Research Article A Nonlinear Creep Model of Rock Salt and...

Research ArticleA Nonlinear Creep Model of Rock Salt and Its NumericalImplement in FLAC3D

Xinrong Liu,1,2 Xin Yang,1,2 and Junbao Wang3

1College of Civil Engineering, Chongqing University, Chongqing 400045, China2Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University,Ministry of Education, Chongqing 400030, China3College of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China

Correspondence should be addressed to Xin Yang; [email protected]

Received 8 February 2015; Accepted 4 March 2015

Academic Editor: Luigi Nicolais

Copyright © 2015 Xinrong Liu et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Creep characteristics are integral mechanical properties of rock salt and are related to both long-term stability and security of rocksalt repository. Rock salt creep properties are studied in this paper through employing combinedmethods of theoretical analysis andnumerical simulation with a nonlinear creep model and the secondary development in FLAC3𝐷 software. A numerical simulationof multistage loading creep was developed with the model and resulting calculations were found consequently to coincide withpreviously tested data.

1. Preface

Rock salt creep research has been the subject of a largenumber of studies: King [1] produced a series of experi-mental research on rock salt creep properties under varioustemperatures and different axial stress levels, identifyingthe relationship between deformation and time. Paul [2]researched the creep properties of four types of rock salt.Hunsche [3, 4] and Cristescu [5, 6] employed diversifiedloading methods to conduct research on rock salt propertiesin multiple creep stages. Chan et al. [7, 8] applied continuumdamage mechanics in the creep analysis of rock salt to studythe unelastic flow caused by damage from the transitionof creep stage to the damage accumulation in acceleratedcreep stage and to the final destruction process. Based onthe rheological model (Lubby2), using continuum damagemechanics and considering the displacement, hardening,softening and recovery mechanism, and the damage anddamage recovery mechanism of rock salt, Lux and Hou [9]proposed theHou/Lux creep damagemodel. Xiande et al. [10,11] researched Changshan andQiaohu rock salt and observedthat, following analysis of the evolution and destructionprocess of cracks on rock salt specimens, the two rock salt

types differed relatively significantly in the creep damageprocess, mainly due to difference in NaCl content, grain size,and cementation between grains. Chen et al. [12] conductedcreep property experiments of two rock salt types, rock saltfrom greisens salt mine and rock salt with interlayer. Creepconstitutive relation was developed under different confiningpressure and axial pressure for each rock salt type.

Rock salt creep modeling research has experienced enor-mous progress marked by numerous research achievements.Experimental conditions and technical limitations, however,have slowed the study of rock salt nonlinear creep modelingas related to the obvious nonlinear properties in the attenua-tion creep and steady-state creep rock salt stages, especiallysoft rock [13–16]. On the basis of rock salt creep modelresearch achievements and according to the indoor creep testresults [17], this study proposes and builds a nonlinear creepmodel of rock salt and develops a secondary correspondingnonlinear creep model with FLAC3D software. Followingnumerical simulation of the creep test with the developedmodel, a comparison of simulated results and experimentalresults indicates that the developed creep model is workableand may even provide reference for creep calculation inengineering practice.

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015, Article ID 285158, 8 pageshttp://dx.doi.org/10.1155/2015/285158

2 Advances in Materials Science and Engineering

𝜎s

𝜎0 𝜎0

GK

𝜂K

(m,t)𝜂B

(n,t)

𝜂M

(m,t)GM

Figure 1: Nonlinear viscoelasticity plasticity creep model.

2. Rock Salt Nonlinear Creep Equation

According to research results [18–20], the viscosity coefficientin the creep model varies over time according to rules, whichhave the following three features: (1) the initial value is not 0;(2) there is monotone escalation with the increasing of time;(3) there exists upper limit value.

Assuming the viscosity coefficient of the Newton modelvaries with time according to the following formula:

𝜂 (𝑡) = 𝜂0

𝑡 + 1

𝑡 + 1 + 𝑚, (1)

where 𝜂0,𝑚 refer to thematerial constant and 𝑡 refers to creep

time.This study proposes the nonlinear creep equation for

enhanced perspective of the nonlinear creep properties ofrock salt (Figure 1).

Thus, by analogical method, the axial creep equation ofrock salt in three-dimensional stress status can be developedas follows.

