sca

W

n 41

Keywords:

Subsea gold mine

Numerical modelling

Safe exploitation

ate

ina

he

the

ana

FL

inuences of sea water pressure as well as mining sequences have been considered. The distributions of

the principal stresses, displacements, plastic zones and pore pressures in the crown pillar are obtained

by simulating the cut-and-ll stoping method at different excavation levels (above level 115 m). The

l resoallengiter haplent

China,

subsea tunnel construction. The size of mining stope is usually

thodcasenesserente the

Numerical modelling is an efcient technique to enhance the

Contents lists available at SciVerse ScienceDirect

.els

InternationalRock Mechanics &

International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256mining conditions [18]. Therefore, we resort to other commerciallidiyuan123@hotmail.com (D. Li).understanding of the mechanical response of crown pillarsassociated with subsea mining. The Itasca software FLAC3D iswidely used in geotechnical and mining engineering. The modelconstruction part in FLAC3D is however not easy for complex

1365-1609/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.ijrmms.2012.08.005

n Corresponding author. Tel.: 86 731 88879612.E-mail addresses: xbli@mail.csu.edu.cn (X. Li),in subsea tunnels cannot be directly applied to subsea minesbecause subsea mining is technically more complicated than

relevant technical problem. However, the inuence of sea waterconstitutes a new challenge.research in this eld is relatively scarce except the Norwegianexperience on subsea tunnels in the Nordic countries and recentlyin China [17]. Nilsen [8], Dahlo and Nilsen [9], Li et al. [4,5] havediscussed the stability problem and the minimum thickness of therock cover in subsea tunnels. However, the Norwegian experience

failure mode analysis of crown pillars, numerical analysis meis a better choice. In addition, the authors have conductedstudies on the determination of safe crown pillar thickbetween underground stope and open-pit mine by using diffanalysis methods [17]. The experience can guide us to handlof coastline is over 32,000 km. Therefore, it is imperative to carryout studies on rock mechanics-related problems with regard tothe safe exploitation of subsea minerals. A key question for subseamining is to determine the minimum required thickness of crownpillar and to keep the sea water out from mining excavations. The

analysis methods and numerical analysis methods. For example,the scaled span method, one of the empirical analysis methodssuggested by Carter [10], has been used to determine the stabilityof surface crown pillars in both active and abandoned mines formore than a decade. However, for stress distribution and rigorous1. Introduction

With the depletion of mineraground, mining exploitation in chas at great depth and under sea watrend all over the world. There arealong and around the coastlines ineld displacement observation shows that the vertical deformation rate of crown pillar is smaller than

0.023%. It reveals that the reserved safety factor is about 1.43 when using cut-and-ll stoping method

from level 165 m to 115 m in the subsea gold mine. The mining activities may extend to level95 m according to the numerical analysis results. A four-year-eld practice shows that the numericalanalysis is helpful to determine the minimum crown pillar thickness in the challenging subsea

gold mine.

& 2012 Elsevier Ltd. All rights reserved.

urces in near surfaceng environments suchs become an inevitabley of mineral resourceswhere the total length

larger than that of tunnels and the blasting induced disturbancein subsea mine is more severe than that in subsea tunnel.Nevertheless, the researches on the stability assessment of crownpillars for underground mines have been extensively reported anddiscussed [1016]. Hutchinson et al. [13] pointed out that threetypes of methods were used to assess the stability of the crownpillar, which included empirical analysis methods, mechanisticCrown pillar

Cut-and-ll stoping methodDetermination of the minimum thicknesof a subsea gold mine based on numeri

Xibing Li n, Diyuan Li, Zhixiang Liu, Guoyan Zhao,

School of Resources and Safety Engineering, Central South University, Changsha, Huna

a r t i c l e i n f o

Article history:

Received 11 October 2011

Received in revised form

8 June 2012

Accepted 17 August 2012Available online 23 October 2012

a b s t r a c t

Sanshandao gold mine, loc

subsea metal mine in Ch

importance to maintain t

excavations. In this paper,

numerical modelling and

the usage of SURPAC and

journal homepage: wwwof crown pillar for safe exploitationl modelling

eihua Wang

0083, China

d at the east coastline of Bohai Sea in the Shandong Province, is the rst

. Since the mining activities are carried out under sea, it is of vital

stability of the crown pillar and to keep the sea water out from the

minimum required thickness of crown pillar is determined based on 3D

lysis. A realistic geometric subsea gold mine is modelled by integrating

AC3D. The numerical analysis is carried out by FLAC3D, in which the

evier.com/locate/ijrmms

Journal ofMining Sciences

software for constructing numerical models, which are then inputinto FLAC3D for further analysis. The mining software SURPAC canrealize a 3D vision of mines conveniently [19]. However, SURPACcannot handle complex stability analysis. One approach to tacklethat problem is to integrate SURPAC and FLAC3D. Some successfulunderground mining model construction examples in China wereintroduced by Lin et al. [20], Liu et al. [21], and Luo et al. [22]through integrating SURPAC and FLAC3D. More recently, Grenonand Hadjigeorgiou integrated a probabilistic limit equilibriumapproach into Gemcom SURPAC for an open pit design and slopestability analysis [23]. Grenon and Laamme carried out slopeorientation assessment for open-pit mines based on the digitalelevation model and GIS algorithms [24]. In this study, a 3D blockmodel for a subsea gold mine is built in SURPAC, which isexported to FLAC3D by a MATLAB program. The crown pillarstability is then numerically assessed by FLAC3D, in which themining sequences and sea water pressure are taken into con-sideration. The in situ rock deformation observation and a four-year-eld practice [25] prove that the numerical modelling basedon integrating SURPAC and FLAC3D is helpful to determine theminimum thickness of the crown pillar for the subsea gold mine.

