Evaluation of the Likelihood of Cave Propagation in Mining Engineering Practice

Germán FloresCodelco Norte Division, CODELCO, ChileAntonio KarzulovicA. Karzulovic & Assoc. Ltd., Santiago, ChileEdwin T Brown Julius Kruttschnitt Mineral Research Centre, University of Queensland, Australia

AbstractThe benchmarking exercise carried out as part of the International Caving Study Stage II (ICS-II) and reported in a companion paper, concluded that there are currently no geotechnical tools available with which to define the likelihood of vertical caving propagating through ore columns having differing heights, stress fields and rock mass qualities. This paper presents the results of analyses of the effects of several aspects of geometry, stress field, and rock mass strength on vertical cave propagation. Using the results of a series of parametric two-dimensional nu-merical analyses, a Caving Propagation Factor is defined and design charts developed to estimate the likelihood of vertical cave propagation during the initial engineering stages of projects involving a transition from open pit to underground mining by caving methods.

1 INTRODUCTION

The essential concept in mining by block or panel caving is to take advantage of gravity by undercutting the base of the mineralized column to induce caving of that column. Therefore, the first geomechanical consideration must be to evaluate whether the rock mass to be mined will cave naturally under gravity alone, or if induced or augmented break-up of part or all of the column of mineralized rock will be required.

After the feasibility of using a caving method of mining has been verified, the second geomech-anical consideration must be to determine the size of the undercut required to initiate the caving pro-cess based on the rock mass quality and the stress field in the mining sector.

Current practice is that this determination is usually, but not invariably, based on empirical correlations between the geotechnical quality of the rock mass, expressed in terms of the MRMR index (Laubscher 1993) and the hydraulic radius of the caved area, HR. However, this correlation must be used with caution and, preferably, as a basis for the development of a correlation adjus-ted to the local conditions at each mine.

Once the area required to initiate caving has been determined, the next step is to evaluate whether the caving will propagate vertically to connect with the ground surface, or whether there is a risk that cave propagation will be arrested

with the cave eventually failing suddenly, poten-tially creating an air blast. Some examples of op-erations that have experienced caving arrest are listed in Table 1.

Table 1: Some Cases of Caving Arrest

Mine Caving Ar-rest Size T Air

Blast? References

Jenifer, California,

USA43 m 85 m 3 Yes Obert and

Long (1962)

Crestmore, California,

USA3,250 m2 (?) No(?) Long and

Obert (1958)

Ertsberg East, Indonesia 75 m 120 m (?) No Julin (1992)

Inca Oeste, Salvador, Chile 90 m 125 m 6 Yes

de Nicola and Fishwick (2000)

Northparkes, Australia

195 m 180 m 23(?) Yes van As and

Jeffrey (2000)

Rio Blanco, Andina, Chile

3 blocks of60 m 60 m

6 YesGodoy and Carpenter

(1973)Ten 4 Sur D,

Central Sector,El Teniente,

Chile

75 m 20 m 3 No Pasten and Cuevas (1999)

Ten 4 Sur D,Fw Sector,

El Teniente, Chile

90 m 45 m 17 No Pasten and Cuevas (1999)

Urad,Colorado, USA 90 m 135 m 11 Yes Kendrick

(1970)T Time taken by the cave arrested to collapse (months)

The evaluation of continuous caving requires a good understanding of the factors that control cavability and caving propagation, the mechanics of the process, and its evolution through time. The mechanics of the caving of rock masses have been discussed by Woodruff (1962), Coates (1970), Morrison (1976), Brown (2003) and oth-ers. This paper considers caving propagation on the basis of the results of parametric numerical analyses, with emphasis being placed on the case of the transition from open pit to underground mining by caving methods.

2 CAVING PROPAGATION MECHANICS

Caving requires the failure or break-up of the rock mass which depends on the surface and sub-surface geometry, stress field, geological struc-tures, characteristics of the rock mass, and groundwater conditions.

Brown (2003) has discussed the possible mech-anisms by which caving occurs. The first mech-anism postulated occurs when the stresses in-duced in the crown of the undercut or cave are low, or tensile, and rock blocks may become free to slide or fall under the influence of gravity. This form of caving has been referred to as stress re-lease caving. These conditions may occur when the horizontal in situ stresses are low or where boundary slots and/or previous mining have re-lieved or redistributed the stresses away from the block or panel being mined. However, even under these conditions, a self-supporting arch could de-velop in the crown of the cave, especially if there is poor draw management.