When 𝜎0

< 𝜎𝑠, the nonlinear viscoelasticity plasticity

creep model equation is

𝜀 =𝜎0

𝐸1

+𝜎0

𝜂10

[𝑡 + 𝑚 ln (𝑡 + 1)]

+𝜎0

𝐸2

{1 − exp{−𝐸2

𝜂20

[𝑡 + 𝑚 ln (𝑡 + 1)]}} .

(2)

When 𝜎0

≥ 𝜎𝑠, the nonlinear viscoelasticity plasticity

creep model equation is

𝜀 =𝜎0

𝐸1

+𝜎0

𝜂10

[𝑡 + 𝑚 ln (𝑡 + 1)]

+𝜎0

𝐸2

{1 − exp{−𝐸2

𝜂20

[𝑡 + 𝑚 ln (𝑡 + 1)]}}

+𝜎0− 𝜎𝑠

𝜂30

𝑡

(1 − 𝑛𝑡)2.

(3)

3. The Realization of Nonlinear Creep Modelin FLAC3D Software

3.1. The Differential Form of Nonlinear Creep Model. As eachpart of the model is in series connection, there is equal stressand added strain; that is,

𝑆𝑖𝑗= 𝑆𝑀

𝑖𝑗= 𝑆𝐾

𝑖𝑗= 𝑆𝐵

𝑖𝑗(4)

𝑒𝑖𝑗= 𝑒𝑀

𝑖𝑗+ 𝑒𝐾

𝑖𝑗+ 𝑒𝐵

𝑖𝑗. (5)

For the nonlinear Kelvin model, deviator stress 𝑆𝑖𝑗and

deviator strain 𝑒𝐾𝑖𝑗have the following relation:

𝑆𝑖𝑗= 2𝜂𝐾

(𝑚,𝑡)𝑒𝐾

𝑖𝑗+ 2𝐺𝐾𝑒𝐾

𝑖𝑗, (6)

where𝐺𝐾 refers to the shear modulus of the nonlinear Kelvinmodel and 𝜂𝐾

(𝑚,𝑡)refers to the viscosity coefficient: 𝜂𝐾

(𝑚,𝑡)=

𝜂𝐾0((𝑡 + 1)/(𝑡 + 1 + 𝑚)).For the nonlinear Maxwell model, deviator stress 𝑆

𝑖𝑗and

deviator strain rate 𝑒𝑀𝑖𝑗have the following relation:

𝑒𝑀

𝑖𝑗=

𝑆𝑖𝑗

2𝐺𝑀+

𝑆𝑖𝑗

2𝜂𝑀(𝑚,𝑡)

, (7)

where 𝐺𝑀 refers to the shear modulus of the nonlinear

Maxwell model and 𝜂𝑀

(𝑚,𝑡)refers to the viscosity coefficient:

𝜂𝑀(𝑚,𝑡)

= 𝜂𝑀0((𝑡 + 1)/(𝑡 + 1 + 𝑚)).

For the nonlinear Bingham model, that is,

𝑒𝐵

𝑖𝑗=

{𝜙 (𝐹)}

2𝜂𝐵(𝑛,𝑡)

, (8)

where 𝐹 refers to yield function, 𝜙(𝐹) refers to switchfunction, 𝐹 = 𝜎

1− 𝜎3− 𝜎𝑠,

𝜙 (𝐹) ={

{

{

0 (𝐹 < 0)

𝐹 (𝐹 ≥ 0) ,

𝜂𝐵

(𝑛,𝑡)= 𝜂𝐵

0((1 − 𝑛𝑡)

3/ (1 + 𝑛𝑡)) ,

(9)

and 𝜂𝐵(𝑛,𝑡)

refers to the viscosity coefficient of nonlinear Bing-ham model, and for secondary development with FLAC3Dsoftware, formula (5) should first be written as incrementform; that is,

Δ𝑒𝑖𝑗= Δ𝑒𝑀

𝑖𝑗+ Δ𝑒𝐾

𝑖𝑗+ Δ𝑒𝐵

𝑖𝑗. (10)