2. Engineering background

Sanshandao gold mine is located at the Sanshandao specialindustrial zone in Laizhou city, Shandong Province, China. It is onthe east coastline of the Bohai Sea. The mining area is about29 km north of Laizhou city and 45 km west of Zhaoyuan city. Viathe Provincial Road S304, the mine is connected with the G206National Road at about 16 km to the east, and it is also connected

to the G18 Expressway at a distance of about 26 km to the east.The railway from Huangye to Yantai is under construction and itwill pass through the mining area only at a distance of about 8 kmto the east.

The Sanshandao gold mine is a medium size underground mine(the production capacity of Sanshandao gold mine is 8000 t/day)facing challenging mining environments. Take the Xinli Zone ofSanshandao gold mine as an example, the geological prole alongthe 31# exploration line is shown in Fig. 1. The main rock typessurrounding the gold mine include metagabbro, monzogranite, andcataclastic rocks. The gold orebody extends from about level 40mto below level 700m under sea level. The orebody has a strike ofNE 60701, and a dip angle of 401to 501 towards southeast.

Different mining methods are commonly used in undergroundmines, including the room-and-pillar method, the cut-and-ll stopingmethod and sublevel caving, etc. [26]. In the Xinli Zone of theSanshandao gold mine, a cut-and-ll stoping method has beenadopted. A typical cut-and-ll stoping method is shown in Fig. 2,which is used from level 400m to 165m. The height of onemining stope is 40 m. The distance between two barrier pillars is100m. The square panel pillar is of a 5m5m cross section. Thespacing between adjacent panel pillars is 15 m in each direction.

Sanshandao gold mine is the rst subsea metal mine along thecoastline of China. Besides this gold mine, Longkou Coal Mine isanother subsea mine in China [27]. About 10m depth of sea water anda 35m thick of sea mud (silty clay) and Quaternary weathering layerexist above the orebody of the Xinli Zone at the Sanshandao goldmine.

How to handle the sea water above the mine is a critical issuefor subsea mining. It would be disastrous if the sea water cannotbe properly kept out from the mine excavation when miningunder the sea. For example, a sea water inrush in a subsea coal

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256 43Fig. 1. The geological prole of Xinli Zone at Sanshandao gold mine along the 31# exploration line.

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 425644mine in Japan occurred in 1916 led to 237 human casualties [28].It is lucky that the seabed rock of the Xinli Zone at the Sanshaodaogold mine is overlain by about a 23 m thick gray silt soil andyellow silty clay layer. Scanning electron microscopic (SEM)studies on the microstructure of the subsea clay revealed thatthe pores connectivity in the clay is quite poor. The permeabilityof the clay is as low as 5.13108 cm/s [25]. This 23 m thickclay layer serves as a nearly impermeable layer to inhibit the seawater from inltrating the seabed rock masses. However, thecohesion strength of the clay is only 4.89 kPa and it can hardlybear any tension stress. Therefore, a certain thickness of crownpillar is necessarily required to ensure the stability and safety ofthe subsea mine, especially when the mining activity goes up tolevel 165 m. In this paper, a numerical method, which takes the

Fig. 2. Cut-and-ll stoping method adopted between level 400 m and 165 m (u(4) reinforced concrete oor pillar; (5) tailing lling; (6) ventilation shaft; (7) drainingrealistic geometric orebody and mining sequences into considera-tion, is used to determine the minimum crown pillar thickness atthe Xinli Zone of the Sanshandao Subsea gold mine. The inuenceof the sea water pressure above the mine has also been con-sidered in the numerical model. The main controlling factor isattributed to the tensile failure zone in the crown pillar, whichmay lead to instability of mining infrastructures and then inrushof sea water into the mining excavations.

3. Preliminary study

Some representative rock samples were selected from themine dumps in the subsea gold mine, which included: (1) Phyllitic

nit: m). Notation: (1) laneway; (2) stope-connection laneway; (3) barrier pillar;

well; (8) steel rod; (9) rock bolt; (10) panel pillar.

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256 45cataclastic granite (SgJ) from hanging wall; (2) Pyritic phylliticcataclastic granite (SgJH) from orebody; and (3) Monzogranite(Zg) from footwall.

In total, 132 standard specimens have been prepared (Fig. 3ac)from the rock samples60 for shear tests (specimen size:50 mm50 mm50 mm), 36 for uniaxial compressive tests(j50 mm100 mm and j60 mm120 mm) and 36 for Braziliansplitting tests (j50 mm50 mm and j60 mm60 mm). The rockspecimens were tested under either natural dry or wet (48 h watersaturation) conditions at room temperature. Shear tests and com-pressive tests were carried out on the INSTRON 1346 hydraulicservo-controlling pressure machine, while Brazilian tests wereconducted on the INSTRON 1342 pressure machine according tothe ISRM suggested methods. The shear angle a is the angle betweenthe applied shear direction and the horizontal direction (Fig. 3d).Three shear angles (a) were used, including 451, 601 and 701 in sheartests. The normal stress (s) and the shear stress (t) along the shearsurface can be calculated by

s NS PS cos a f sin at QS PS sin afcos a

)1

where N is the total normal force; Q is the total shear force; S is theshear surface area, which is equal to the cross-section area of thecubic specimen; P is the maximum load when the specimen failsunder shear test; f is the friction coefcient between the cylindrical

Fig. 3. Some prepared rock specimens: (a) natural dry specimens for shear test; (b)specimens for compressive test and Brazilian test and (d) shear angle in a rock shear troller and the upper and lower platen, which can be assumed to bezero in the roller-support system.