The second possible mechanism occurs when the induced tangential stresses are high compared with the strength of the rock mass and its discon-tinuities. Failure may occur at or near the bound-ary of the cave, releasing blocks of rock that be-come free to fall under the influence of gravity. Under these conditions, the dominant mechan-isms for the break-up of the rock mass are brittle fracture of the rock between discontinuities and the shear failure and slip on discontinuities, espe-cially those that are flat dipping. This form of caving is often referred to as stress caving.

A third mechanism occurs when the horizontal in situ and the tangential stresses induced in the crown of the undercut or cave are high enough to develop clamping forces which may stall gravity-induced caving, but are not high compared with the compressive strength of the rock mass. In this case, a stable arch may develop, arresting the up-ward propagation of caving. Under these circum-stances, some form of caving induction may be

required to weaken the rock mass, relieve the tan-gential stresses or induce slip on discontinuities (eg Kendrick 1970, van As and Jeffrey 2000).

Brown (2003) also indicated that other caving mechanisms such as subsidence caving, chimney caving, and plug subsidence may occur under cer-tain conditions.

In block and panel caving the idea is to under-cut the base of the ore column to be caved in such way that the gravity induced stresses will cause the progressive failure or break-up and caving of the rock mass above the cave back.

Initially, undercutting the base of the block to be caved generates a flat, tabular cavity. The act-ive volume of rock undergoing downward dis-placement is located above the roof of this flat cavity. This active volume in which the rock mass is fracturing and caving corresponds to the com-bination of the seismogenic zone and the zone of discontinuous deformation defined by Duplancic and Brady (1999).

If the stresses induced above the roof of the un-dercut are low, or tensile, then stress release cav-ing will occur. On the other hand, when the in-duced stresses are high compared with the strength of the rock mass and its discontinuities, stress caving will occur.

If the undercut area and geometry are such that caving initiates, the rock mass above the roof of the undercut will begin to break-up and cave, filling the cave and making possible the extrac-tion of ore. In the case of hard rock, this failure process can be expected to generate seismic events inside the seismogenic zone.

The falling of broken rock from the zone of loosening changes the geometry of the cave from its initial flat, tabular shape into a curved shape as shown in Figure 1. This not only modifies the location and geometry of the active volume, but also causes the stresses acting on the cave bound-ary to become more compressive. The mag-nitudes of the tensile stresses, if any, will de-crease while the magnitudes of the compressive stresses will increase.

Therefore, although stress release caving can occur at the initiation of caving, once the cave starts growing upwards stress caving becomes the main mechanism of caving propagation in mod-ern mines. Hence, the principal stress difference, S1 - S3, acting in the cave back is a good para-meter for use in evaluating the likelihood of cav-ing propagation because it defines the shear stress available for failing the rock mass either by rock fracture or by slip on pre-existing or induced dis-continuities.

(a) Initial undercutting defining a flat, tabular cavity where the stress release caving mechanism predominates.

(b) The upward caving propagation makes the cave back curve, increasing the importance of the stress caving mechanism.

(c) Additional upward caving propagation increases the curvature of the cave back, and makes predominant the stress caving mechanism.

Figure 1: Evolution of the cave back and caving mechanisms through time due to the upward propaga-tion of caving.

As caving propagates upwards, the cave height, h, measured from the floor of the undercut, in-creases. This changes the location at which the maximum stress concentration occurs (initially at the sides of the tabular undercut, but subsequently at the cave back). The magnitude and distribution of the stresses on the cave boundary depend not only on the initial conditions (eg in situ stress field, geometry of the open pit), but also on the geometry of the cave.

For convenience, assume that the cave is sym-metrical (ie h is a maximum at its centre). Then the cave geometry can be described in terms of the ratio between h and B, the basal width of the caved area, and HC, the height of the block to be caved. An increase in h/B may have a number of possible effects on the magnitude of the principal stress difference acting on the cave back, S1 - S3: (1) an increment, facilitating the break-up of the

rock mass and increasing the likelihood of further caving propagation; (2) no change, maintaining the likelihood of rock break-up and caving propagation; or, (3) a decrement, making the break-up of the rock mass more difficult and de-creasing the likelihood of further caving propaga-tion.

If the rock mass failure or break-up process be-comes more difficult, the rate of cave propagation will decrease. On the other hand, the likelihood of sudden and larger ruptures occurring in the seis-mogenic zone may increase, as may the risk of excessive seismicity that could eventually trigger rockbursts (especially in hard and massive rock masses). Obviously, this evolution, from the con-dition of caving initiation to a condition where the cave might become stable, depends on the geometry of the cave and the stress field.