Applying central difference, formula (6) should be

𝑆𝑖𝑗Δ𝑡 = 2𝜂

𝐾

(𝑚,𝑡)Δ𝑒𝐾

𝑖𝑗+ 2𝐺𝐾𝑒𝐾

𝑖𝑗Δ𝑡, (11)

where Δ𝑒𝐾𝑖𝑗

= 𝑒𝐾,𝑁𝑖𝑗

− 𝑒𝐾,𝑂𝑖𝑗

, 𝑆𝑖𝑗= (𝑆𝑁𝑖𝑗

+ 𝑆𝑂𝑖𝑗)/2, and 𝑒

𝐾

𝑖𝑗= (𝑒𝐾,𝑁𝑖𝑗

+

𝑒𝐾,𝑂𝑖𝑗

)/2, among which 𝑆𝑖𝑗, 𝑒𝐾𝑖𝑗refer to the average deviator

stress anddeviator strain, respectively, of the nonlinearKelvinmodel; 𝑆𝑁

𝑖𝑗, 𝑆𝑂𝑖𝑗refer to the deviator stress tensors of Step i and

Step i-1, respectively; 𝑒𝐾,𝑁𝑖𝑗

, 𝑒𝐾,𝑂𝑖𝑗

refer to the deviator straintensors of Step i and Step i-1, respectively.

Consolidating the formula (11), the updated deviatorstrain formula of Step i in the nonlinear Kelvin model canbe

𝑒𝐾,𝑁

𝑖𝑗=

1

𝐴[(𝑆𝑁

𝑖𝑗+ 𝑆𝑂

𝑖𝑗)

Δ𝑡

4𝜂𝐾(𝑚,𝑡)

− 𝐵𝑒𝐾,𝑂

𝑖𝑗] , (12)

where 𝐴 = 1 + 𝐺𝐾Δ𝑡/2𝜂𝐾(𝑚,𝑡)

and 𝐵 = 𝐺𝐾Δ𝑡/2𝜂𝐾(𝑚,𝑡)

− 1.

Advances in Materials Science and Engineering 3

Table 1: Calculating parameter of creep model.

𝐾/MPa 𝐺1/MPa 𝐺

2/MPa 𝜂

10/MPa⋅h 𝜂

20/MPa⋅h 𝑚

2409 1112 3553 356650 50678 40𝜂30/MPa⋅h 𝑛 𝑐/MPa 𝜑/∘ 𝜎

𝑡/MPa 𝜎

𝑠/MPa

300000 0.2 5.8 40 1 35

Further, consolidating formula (12), we can acquire

Δ𝑒𝐾

𝑖𝑗= 𝑒𝐾,𝑁

𝑖𝑗− 𝑒𝐾,𝑂

𝑖𝑗

=1

𝐴[(𝑆𝑁

𝑖𝑗+ 𝑆𝑂

𝑖𝑗)

Δ𝑡

4𝜂𝐾(𝑚,𝑡)

− (𝐴 + 𝐵) 𝑒𝐾,𝑂

𝑖𝑗] .

(13)

Similarly, the increment form of formula (7) can beexpressed as

Δ𝑒𝑀

𝑖𝑗=

Δ𝑆𝑖𝑗

2𝐺𝑀+

𝑆𝑖𝑗

2𝜂𝑀(𝑚,𝑡)

Δ𝑡. (14)

For the nonlinear Bingham model, when 𝐹 < 0, theincrement form of formula (8) is

Δ𝑒𝐵

𝑖𝑗= 0. (15a)

When 𝐹 ≥ 0, its increment form is

Δ𝑒𝐵

𝑖𝑗=

𝑆𝐵

𝑖𝑗− (2/3) 𝜎

𝑠


Δ𝑡. (15b)

Substitute formula (10) with formulas (13), (14), and (15a)and (15b) and consolidate.The updated stress formula of Stepi in nonlinear viscoelasticity plasticity creep model is

𝑆𝑁

𝑖𝑗=

{{{{

{{{{

{

1

𝑎[Δ𝑒𝑖𝑗+ (

𝐵

𝐴+ 1) 𝑒𝐾,𝑂

𝑖𝑗+ 𝑏𝑆𝑂𝑖𝑗] 𝐹 < 0,

1

𝑎[Δ𝑒𝑖𝑗+ (

𝐵

𝐴+ 1) 𝑒𝐾,𝑂

𝑖𝑗+ 𝑏𝑆𝑂𝑖𝑗+

𝜎𝑠Δ𝑡


] 𝐹 ≥ 0,

(16)

where when 𝐹 < 0, 𝑎 = 1/2𝐺𝑀 + Δ𝑡/4𝜂𝑀(𝑚,𝑡)