According to Eq. (1), a series of values of shear stress t andnormal stress s can be obtained under different shear angles.Based on the MohrCoulomb criterion (t cstan f) and linearregression method, the cohesion (c) and internal friction angle (j)of the tested rocks can be obtained consequently.

The testing results of the strength and deformability of thethree representative rock formations are listed in Table 1. Thetesting results in Table 1 are obtained from four different tests.The density (r) is measured from cubic rock specimens preparedfor shear test. The uniaxial compressive strength (sc), Youngsmodulus (E), and Poissons ratio (n) are obtained from uniaxialcompressive tests on long cylindrical rock specimens. The tensilestrength (st) is measured from the Brazilian test on shortcylindrical specimens. The shear strength associated with cohe-sion (c) and internal friction angle (j) are obtained from sheartest by using the best linear curve tting method according to theMohrCoulomb criterion. The number of samples used, thestandard variation, and the determination coefcient for eachtest type are also listed in Table 1.

Visual observation shows that the SgJ rock specimens containmore visible cracks than the SgJH rock specimens do, while fewvisible cracks can be observed in the Zg rock specimens. Thetesting results reveal that the hanging wall rock (SgJ) has the leastuniaxial compressive strength, the least stiffness and theleast shear strength, while the orebody rock (SgJH) has the least

water saturated specimens for shear test; (c) natural dry and water saturated

est.

.iaxia

(MP

26

.36)

27

.94)

Orebody SgJH Dry 2709 80.87(14) (14.60)

08

.41)

.95

.56)

53

.19)

h te

t co

ear

truc

umb

umb

umb

umb

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 425646splitting tensile strength. The three tested rock types belong tohard rock (RcZ60 MPa) and middle hard rock (30 MParRco60 MPa) according to the Chinese Standard for engineeringclassication of rock masses [29], where Rc denotes the uniaxialcompressive strength of saturated rock specimen. The softening

Saturated 2711 62.

(33) (16

Footwall Zg Dry 2635 126(20) (27

Saturated 2628 79.

(7) (21

n E denotes the secant Youngs modulus at 50% strength point.a The number in the brackets represents the number of specimens used in eacb The number in the parentheses represents the standard variation of each tesc The equation in the braces represents the determination coefcient of the lin

Table 2Data structure of the four tables in the data sheets.

Table name Main data s

Drilling table Drill hole n

Measurement table Drill hole n

Geological table Drill hole n

Mineral grade table Drill hole nTable 1Mechanical properties of intact rock from the three representative rock formations

Location Rock formation Rock condition Density [6]a Un

r (kg/m3) sc

Hanging wall SgJ Dry 2706 71.(76)b (18

Saturated 2677 41.

(28) (14coefcients of water effect on the uniaxial compressive strengthare 0.58, 077 and 0.63 for the three rocks SgJ, SgJH and Zg,respectively. Generally speaking, water has a reduction effect onthe strength and stiffness of all the three rock types, moreremarkably on the hanging wall rock mass (SgJ), which is themost critical part of the crown pillar stability at the subsea goldmine. Therefore, for the sake of safety, the water-saturatedmechanical properties of surrounding rock masses should be usedin the numerical analysis of the crown pillar stability at thesubsea gold mine.

The mining history in the Sanshandao subsea gold mineshowed that the crown pillar was stable and no active sea waterinow was observed for mining activity below sea level 165 m,i.e., the crown pillar thickness was about 120 m. What willhappen if the mining activity goes up to level 115 m and evenmore (the crown pillar thickness will be less than 70 m)? Toanswer this question, a 3D numerical modelling is used to analyzethe stability problem and to determine the minimum thickness ofthe crown pillar at the subsea gold mine.

4. Numerical model construction

In order to establish a more realistic 3D model, the geologicaldatabase and engineering information of drill holes from the XinliZone are rst compiled in the mining software SURPAC. Accordingto the data structure requirements of the drill holes in SURPAC,the data is reconstructed and organized into four data tables:drilling table, measurement table, geological table and mineralgrade table. The data structure of the four tables is shown inTable 2. These data sheets can serve as the geological databasesources, which are the basis of the deposits in the 3D modellingprocess.

After establishing the geological database in SURPAC, 3D spacelocations and shapes of the drill holes can be conveniently shownin SURPAC, which also include the mineral grade information of

l compressive test [6] Brazilian test [6] Shear test [10]

a) E* (GPa) n st (MPa) c (MPa) j (1)

13.44 0.20 6.24 11.44 30.6

(3.90) (0.04) (2.19) {R20.839}c9.22 8.22 7.18 33.9

(2.87) (2.36) {R20.919}14.73 0.21 4.91 21.45 32.6

(1.87) (0.02) (0.27) {R20.946}11.63 3.70 17.11 33.7

(1.73) (0.88) {R20.991}17.10 0.24 8.54 42.77 36.9

(3.55) (0.05) (2.85) {R20.922}15.73 10.09 39.29 36.8

(2.67) (0.61) {R20.885}

st condition.

ndition.

regression by MohrCoulomb criterion from shear test.

ture and date information

er; X, Y, Z coordinates; the maximum depth of drill holes

er; depth, dip angle, dip direction of the measurement point

er; initial point and ending point of ore samples; rock types

er; initial point and ending point of ore samples; mineral gradeore samples. A vertical section view of drill holes, mineral gradeinformation of ore samples and surrounding rock types from twotypical drill holes are shown in Fig. 4. Based on the geologicaldatabase, the orebody of this gold mine is modeled in SURPAC andshown in a 3D view and projected to the XY base plane, as shownin Fig. 5.