3 PARAMETRIC NUMERICAL STRESS ANALYSES

In order to evaluate the effects of a range of parameters on the likelihood of caving propaga-tion, a series of parametric two-dimensional nu-merical stress analyses was carried out for the fol-lowing assumptions and problem configuration:a. In the plane normal to that of Figure 2, the un-

dercut and cave are long compared with the undercut width B so that plane strain condi-tions may be assumed.

b. The initial ground surface is horizontal. There may be an open pit with a depth of HP, 45o

overall slopes, and a minimum width of 200 m at its maximum depth. Four cases are con-sidered - no open pit, and pits with depths of 400, 800 and 1,200 m.

c. The area and geometry of the undercut are sufficient for caving initiation for the given geotechnical quality of the rock mass.

d. Five possible block heights of 100, 200, 300, 400 and 500 m are considered.

e. Two locations for the undercut are con-sidered, centrally below the floor of the open pit, and displaced such that the edge of the undercut is below the toe of the pit slope.

f. The in situ stress field (existing before any open pit mining) is defined by a vertical stress proportional to the depth below ground sur-face, and horizontal stresses defined by a stress ratio K, that is equal to 1 in the longit-udinal direction of the footprint, and equal to 0.5, 1.0, 1.5, 2.0 and 2.5 in the plane of Figure 2.

g. The rock mass is assumed to be homogen-eous, isotropic and linearly elastic.

h. The depth of the undercut level (UCL) with respect to the ground surface, HT, may be shallow (up to 500 m), moderate (500 to 900 m), deep (900 to 1,300 m), or very deep (1,300 to 1,700 m).

The geometry of the model is shown in Figure 2 for the case in which undercut is located cent-rally below the pit floor. Finite element analyses were carried out using the software PHASE2

(Rocscience 2002) and adopting the following procedures:a. The open pit (when there one exists) is excav-

ated in stages, each of which increases the pit depth by 100 m until the final depth, HP, is reached.

b. Once the pit (when there one exists) has reached its final depth, the base of the block is undercut defining a 10 m high flat, tabular cav-ity.

c. The continuous extraction of broken ore allows the propagation of caving, generating a cave that grows vertically upwards. For modelling purposes it is assumed that this cave has a para-bolic shape with its maximum height, h, situ-ated vertically over the centre of the undercut. The vertical growth of this cave occurs in dis-crete height increments of 25 m until h reaches 100 m, and in increments of 50 m above this height.

d. As the vertical propagation of the caving re-quires the break-up of the rock mass above the cave back, it is assumed that this occurs in a window having a width equal to 10% of the un-dercut width, as shown in Figure 3.

e. As stress caving is the main mechanism of cav-ing propagation, the principal stress difference, S1 - S3, acting in the cave back is used to evalu-ate the likelihood of caving propagation. The magnitude of S1 - S3 is assumed to be the aver-age of the stresses acting in the window defined in Figure 3.

f. To facilitate the graphical representation and the comparison of the results obtained, this av-erage magnitude of S1 - S3 is normalized by the initial vertical stress at the UCL, HT, where is the unit weight of the rock mass and HT is the depth of the UCL.A comparison of the results obtained for differ-

ent values of K and given values of the other parameters (Flores and Karzulovic 2003), shows that normalizing the results by K and using the average of the normalized values, produces an er-ror of not larger than 20% when h/B > 0.5 (which is the range of interest in practice).

Figure 2: Geometry of the model analysed for the case of an undercut located centrally below the pit floor.

This permits the use of a single, normalized curve to represent the results for all the K values used in the analyses. The evaluation of the nor-malized results shows that the vertical propaga-tion of caving depends on the relative height of the block to be caved, HC /B.

As illustrated in Figure 4, the possibilities for caving propagation may be evaluated by consid-ering the change in the normalized deviatoric stress, (NDS), ((S1 – S3)/HT), caused by an in-crement in the cave height, h.

If an increase of h in the cave height induces an increment in the NDS acting in the cave back, then the break-up of the rock mass becomes easier and this facilitates the vertical propagation of caving. On the other hand, if h does not in-duce an increment in the NDS, the break-up of the rock mass will not become easier and this will not facilitate the vertical propagation of caving.

Figure 3: Window used to evaluate the stresses acting in the cave back and the likelihood of the break-up of the rock mass and upward caving propagation.

Figure 4: Diagram illustrating possible caving propagation scenarios as a function of the relative height of the block to be caved, HC /B.