+ Δ𝑡/4𝐴𝜂𝐾(𝑚,𝑡)

and 𝑏 = 1/2𝐺𝑀 − Δ𝑡/4𝜂𝑀(𝑚,𝑡)

− Δ𝑡/4𝐴𝜂𝐾(𝑚,𝑡)

; when 𝐹 ≥ 0, 𝑎 =

1/2𝐺𝑀+Δ𝑡/4𝜂𝑀(𝑚,𝑡)

+Δ𝑡/4𝐴𝜂𝐾(𝑚,𝑡)

+Δ𝑡/4𝜂𝐵(𝑚,𝑡)

and 𝑏 = 1/2𝐺𝑀−

Δ𝑡/4𝜂𝑀(𝑚,𝑡)

− Δ𝑡/4𝐴𝜂𝐾(𝑚,𝑡)

− Δ𝑡/4𝜂𝐵(𝑚,𝑡)

; 𝐴, 𝐵 mean the same asthose appearing in formula (12).

Thus, stress-strain relations of the nonlinear viscoelastic-ity plasticity creep model can be expressed by formula (16) inthe program.

Yield function is derived when the software automaticallyreads and recognizes the loaded stress level, introduced in thisstudy as the concept of stress intensity:

𝑞 = 𝜎𝑖

=1

√2[(𝜎1− 𝜎2)2+ (𝜎2− 𝜎3)2+ (𝜎3− 𝜎1)2]0.5

.(17)

Known from the classic elastic-plastic mechanics,

𝑞 = √3

2𝑆𝑖𝑗𝑆𝑖𝑗

𝑆𝑖𝑗= 𝜎𝑖𝑗− 𝜎𝑚𝛿𝑖𝑗

𝜎𝑚

=1

3(𝜎11

+ 𝜎22

+ 𝜎33) ,

(18)

where 𝑆𝑖𝑗refers to deviator tensor of stress; 𝜎

𝑖𝑗refers to stress

tensor; 𝜎𝑚refers to spherical tensor of stress.

Each component of the stress tensor can be indicated bythe corresponding pointer with FLAC3D software, and thestress intensity 𝑞 can be calculated according to formula (18).After reading stress intensity with relevant yield function,software can automatically identify yield condition accordingto the definition of stress intensity; if there is uniaxialcompression 𝑞 = 𝜎

1and triaxial compression with equal

confining pressure, 𝑞 = 𝜎1

− 𝜎3. As recursive function

cannot be applied in FLAC3D software, the nonstationarynormalizing of model viscosity coefficient in this study isderived mainly by the accumulation of ps->Creep pointer(indicating the creep time increment Δ𝑡) internally installedin the FLAC3D software.

3.2. Verification of the Model Program

3.2.1. Experiment Simulation. A triaxial compression creepexperiment is simulated with the program in this sectionto verify validity of the nonlinear viscoelasticity plasticitycreep model computing program. The simulated test sampleis a cylindrical standard sample with diameter of 50mmand height of 100mm and divided into 2560 units and2827 points. Apply normal constraint to the bottom of thesample, vertical and uniformly distributed load to the top,and confining pressure to the circumferential surface area,respectively. Nonlinear viscoelasticity plasticitymodel is thenapplied as the creep model with experiment results [17]utilized as creep parameters and the loading scheme appliedusing fixed confining pressure and four-stage axial pressure(20MPa, 25MPa, 30MPa, and 37MPa), respectively. As thetriaxial compression creep of rock salt did not enter intothe accelerated creep stage in the experiment [17], criticalload is unknown 𝜎

𝑠, and the model parameter 𝜂

30and 𝑛 in

its accelerated creeping stage. Validity of the nonlinear vis-coelasticity plasticity creep model computing program, withspecific parameter values provided in Table 1, is established as𝜎𝑠= 35MPa, 𝜂

30= 30000MPa⋅h, and 𝑛 = 0.2.