The orebody model helps visualize the geometric shape of themine, but it does not show the grade distribution and it cannot beused directly to calculate the volume of the mine. Therefore, adetailed 3D block model was constructed on the basis of theorebody model. It contains a large number of discrete cubic blockelements, which include the spatial locations of ore propertiesand constraint characteristics of the blocks.

The numerical model constructed in SURPAC is exported toFLAC3D by a data conversion in MATLAB. There are 12 primitivemesh shapes in FLAC3D, in which the brick mesh shape and thetetrahedron mesh shape can be connected with the block zone inSURPAC. Here the brick mesh shape was taken as an example toshow the data conversion process. A link program named STOF.mis compiled in MATLAB to achieve an automatic data conversionand model construction. The program can read the data le fromthe 3D block model in SURPAC and then convert the text formatto a series of acceptable commands by FLAC3D. Finally, thecommands are imported into FLAC3D and a meshed numericalmodel is generated. The implementation of the program isillustrated as a ow chart in Fig. 6.

Based on the geological data from drill holes, the entirenumerical model of Xinli Zone at Sanshandao gold mine is builtby integrating SURPAC and FLAC3D with the following coordi-nates: bottom left corner (X93760 m, Y40150 m, Z450 m)and top right corner (X95530 m, Y41000 m, Z10 m). It is a

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256 47very large model and contains 345,983 zones. Since the presentstudy is concentrated on the mining activity carried out abovelevel 165 m, the size of the numerical model is then reduced toa bottom left corner (X94384 m, Y40469 m, Z205 m) andtop right corner (X95052 m, Y40863 m, Z10 m). Thereduced numerical model, which is 668 m in X direction, 394 min Y direction and 195 m in Z direction, contains 199,047 zones.The entire numerical model and the geometry of mining infra-structure of stopes and pillars are shown in Fig. 7. According tothe design above level 165 m, the mining stope is 100 m inlength, 10 m in height and 36 m in width. The panel pillars are of4 m4 m cross section with 12 m12 m spacing. The 5 m thickbarrier pillar is separated at a distance of 100 m.

Fig. 4. Visualization of drill holes in SURPAC (a) XOZ cross-section representation of dtypical drill holes.5. Numerical modelling and analysis

5.1. Initial stresses and boundary conditions

According to in-situ stress measurement results by the stressrelease method, the maximum horizontal stress, the minimumhorizontal stress and the vertical stress vary almost linearly withthe depth in the mining area. The in-situ stresses can be describedby the following equations [25]:

shmax 0:0539H0:11shmin 0:0181H0:13sz 0:0315H0:08

8>: 2

rill holes and (b) Au grade of ore samples and the corresponding rock type in two

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 425648where shmax, shmin and sz are the maximum horizontal stress, theminimum horizontal stress and the vertical stress (MPa), respectively;H is the depth of the measurement point in meter. The initial stressesin the model are given by Eq. (2). The in-situ stress measurements

Fig. 5. 3D visualization of the orebody at the Xinli Zone at Sanshandao gol

Write the group information for the zones by commname is the group name; il and iu are the lower an

Read the data file of 3D block m

Determine the group of the zones accor

Calculate the X,Y,Z positions of the

Judge the reiteration of gridpoints number and wthe command: G n Xn Yn Zn, where n

Inquire gridpoints of each zone and write zone inform Z B8 m P0 P1 P2 P3 P4 P5 P6 P7 P8, w

Import the file into FLAC3D by the command: imporFLAC3

Fig. 6. Flow chart illustrating the compilation of the linkreveal that the maximum principal stress (s1shmax) trends about3251with an almost zero plunge, while the minimum principal stress(s3shmin) trends about 1451 with an almost zero plunge. Themiddle principal stress (s2sz) is in an almost vertical direction.

d mine in SURPAC (a) 3D view and (b) Projection of the XY base plane.

and: GROUP name range id il iu, where d upper limits of zone number respectively

odel from SURPAC

ding to the zone attribution

gridpoints for each zone

rite gridpoints into the model file by is the number of gridpoints

ation into the model file by the command: here m is the number zones

t grid and generate the numerical model in D

age program STOF.m between SURPAC and FLAC3D.

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256 49The displacement boundary conditions of the model include:(1) xed X-direction displacement at the left and right bound-aries; (2) xed Y-direction displacement at the front and backboundaries; (3) xed all the X, Y, Z direction displacements at thebottom boundary; (4) free boundary at the top of the model.

Since the sea water pressure acting on the top of the model hasbeen considered, the uid-mechanical interaction function availablein FLAC3D is used in the numerical analysis [30], which can model theuid ow through permeable mediums and provide the distributionof pore pressure after underground excavation [31]. For the uid-owboundary conditions, impermeable boundaries are set by default inFLAC3D. All gridpoints are initially free, i.e., the pore pressure at suchgridpoints is free to vary according to the net inow and outow fromneighboring zones. Fixed-pressure gridpoints can act as a source or asink to be a permeable boundary. In addition, chemical analysis onthe ground water from the subsea mine shows that that the groundwater has almost the same or even higher salinity than the sea water.It indicates that the ground water belongs to sea water or ancientseawater. Therefore, to model the 10m depth of sea water pressure, aconstant xed pore pressure of 0.1MPa is applied on the topboundary of the model. The excavation boundary is modelled by afree water seepage boundary where the adjacent underground waterwill inltrate into the opening.

