= 1903MPa 120578 =

31671198905MPasdoth and 1205830





119888) are


0= 10 h



0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900



(a)

0 100 200 300 400 500

025

030

035

040

045

050

055

060

Ratio

of s

tabl

e rec

over

y str

ess t

o in

situ

stre

ss

GTGc

(b)











infin that is the




5 Field Test



0 200 400 600 800 100000

02

04

06

08

10

t (h)

q(t

)1205900

G1G2 = 1 5G1G2 = 4 1G1G2 = 1 2G1G2 = 10 1

G1G2 = 1 1G1G2 = 20 1G1G2 = 2 1G1G2 = 50 1

(a)

0 10 20 30 40 5001

02

03

04

05

06

07

08

09

10

Fina

l rec

over

y str

ess r

atio

GiniGinfin

(b)



Parameter 1205901

1205902

1205903








Syncline

N

Anticline

Normal fault

Reverse fault

Coal mine

Likou syncline

Niuzhuang syncline

Baishigou anticline

Guozhuang anticline

Xiangxia fault

Lingwushan syncline

Guodishan

normal fault

Xiaxian

fault

No 9

No 5

No 7No 2

No 8

No 1

No 10

No 12

No 4

No 6No 11

No 3

Beijing

Test area

Pingdingshan city

150

(km)


Roadway

Horizontal borehole

Vert

ical

bor

ehol

e

10∘


Dep

th=30

m d

iam

eter=130

mm











Boreholeposition

1205901

1205902

1205903


0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e



minus1000




0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)






N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










G1

G2

120578


where

1198753=

120578

1198661+ 1198662

1198763=

11986611198662

1198661+ 1198662

1198764=

1205781198661

1198661+ 1198662

(25)


119902 (119905) = 1199020(119905) + 119902

1(119905) cos 2120579 =

1 + 120582

2

119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198771+ 119866infin1198772

(1 minus exp(minus

1198771+ 11987631198772

11987531198771+ 11987641198772

119905))

+

1 minus 120582

2

(3 minus 41205830) 119875(1 minus

119866infin

119866ini)

sdot

exp (minus11986621199050120578)

1198773+ 119866infin1198774

(1 minus exp(minus

1198773+ 11987631198774

11987531198773+ 11987641198774

119905))

sdot cos 2120579

(26)

where119866infin



1198771=

1198661198791198991015840

1198880+ 1198661198881198981198790

1198661198791198981015840

1198880

1198772=

1198661198791198991015840

1198881+ 1198661198881198981198791

1198661198791198981015840

1198881

5 minus 61205830

3

1198773=

11986611987911989811988801198991015840

1198880minus 11986611987911989911988801198981015840

1198880+ 1198661198881198981198790

1198981198880

1198661198791198661198881198981015840

1198880

1198774=

11986611987911989811988811198991015840

1198881minus 11986611987911989911988811198981015840

1198881+ 1198661198881198981198791

1198981198881

1198661198791198661198881198981015840

1198881

(27)




0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900

t0 = 0

t0 = 10ht0 = 20ht0 = 50h

t0 = 100ht0 = 200ht0 = 500h







0= 65mm 119903

1= 55mm 119903

2= 50mm 119875 = 1MPa and


=

4GPa 120583119888= 035 119866

119879= 80GPa and 120583



1= 2576MPa 119866

2= 1903MPa 120578 =

31671198905MPasdoth and 1205830





119888) are


0= 10 h



0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900



(a)

0 100 200 300 400 500

025

030

035

040

045

050

055

060

Ratio

of s

tabl

e rec

over

y str

ess t

o in

situ

stre

ss

GTGc

(b)











infin that is the




5 Field Test



0 200 400 600 800 100000

02

04

06

08

10

t (h)

q(t

)1205900

G1G2 = 1 5G1G2 = 4 1G1G2 = 1 2G1G2 = 10 1

G1G2 = 1 1G1G2 = 20 1G1G2 = 2 1G1G2 = 50 1

(a)

0 10 20 30 40 5001

02

03

04

05

06

07

08

09

10

Fina

l rec

over

y str

ess r

atio

GiniGinfin

(b)