Rotation:Center:X: 0.000e + 000

Y: 5.000e − 002Z: 0.000e + 000

X: 90.000Y: 0.000Z: 0.000

Dist: 1.883e − 001 Mag.: 0.512Ang.: 22.500

Contour of Y-displacementMagfac = 0.000e + 000

Interval = 1.0e − 004

−6.9606e − 004 to −6.0000e − 004

−6.0000e − 004 to −5.0000e − 004

−5.0000e − 004 to −4.0000e − 004

−4.0000e − 004 to −3.0000e − 004

−3.0000e − 004 to −2.0000e − 004

−2.0000e − 004 to −1.0000e − 004

0.0000e + 000 to 0.0000e + 000

−1.0000e − 004 to 0.0000e + 000

(a) Axial pressure 20MPa

Center:X: 0.000e + 000

Y: 5.000e − 002

Z: 0.000e + 000

Rotation:X: 90.000Y: 0.000Z: 0.000

Dist: 1.883e − 001 Mag.: 0.512Ang.: 22.500



−9.7495e − 004 to −9.0000e − 004

−9.0000e − 004 to −8.0000e − 004

−8.0000e − 004 to −7.0000e − 004

−7.0000e − 004 to −6.0000e − 004

−6.0000e − 004 to −5.0000e − 004

−5.0000e − 004 to −4.0000e − 004

−4.0000e − 004 to −3.0000e − 004

−3.0000e − 004 to −2.0000e − 004

−2.0000e − 004 to −1.0000e − 004

0.0000e + 000 to 0.0000e + 000

−1.0000e − 004 to 0.0000e + 000

(b) Axial pressure 25MPa

Center:X: 0.000e + 000

Y: 5.000e − 002

Z: 0.000e + 000

Rotation:

Dist: 1.883e − 001 Mag.: 0.512Ang.: 22.500



X: 90.000Y: 0.000Z: 0.000

−1.2539e − 003 to −1.2000e − 003

−1.2000e − 003 to −1.0000e − 003

−1.0000e − 003 to −8.0000e − 004

−8.0000e − 004 to −6.0000e − 004

−6.0000e − 004 to −4.0000e − 004

−4.0000e − 004 to −2.0000e − 004

−2.0000e − 004 to 0.0000e + 000

0.0000e + 000 to 0.0000e + 000

(c) Axial pressure 30MPa

Center:X: 0.000e + 000

Y: 5.000e − 002Z: 0.000e + 000

Rotation:X: 90.000Y: 130.000Z: 360.000

Dist: 1.883e − 001 Mag.: 0.512Ang.: 22.500



−2.6242e − 003 to −2.3100e − 003

−2.3100e − 003 to −1.9800e − 003

−1.9800e − 003 to −1.6500e − 003

−1.6500e − 003 to −1.3200e − 003

−1.3200e − 003 to −9.9000e − 004

−9.9000e − 004 to −6.6000e − 004

−6.6000e − 004 to −3.3000e − 004

−3.3000e − 004 to 0.0000e + 000

0.0000e + 000 to 0.0000e + 000

(d) Axial pressure 37MPa

Figure 2: The 𝑌-direction (vertical) displacement nephogram for the test sample under different stress levels.

Figure 2 is the 𝑌-direction (vertical) displacement con-tour line nephogram for the test sample under differentstress levels. The calculated time for creep in the first threestages of loading is 15 h and is 4.5 h for the fourth stageof loading. Observations of the figure indicate that verticaldisplacement is the largest at the upper end and reduceswith progression toward the bottom. Under the first threestages of loading, maximum vertical displacement of the testsample gradually increases with the increase of axial stress, at0.696mm, 0.975mm, and 1.254mm, respectively. Under thefourth stage of loading, however, as axial stress exceeds thecritical load setting of accelerated creep, vertical displacementof the test sample increases rapidly.

Figure 3 is the curve indicating axial pressure values forthe relationship between time and the vertical displacementat the upper surface center of the test sample under differentstress levels. Creep curve under the first three stages ofloading alters with similar rules undergoing the two stagesof attenuation creep and steady state creep. All instantaneousdeformation, including creep deformation within the same

time and the creep rate of the test sample, with the increaseof triaxial compression, increases gradually. Simulated creepexperiment in the program increases gradually aligningwith the indoor experiment result. Under the fourth stageof loading, as the axial stress exceeds the critical load ofaccelerated creep, the creep curve experiences three stages,attenuation creep, steady state creep, and accelerated creep.The test sample is vulnerable to damage upon entering theaccelerated creep stage resulting in the nonlinear acceleratedincrease of deformation over time. This also agrees withthe actual situation, proving the rationality and validityof the secondary development program for the nonlinearviscoelasticity plasticity creep model in this paper.