5.2. Calculation parameters and failure criterion

Calculation parameters include mechanical parameters andpermeability coefcients of rock masses and llings in the model.

Fig. 7. Numerical model of the Xinli Zone and surrounding rock masses in FLAC3D (a) Eand (b) the mining infrastructure (stopes and pillars).On the one hand, the mechanical parameters of intact rocksobtained by laboratory tests should be converted to those of rockmasses in the numerical modelling. The empirical relationships ofstrength and modulus between rock masses and intact rocks havebeen carefully studied by using the geological strength index(GSI) and the rock mass rating (RMR) system [3235]. On theother hand, Rocscience Inc. has put forward commercial softwareRocData to realize the transformation based on the GeneralizedHoekBrown strength criterion [36],

s10 s30 sci mbs30

scis

a3

where s01 and s03 are the maximum and minimum effectiveprincipal stresses at failure; mb is the value of the HoekBrownconstant m for the rock mass; s and a are constants which dependupon the rock mass characteristics, and sci is the uniaxialcompressive strength of the intact rock pieces. The values ofthese constants should be determined by statistical analysis of theresults of a set of triaxial tests on carefully prepared core samples.The inuence of blast damage on the near surface rock massproperties has been taken into account in the 2002 version of theHoek-Brown criterion as follows [37]:

mb miexpGSI1002814D

4

s exp GSI10093D

5

ntire model: 1770 m in X direction, 850 m in Y direction and 440 m in Z direction

a 12 16

eGSI=15e20=3

6

where mi is a HoekBrown constant for intact rock; D is a factorwhich depends upon the degree of disturbance due to blastdamage and stress relaxation. It varies from 0 for undisturbedin situ rock masses to 1 for very disturbed rock masses. Since thecut-and-ll stoping method is used in the subsea mine, theblasting disturbance is not so heavy to the surrounding rockmass. The D value is assigned with 0.2.

According to the shear testing results, equivalent triaxialtesting data can be obtained by using the MohrCoulombstrength criterion on intact rock. By inputting the equivalenttriaxial testing data into the software of RocData (version 3.0), thebest-tting mechanical parameters of rock mass can be obtainedif the GSI, D, and mi values are given. These parameters includethe global uniaxial compressive strength (scm), the tensilestrength (stm), the Youngs modulus (Em), the cohesion (cm) andthe internal friction angle (jm) of rock mass. The Poissons ratio(n) and the density (r) of rock mass are assumed to be equal tothe values of intact rock. The similar data processing method has

It can be found that the GSI values have great inuence on themechanical parameters of the rock mass, which also proves thatthe in-site joint surveys are very important for the numericalmodelling analysis. In the present study, the calculation para-meters from a typical GSI value of 50 are used. It should bepointed out that if the in-site joint conditions become worsewhich lead to a GSI value less than 50, the calculation parametersof the modelling should be adjusted and the modelling resultsmay be different. In order to take into consideration of theinuence of groundwater, the mechanical parameters based onthe water saturated condition are conservatively used since thesevalues are less than those under natural dry condition.

The MohrCoulomb failure criterion with a tension cut-off isadopted for the rock mass and backll in the numerical model-ling, which is

f s s01s031sinjm1sinjm

2cm1sinjm1sinjm

s7

f t s03stm 8Based on these two equations, the safety factor under shear

ical

Pa

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 425650been used by Justo et al. [38].Before this numerical study, a number of site surveys have

been carried out to investigate the distribution of rock joints andfractures in the subsea gold mine. It shows that the jointconditions belong to fairly good to good status, which indicatesthat the GSI value of the rock mass is about 50 based on the Hoekand Browns experience [39]. Consequently, three typical GSIvalues (40, 50, and 60) in such joint conditions are consideredfor the surrounding rock mass. In addition, the selected level of s3has an inuence on the values of the MohrCoulomb parameters(cm and jm) in this analysis. Specically, the present miningactivities will be conducted from level 115 m to level 65 m.According to the in-situ stress calculation Eq. (2), the value of s3varies between 1.3 MPa and 2.2 MPa. In average, three stresslevels of 1.4 MPa, 1.8 MPa, and 2.2 MPa are used for the hangingwall, orebody and foot wall, respectively, to obtain the corre-sponding MohrCoulomb tting parameters in the present study.The mechanical parameters of the surrounding rock masses arelisted in Table 3, including both natural dry and water saturatedconditions. Moreover, the mechanical properties of backll arealso listed in Table 3, since the cut-and-ll stoping method is usedin the numerical analysis.

Table 3Calculation parameters of rock masses from RocData 3.0 and backll in the numer

Material s3 (MPa) D GSI scm (MPa) stm (M

Hanging wall (dry) 1.4 0.2 40 3.28 0.08

50 4.27 0.17

60 5.65 0.38

Orebody (dry) 1.8 0.2 40 6.73 0.14

50 8.72 0.31

60 11.47 0.68

Footwall (dry) 2.2 0.2 40 16.54 0.24

50 21.28 0.53

60 27.63 1.17

Hanging wall (saturated) 1.4 0.2 40 2.35 0.05

50 3.04 0.10

60 3.99 0.22

Orebody (saturated) 1.8 0.2 40 5.69 0.11

50 7.36 0.23

60 9.64 0.52

Footwall (saturated) 2.2 0.2 40 15.12 0.22

50 19.46 0.49

60 25.28 1.08Filling 2.1 0.20failure or tension failure can be obtained with the form of

Fs cmcosjms01s03

2sinjm

=s01s03

2

9

Ft stm=s03 10where Fs and Ft are the safety factors under shear failure andtension failure, respectively. If Fso1 or Fto1, then shear failureor tension failure occurs in the corresponding rock zone ofthe model.