Parameter 1205901

1205902

1205903








Syncline

N

Anticline

Normal fault

Reverse fault

Coal mine

Likou syncline

Niuzhuang syncline

Baishigou anticline

Guozhuang anticline

Xiangxia fault

Lingwushan syncline

Guodishan

normal fault

Xiaxian

fault

No 9

No 5

No 7No 2

No 8

No 1

No 10

No 12

No 4

No 6No 11

No 3

Beijing

Test area

Pingdingshan city

150

(km)


Roadway

Horizontal borehole

Vert

ical

bor

ehol

e

10∘


Dep

th=30

m d

iam

eter=130

mm











Boreholeposition

1205901

1205902

1205903


0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e



minus1000




0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)






N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 200 400 600 800 100000

01

02

03

04

05

06

t (h)

q(t

)1205900



(a)

0 100 200 300 400 500

025

030

035

040

045

050

055

060

Ratio

of s

tabl

e rec

over

y str

ess t

o in

situ

stre

ss

GTGc

(b)











infin that is the




5 Field Test



0 200 400 600 800 100000

02

04

06

08

10

t (h)

q(t

)1205900

G1G2 = 1 5G1G2 = 4 1G1G2 = 1 2G1G2 = 10 1

G1G2 = 1 1G1G2 = 20 1G1G2 = 2 1G1G2 = 50 1

(a)

0 10 20 30 40 5001

02

03

04

05

06

07

08

09

10

Fina

l rec

over

y str

ess r

atio

GiniGinfin

(b)



Parameter 1205901

1205902

1205903








Syncline

N

Anticline

Normal fault

Reverse fault

Coal mine

Likou syncline

Niuzhuang syncline

Baishigou anticline

Guozhuang anticline

Xiangxia fault

Lingwushan syncline

Guodishan

normal fault

Xiaxian

fault

No 9

No 5

No 7No 2

No 8

No 1

No 10

No 12

No 4

No 6No 11

No 3

Beijing

Test area

Pingdingshan city

150

(km)


Roadway

Horizontal borehole

Vert

ical

bor

ehol

e

10∘


Dep

th=30

m d

iam

eter=130

mm











Boreholeposition

1205901

1205902

1205903


0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e



minus1000




0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)






N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 200 400 600 800 100000

02

04

06

08

10

t (h)

q(t

)1205900

G1G2 = 1 5G1G2 = 4 1G1G2 = 1 2G1G2 = 10 1

G1G2 = 1 1G1G2 = 20 1G1G2 = 2 1G1G2 = 50 1

(a)

0 10 20 30 40 5001

02

03

04

05

06

07

08

09

10

Fina

l rec

over

y str

ess r

atio

GiniGinfin

(b)



Parameter 1205901

1205902

1205903








Syncline

N

Anticline

Normal fault

Reverse fault

Coal mine

Likou syncline

Niuzhuang syncline

Baishigou anticline

Guozhuang anticline

Xiangxia fault

Lingwushan syncline

Guodishan

normal fault

Xiaxian

fault

No 9

No 5

No 7No 2

No 8

No 1

No 10

No 12

No 4

No 6No 11

No 3

Beijing

Test area

Pingdingshan city

150

(km)


Roadway

Horizontal borehole

Vert

ical

bor

ehol

e

10∘


Dep

th=30

m d

iam

eter=130

mm











Boreholeposition

1205901

1205902

1205903


0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e



minus1000




0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)






N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Syncline

N

Anticline

Normal fault

Reverse fault

Coal mine

Likou syncline

Niuzhuang syncline

Baishigou anticline

Guozhuang anticline

Xiangxia fault

Lingwushan syncline

Guodishan

normal fault

Xiaxian

fault

No 9

No 5

No 7No 2

No 8

No 1

No 10

No 12

No 4

No 6No 11

No 3

Beijing

Test area

Pingdingshan city

150

(km)


Roadway

Horizontal borehole

Vert

ical

bor

ehol

e

10∘


Dep

th=30

m d

iam

eter=130

mm











Boreholeposition

1205901

1205902

1205903


0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e



minus1000




0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)






N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Boreholeposition

1205901

1205902

1205903


0 5 10 15 20 25 30 35

0

1000

2000

3000

4000

5000

6000

Mic

rostr

ain

valu

e



minus1000




0 100 200 300 400 500

0

2

4

6

8

10

12

14

16

1234

56Temperature

Time (day)Re

cove

ry st

ress

(MPa

)

10

15

20

25

30

35

Tem

pera

ture

(∘C)






N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










N






7 Conclusions








Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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