3.2.2. Analysis of Examples

(1) Calculation Model and Parameter. Viability of this modelcalculation program for practical engineering is demon-strated with a simple rock salt gas storage model and bycomparing the calculation results with the Cvisc model


0.4

0.8

1.2

1.6

2

0 3 6 9 12 15

20MPa25MPa

30MPa37MPa

Stra

in (%

)

Time (h)

Figure 3: Creep curve for test sample under different stress levels.

Figure 4: Rock salt gas storage model.

installed in FLAC3D. A portion of the model (1/4) was sym-metrically set up to conserve calculation time for calculatingthe creep during a period of 2 years. Gas storage occurredspherically with a radius of 20m and the origin of coordinatesplaced in the center of the sphere. Horizontal, upper, andlower boundaries of the model were at 200m resulting in arectangular calculation area of 200m × 200m × 400m asdisplayed in Figure 4. Normal constraint was applied to thebottom and four vertical surfaces of the model and 20MPawas applied to equally distribute load to the top surface of themodel.

Accelerated creep calculation with the Cvisc model is notavailable; thus, a very large value is assumed as the critical

load of accelerated creep for calculation in the study modelto prevent the surrounding rock of the storage cavern fromentering the accelerated creep stage. Deducting to a certainextent with themethod provided in literature [21], we convertthe elastic-plastic mechanics parameters obtained from theindoor compression experiment of rock salt samples into theparameter of the rock mass with the same creep parametersshown in Table 1. Refer to Table 2 for the specific parametervalues. Calculations with the nonlinear model of this studyutilize all parameters in Table 2 while calculations with theCvisc model utilize all parameters except𝑚 in Table 2. Com-parisons then reveal the influence of nonlinear coefficient 𝑚to the calculation results under identical parameters.

(2) Comparison of the Calculation Results. Figure 5 displaysthe displacement contour line calculated by two models forthe surrounding rock following two years of creep. Dis-placement distribution rules then, as calculated with the twomodels, are essentially consistent. Calculations by the studymodel are slightly larger, with maximum displacement of1.27m while maximum displacement calculated by the Cviscmodel was 1.21m. Displacement distribution range of thecavity walls varies as the red zone (parts with displacementabove 1.1m) of the study model nearly completely covers allcavity walls, while the red zone of the Cvisc model mainlyconcentrates at the top and shoulder of the cavity.

Figure 6 displays curves, calculated by the two models,for vertical displacement changes over time at the vaultpoint of the cavity. Instantaneous deformation at the cav-ern excavation moment is nearly consistent as calculatedby the two models. The two curves transform over timesimilarly through the attenuation deformation stage to thesteady deformation stage. Compared with the Cvisc model,the attenuation deformation stage in the nonlinear modelpersists for a shorter time with larger deformation and higherdeformation rate in the same period.The above indicates thatwhen all the other parameters are the same, the nonlinearcoefficient𝑚 in this model works to larger calculation results.

Figure 7 illustrates the distribution of plastic zonesaround the cavern as calculated by the two models. Thedistribution range of plastic zones calculated by the studymodel is slightly larger than the range calculated by the Cviscmodel. Utilizing the Fish language programming, volumes ofthe plastic zones calculated by the studymodel were 13649m3and 12542m3 as calculated by the Cvisc model, indicatingthat the nonlinear coefficient 𝑚 in this model affects thecalculation.

4. Conclusions

Secondary development of the nonlinear viscoelasticity plas-ticity creep model of rock salt is produced in this study andverifies the obtainedmodel calculation program, drawing thefollowing conclusions.

(1) Based on finite difference theory, this study deducesthe finite difference expression form in detail forthe nonlinear viscoelasticity plasticity creep model ofrock salt in combination with the favorable secondary


Table 2: Calculation parameters of the rock salt gas storage example.