The permeability coefcient (k) of the rock mass was deter-mined by the steady-state water ow method on eight cylindricalrock specimens containing natural cracks under a triaxial com-pressive machine. The permeability coefcients of the threerepresentative rock types are also listed in Table 3. The maximumvalues of the permeability coefcients, which are 13.5107 m/s,10.3107 m/s and 3.3107 m/s for hanging wall, orebodyand footwall rock masses, respectively, are used in the numericalanalysis in FLAC3D. It should be pointed out that since the sea mudlayer has a very low permeability coefcient (k5.131010 m/s),a 3 m thick layer of low permeability coefcient in the hanging wallwas used to represent this layer below the sea water in the model.

analysis.

) Em (GPa) cm (MPa) jm (1) n r (kg/m3) k (107m/s)

3.20 0.37 34.1 0.20 2706 1.413.5

5.70 0.52 37.3

10.13 0.81 39.8

4.48 0.60 38.3 0.21 2709 1.210.3

7.97 0.88 41.4

14.17 1.42 43.5

5.06 1.02 45.0 0.24 2635 0.33.3

9.00 1.56 47.8

16.00 2.67 49.5

2.62 0.32 32.1 0.20 2677 7.4

4.66 0.42 35.5

8.29 0.60 38.4

4.05 0.54 37.4 0.21 2710 5.8

7.17 0.77 40.6

12.80 1.19 43.0

5.06 0.97 44.3 0.24 2628 1.8

9.00 1.47 47.1

16.00 2.48 48.9

0.23 0.19 38.7 0.17 2100

5.3. Mining sequences and modelling stages

The excavation and lling steps are taken into consideration inthe numerical analysis. The distributions of principal stresses,displacements and pore pressures in the crown pillar and sur-rounding rock masses are obtained by simulating the differentexcavation and lling stages. According to the mining history in

Sanshandao gold mine, the crown pillar is stable when miningactivities are carried out below level 165 m. In the numericalmodel, it is considered that the stopes below level 165 m are allbacklled and the orebody will be excavated above level 165 m.The numerical analysis is carried out to assess the stability of thecrown pillar when excavation takes place above level 165 m atthe subsea gold mine, for example, from level 115 m to level

Table 4Excavation and backll stage in each mining sequence and corresponding variation indexes in the numerical model.

Mining stage Mining sequence Z elevation (m) Stage height (m) Subsidence (mm) d (%) kf (%) Note

First stage Excavate 1 115 to 105 10 8.6 0.009 0.11 Mining stopes: 100 m in length and 10 m in height.Panel pillars: square pillars of 4 m4 m cross sectionwith 12 m12 m spacing;Barrier pillars: 5 m thick separated at a distance of 100 m

Fill 1 115 to 105 10 8.9Second stage Excavate 2 105 to 95 10 10.1 0.012 0.15

Fill 2 105 to 95 10 10.4Third stage Excavate 3 95 to 85 10 12.0 0.016 0.22

Fill 3 95 to 85 10 12.2Fourth stage Excavate 4 85 to 75 10 14.5 0.023 1.03

Fill 4 85 to 75 10 14.8Fifth stage Excavate 5 75 to 65 10 17.0 0.033 1.25

Fill 5 75 to 65 10 17.2

-3.3-3.0-2.7

-2.4

-2.1

-1.8-1.5

-1.2-0.9

-0.6-0.3-0.3

-0.6-0.9

-1.2

-1.5-1.8

-2.1

0

Y direction40469 m 40863 m

-20

5 m

-10

mZ

dire

ctio

n

-3.6

-6.0-6.0-5.0 -5.0

-4.0-4.0

-3.0 -3.0-2.0

-2.0

ectio

-10

mZ

dire

ctio

n

aft

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256 51-10.0

-9.0-8.0

-7.0

Y dir40469 m

-20

5 m

Fig. 8. Contour diagrams of the principal stresses at the cross section of X94,784 m

maximum principal stress (s1, unit: MPa) and (b) the minimum principal stress (s3, un 40863 m

er excavating and lling of all the ve stages from level 115 m to 65 m. (a) The

nit: MPa).

65 m. Therefore, the initial model is based on the llingcondition of level 165 m. The model then simulates the sub-sequent excavation stages and stope lling stages. Each incre-mental stage is 10 m high, spanning from level 115 m to level65 m. The excavation and lling stages of the orebody miningsequences are listed in Table 4. Meanwhile, the sizes of themining infrastructures and the maximum seabed subsidence ineach mining sequence obtained from the numerical analysis arealso provided in Table 4.

5.4. Modelling results

The numerical results are represented by the distributions ofprincipal stresses, displacements, pore pressures, and plastic zonedevelopment associated with the excavation steps. Since the pre-valence of tensile stresses in surrounding rock masses can easily leadto crack opening, the tensile stresses are particularly monitored in thenumerical models. With the rising of mining level, the stress condi-tions become more severe in the subsea mine. For instance, afterexcavation and lling all the ve stages (totally 50 m high excava-tion), the distributions of the maximum and minimum principalstresses at the cross section of X94784m are shown in Fig. 8.