𝐾/MPa 𝐺1/MPa 𝐺

2/MPa 𝜂

10/MPa⋅h 𝜂

20/MPa⋅h 𝑐/MPa 𝜑/∘ 𝜎

𝑡/MPa 𝑚

1927 890 3553 356650 50678 1.74 34 1 40

Center:X: 1.000e + 002

Y: 0.000e + 000

Z: −1.000e + 002

Rotation:X: 90.000Y: 50.000Z: 0.000

Dist: 7.530e + 002 Mag.: 0.512Ang.: 22.500

Contour of displacement mag.Magfac = 0.000e + 000

1.0000e − 001 to 2.0000e − 001

2.0000e − 001 to 3.0000e − 001

3.0000e − 001 to 4.0000e − 001

4.0000e − 001 to 5.0000e − 001

5.0000e − 001 to 6.0000e − 001

6.0000e − 001 to 7.0000e − 001

7.0000e − 001 to 8.0000e − 001

8.0000e − 001 to 9.0000e − 001

9.0000e − 001 to 1.0000e + 000

1.0000e + 000 to 1.1000e + 000

1.1000e + 000 to 1.2000e + 000

1.2000e + 000 to 1.2744e + 000


0.0000e + 000 to 1.0000e − 001

(a) The nonlinear model of this paper

Center: Rotation:X: 90.000Y: 50.000Z: 0.000Mag.: 0.512Ang.: 22.500

Contour of displacement mag.Magfac = 0.000e + 000

0.0000e + 000 to 1.0000e − 001

1.0000e − 001 to 2.0000e − 001

2.0000e − 001 to 3.0000e − 001

3.0000e − 001 to 4.0000e − 001

4.0000e − 001 to 5.0000e − 001

5.0000e − 001 to 6.0000e − 001

6.0000e − 001 to 7.0000e − 001

7.0000e − 001 to 8.0000e − 001

8.0000e − 001 to 9.0000e − 001

9.0000e − 001 to 1.0000e + 000

1.0000e + 000 to 1.1000e + 000

1.1000e + 000 to 1.2000e + 000

1.2000e + 000 to 1.2143e + 000


X: 1.000e + 002

Y: 0.000e + 000

Z: −1.000e + 002

Dist: 7.530e + 002

(b) Cvisc model

Figure 5: Contour lines for the displacement around the cavern calculated by the two models.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.4 0.8 1.2 1.6 2.0

Disp

lace

men

t (m

)

Cvisc model

Creep time (a)

Nonlinear creep model

Figure 6: Curves for displacement at the vault point calculated bythe two models.

development platform of FLAC3D software.The studyrealizes the secondary development of creep modelwith vc++ program, obtaining the dynamic linkingcalculation program of this model.

(2) Results of the triaxial compression creep experimentsimulation indicate that when axial stress is lowerthan critical load of accelerated creep, the test sam-ple’s creep curve undergoes two stages, attenuationcreep and steady state creep; instantaneous strain,creep strain, and creep rate of the samples graduallyincrease with the increase of stress level; when axialstress attains critical load of accelerated creep, thecreep curve undergoes three stages: attenuation creep,steady state creep, and accelerated creep. Simulationresults align with the actual situation, proving thevalidity and rationality of the secondary developmentcalculation program for the study model.

(3) Comparing engineering examples simulated by thestudy model in this paper to samples simulated bythe Cvisc model installed in FLAC3D software, bothdisplacement andplastic zones calculated by the studymodel were larger than those calculated by the Cviscmodel.

Conflict of Interests

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


Center:X: 1.000e + 002

Rotation:

Block state

Dist: 7.530e + 002

Y: 50.000Z: 0.000Mag.: 1.25Ang.: 22.500

Z: −1.000e + 002

X: 90.000Y: 0.000 + 000

NoneShear-n shear-pShear-n shear-p tension-p

Shear-pShear-p tension-pTension-n shear-p tension-pTension-n tension-pTension-p

Shear-n tension-n shear-p tension-p

(a) The nonlinear model of this paper

Center:X: 1.000e + 002

Y: 0.000e + 000

Z: −1.000e + 002

Rotation:X: 90.000Y: 50.000Z: 0.000

Dist: 7.530e + 002 Mag.: 1.25Ang.: 22.500

Block stateNoneShear-n shear-pShear-n shear-p tension-pShear-pShear-p tension-pTension-n shear-p tension-pTension-n tension-pTension-p

(b) Cvisc model

Figure 7: Distribution of plastic zones around the cavern calculated by the two models.

Acknowledgments

This study is supported by the Fundamental ResearchFunds for Central Universities of China (Project no.CDJXS12200005) and National Key Basic Research Programof China (Project no. 2009CB724606); the authors gratefullyacknowledge these supports.

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