It can be seen in Fig. 8a that the maximum principal stress islarger than zero (which means tensile stress in FLAC3D) near themining stopes, and it also occurs at the seabed. When mining

activity reaches the level from 75 m to 65 m, the maximumtensile stress is about 0.10.2 MPa in the sea bed, which isgenerally larger than the maximum tensile strength of thehanging wall rock (0.10 MPa). Meanwhile, it can be found inFig. 8b that the contour density of the minimum principal stressnear the excavation and lling zone is very high, which indicates asignicant stress concentration around the stope. The maximumcompressive stress near the stopes reaches about 8.010.0 MPa inFig. 8b, which also approaches the uniaxial compressive strengthof the hanging wall and footwall rock masses. Therefore, it can beconcluded that the mining activity should be limited below level75 m from the consideration of principal stress distribution.

From the viewpoint of the vertical displacement in the numericalmodel, seabed subsidence has occurred because of the excavation ofthe subsea gold mine. Contour diagrams of the vertical displacementat the cross section X94784m for the fourth and fth mining stagesare shown in Fig. 9. It can be seen that the vertical displacement ofthe crown pillar increases as excavation proceeds. When the mininglevel increases from level 75m to 65m, the vertical displacementof the crown pillar at the seabed reaches about 18mm after back-lling. The maximum subsidence of the crown pillar is relativelysmall, because the mining stopes are fully lled after excavation atthe subsea gold mine in the numerical model. The relative deforma-tion rate (d) of the crown pillar after the fth mining stage is

d 18=55 1000 0:033%o0:1% 11

-2.5

-

2.5 0

-5.0

-5.0

-7.5

-10.0

-12.5-12.5

-10.0

-7.5

-15.0

-10

mZ

dire

ctio

n

ecti

-7

-1 0 .

.5

ecti

irec

4 m

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256520

Y dir40469 m

-20

5 m

Z d

Fig. 9. Contour diagrams of vertical displacement at the cross section of X94,78-20

5 m

Y dir40469 m

-1 2-15.0

-15.0-12.5

-10.0

-

7 .5

-5.0

-2.5

-10

mtio

n85 m to 75 m and (b) excavating and lling the 5th step from level 75 m to 6on 40863 m

-2.5

-5.0

.50

on 40863 m

after backlling of the stopes. (a) Excavating and lling the 4th step from level5 m (displacement unit: mm).

he n

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256 53Fig. 10. Development of plastic zones on the seabed surface of crown pillar in t(b) excavating the 4th step from level 85 m to 75 m.The value is as small as 0.033%, which can be considered aslocated in a safety range. The relative deformation rates of thecrown pillar after each excavation stage are listed in Table 4. Thenumerical model thus indicates that the cut-and-ll stopingmining method is effective to decrease the seabed subsidenceand hence is favorable to the safe exploitation of Sanshandaosubsea gold mine. Tesarik et al. [40] reported a similar miningmethod (backlled room-and-pillar method), which can helpkeeping the long-term stability of the underground mining sec-tions at the Buick Mine, Missouri, USA.

The distribution of plastic zones (including shear failure zonesand tension failure zones) at the seabed rock of the crown pillar isshown in Fig. 10, associated with different excavation levelsobtained from the numerical analysis. It can be seen in Fig. 10athat a few tension plastic zones are developing at the seabed,which have not coalesced together when excavating the thirdstep from level 95 m to level 85 m. As in Fig. 10b, moretension failure zones are developing than that in Fig. 10a, whichhave coalesced together when excavating the fourth step fromlevel 85 m to 5 m. It indicates that the crown pillar maybecome unstable and tension failure zones may form macrofractures when the mining excavation reaches level 75 m. Thesetension failure zones may lead to sea water inrush into the miningexcavations. According to Eqs. (9) and (10), the ratio (kf) betweenthe volume of the zones with Fso1 (or Fto1) and the entirevolume of the model is monitored during the numerical model-ling process. The results are listed in Table 4. It can be found thatonly a few zones have safety factor less than 1 in the surroundingrock mass, while most of zones have safety factor larger than 1.However, it nds that the ratio kf increases quickly when themining activity moves from level 85 m to 75 m, which meansa potential crown pillar failure may occur at this excavation stage.Based on this numerical result, the maximum excavationTension zones (failure past)

Elastic zones

Tension zones (failure past)

Tension zones (failure now and past)

Elastic zones

umerical analysis: (a) excavating the 3rd step from level 95 m to85 m andelevation of the Xinli Zone at the Sanshandao gold mine shouldbe limited below level 85 m.

Another important factor is the inuence of sea water pressure forthe subsea gold mine. Fluid ow will occur when the miningexcavation is conducted. In the present numerical analysis, porepressure distributions of surrounding rock masses in some typicallevel are plotted in Fig. 11, after the corresponding excavation stages.It can be seen that with the rise of mining levels, the pore pressurearound the mining excavations increases too, hence increasing therisk of the sea water inow and inrush into the mine. A signicantincrease of pore pressure is particularly observed as one proceedsfrom level 85m to level 75m. Therefore, for the mining excava-tion up to level 85m, the pore pressure change should becautiously monitored. It should be pointed out that in the presentnumerical modeling, a constant water pressure of 0.1 MPa is assumedto act on the top of the model and water can ow freely to theopenings when excavation takes place. This is the worst condition forthe subsea gold mine. In reality, the pore pressure should be less thanthe numerical analysis result due to the more restrained water ow.Nonetheless, the variation trend of pore pressure with excavationstages denitely shows the inuence of sea water on the stability ofthe crown pillar of the subsea gold mine. Therefore, from theviewpoint of pore pressure distribution, the excavation elevation ofthe subsea gold mine should be limited below level 95m. In otherwords, in the presence of a 10m depth of sea water, and a 35m thicksea mud (silty clay) and Quaternary deposit in the seabed, thethickness of crown pillar should be at least 50 m.

6. Field deformation observation

During the past four years, the underground mining activitieshave been carried out from level 165 m to 115 m. To monitor

44

40700

4

4

4

4

4

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256549440040500

40600

40700

40800

40500

40600

40700

40800

94500 94600 94700 94800 94900 95000the deformation of the crown pillar, four 3-point boreholeextensometers were used (located at boreholes A, B, C and D)along the exploration lines of 55#, 63# and 71#, about 20 m to30 m away from the mining chamber at level 165 m of the XinliZone (Fig. 12a). The borehole had a diameter of 40 mm and alength of 30 m. The 3-point extensometer was monitored at every10 m length along each observation borehole. For example, A10,A20 and A30 stood for the three measurement points above 10 m,20 m and 30 m of the laneway along the observation borehole A.The convergence signals of the borehole extensometers werecollected by the data reader and then transmitted to a personalcomputer. The in-situ displacements of the surrounding rockmasses recorded in the four boreholes from April 11, 2008 toDecember 8, 2008 are plotted in Fig. 12b.

It can be seen that the vertical displacement of the crown pillarincreases with time and nally it becomes stabilized, when miningactivities are conducted from level 165m to 115m. The max-imum displacement of the crown pillar is about 2.9 mm occurred inB30 extensometer point. Taking the largest deformation extens-ometer point B30 and the largest deformation rate extensometerpoint C10 as examples, the corresponding deformation rates are

dB30 2:9=30 1000 0:01% 12

dC10 2:3=10 1000 0:023% 13

40500

40600

40700

40800

4

4

4

4

94400 94500 94600 94700 94800 94900 95000

94400 94500 94600 94700 94800 94900 95000

Fig. 11. Contour diagrams of pore pressure distribution after each corresponding excava85 m; (e) level 75 m and (f) level 65 m. (Pore pressure unit: MPa.)94400 94500 94600 94700 94800 94900 95000

0500

0600

0500

0600

0700

08000800Both of them are less than the numerical calculation result(0.033%) for the crown pillar when the mining activity goes up tolevel 65 m. Based on the relative deformation rate of the crownpillar, it shows that the present numerical calculation parametersbased on a GSI value of 50 are conservative. In other words, thereserved safety factor of crown pillar in the present numericalmodelling is about 0.033/0.0231.43.

The results from eld deformation observation and numericalmodelling can encourage further mining excavations above level115 m. The mining activities have been conducted from level165 m to level 115 m since 2007, which can possibly be risento level 95 m in the future with necessary ground treatmentand groundwater pressure monitoring. A four-year-eld practiceshowed that the numerical modelling by integrating SURPAC andFLAC3D was helpful to determine the minimum thickness of thecrown pillar in the subsea gold mine. Plenty of gold orebody canbe safely mined out from the subsea gold mine.

7. Conclusions

A cut-and-ll stoping method is successfully used in the rstsubsea gold mine (Sanshaodao gold mine) in China. By integratingSURPAC and FLAC3D, a realistic geometric numerical model hasbeen built based on the geological information of drill holes. The

94400 94500 94600 94700 94800 94900 95000

94400 94500 94600 94700 94800 94900 95000

0500

0600

0700

0800

tion stage reaching (a) level 115 m; (b) level 105 m; (c) level 95 m; (d) level

X. Li et al. / International Journal of Rock Mechanics & Mining Sciences 57 (2013) 4256 55numerical model includes different groups to represent themining infrastructure such as stopes, panel pillars and barrierpillars. The excavation and backll sequences, the mechanicalproperties of surrounding rock masses in a water-saturatedcondition, and the inuence of sea water pressure have beenconsidered in the numerical analysis. The minimum requiredthickness of the crown pillar is found to be at least 50 m at theXinli Zone of the Sanshandao gold mine, in the presence of a 10 mdepth of sea water, and 35 m thick sea mud (silty clay) andQuaternary deposit in the seabed. Field displacement observationshows that the vertical deformation rate of the crown pillar issmaller than 0.023%, which is also less than that of the numericalresult (0.033%). It reveals that the reserved safety factor is about1.43 when using the cut-and-ll stoping method from level165 m to 115 m in the subsea gold mine. The miningactivities may extend to level 95 m based on the presentnumerical analysis. A four-year-eld practice shows that thenumerical modelling by integrating SURPAC and FLAC3D is helpfulto determine the minimum thickness of the crown pillar in thesubsea gold mine.

Acknowledgements

The authors would like to acknowledge the nancial supportsfrom the 973 Program (no. 2010CB732004), the National NaturalScience Foundation of China (no. 50934006 and 11102239), and

Fig. 12. Field deformation observation: (a) plane-view layout of the observation borehpillar obtained at the four boreholes A, B, C and D by 3-point borehole extensometers.Hunan Provincial Natural Science Foundation of China (no.09JJ7003). The contribution of the Shandong Gold Group Co.,Ltd. at Xinli Zone of Sanshandao gold mine is gratefully acknowl-edged. Finally, the authors would like to thank Assistant ProfessorLouis Ngai YuenWong at the Nanyang Technological University toimprove the English of the manuscript and the two anonymousreviewers to provide constructive suggestions.

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Determination of the minimum thickness of crown pillar for safe exploitation of a subsea gold mine based on numerical...IntroductionEngineering backgroundPreliminary studyNumerical model constructionNumerical modelling and analysisInitial stresses and boundary conditionsCalculation parameters and failure criterionMining sequences and modelling stagesModelling results

Field deformation observationConclusionsAcknowledgementsReferences