Therefore, for a given value of HC /B, there are several possibilities for caving propagation as il-lustrated in Figure 4:a. If HC /B < 2 an increment of h in the height of

the cave generates an increment in the NDS, making vertical cave propagation easier. As h increases, the slope of the NDS versus h/B curve becomes steeper; hence, caving would probably propagate upwards easily, and a con-nection to the ground surface or pit floor could be achieved (curve (1)(2)(5)(6) in Figure 4). This connection may be achieved with little difficulty if the crown pillar, CP, between the cave back and the ground surface or the pit floor fails by breaking progressively into pieces. If the draw management has been ad-equate so that the air gap is small there will be no risk of an air blast occurring. On the other hand, it also possible that the CP may fail as an intact block, as in the plug subsidence mechan-ism of chimney caving described by Brady and Brown (1993). In this case, shear failure occurs on the lateral boundaries of the CP which fails essentially as a rigid body without breaking up or dilating. This mechanism can occur when major geological structures define one or more of the cave boundaries. It may be analysed by limit equilibrium methods (Brady and Brown 1993). Therefore, for a path like (1)(2)(5)(6) in Figure 4, the likelihood of chimney caving and the risk of generating a hazardous plug subsidence condition should be evaluated.

b. If 2 ≤ HC /B ≤ 5 initially an increment h in the height of the will cave generate an increment in the NDS, making the propagation of caving easier. This trend continues until the cave reaches a certain critical height beyond which the slope of the curve can become either steeper or flatter, depending on the rock mass strength. If it becomes steeper, caving will probably propagate upwards easily, and a con-nection to the ground surface or pit floor will be achieved (path (1)(2)(5)(6) in Figure 4). If the curve becomes flatter, caving will probably propagate upwards with difficulty, and a connection to the ground surface or pit floor will not be achieved (path (1)(2)(3)(4) in Figure 4).

c. If HC /B < 5, initially an increment h in the height of the cave generates an increment in the NDS, but at a decreasing rate as the cave height increases. Beyond a certain cave height the curve becomes almost horizontal. Caving will probably propagate upwards with difficulty, and a connection to the ground surface or pit floor will not be achieved (path (1)(2)(3)(4) in Figure 4). This means that caving will propagate until a certain cave height (lower than HC) is reached, and then it will be arrested, forming a metastable cavity.The results of the numerical models indicate

that, for a given rock mass, the influence of the in situ stress field on cave propagation may be sum-marised as follows:a. The initiation of caving and its subsequent ver-

tical propagation depend on the stress field as defined by the in situ stresses (depth and stress ratio, K), the ground surface geometry (defined by the pit depth, HP, in the case of a transition from open pit to underground mining), and the subsurface geometry (defined by the geometry of the cave).

b. Given HP and HC, an increment in K increases the magnitude of the shear stresses acting in the cave back, facilitating caving propagation to-wards the ground surface.

c. Given K and HC, an increment in HP increases the magnitude of the shear stresses acting in the cave back, facilitating caving propagation to-wards the ground surface.

d. Given K and HP, an increment in HC increases the vertical distance through which the cave must propagate in order to connect with the surface. If HC is small in relation to the caved area (eg HC /B < 1), the cave must propagate only a short distance to connect to surface, and so a connection probably will occur. On the

other hand, if HC is too high in relation to the caved area (eg HC /B > 5), the cave must propagate through a large distance to connect to surface, and this may not occur.Therefore, even under favourable circum-

stances for caving, there are some conditions un-der which (with a constant undercut area), as the cave propagates vertically, the shear stresses act-ing in the cave back decrease, making the cave less unstable and decreasing the rate of caving propagation. If the ore column to be caved is high, cave propagation could be arrested and a metastable cavity formed. In some cases, this could generate a geotechnical hazard through the sudden failure of the cave back that could trigger an air blast.

This result is particularly important because it shows that the value of HC is not totally independ-ent of the geometry of the footprint since, de-pending on the minimum footprint width, B, the vertical propagation of caving may become easy or difficult. It is also important to note that the presence of a deep open pit produces stress con-centrations that facilitate the break-up of the rock mass, making cave propagation easier.

If the simultaneous operation of the open pit and the underground mine is expected, at least for a limited period, the definition of the time re-quired by the cave to connect with the pit floor becomes a key issue. This time will depend mainly on the rock mass characteristics, the stress field, the presence of major geological structures and, of course, the progress of mining.

4 CAVING PROPAGATION FACTOR

In order to include the effect of the rock mass strength on the evaluation of the likelihood of cave propagation, the Hoek-Brown criterion was used to define the peak strength of the rock mass (Hoek et al 2002):

(1)

where and are the principal effective stresses at failure, is the uniaxial compressive strength of the intact rock, and , and are material constants given by:

(2)

(3)

(4)

where is the value of the parameter for the intact rock, is the Geological Strength Index first defined by Hoek (1994), which is a function of the blockiness of the rock mass and the condi-tion of its structures, and is a factor that takes into account the disturbance of the rock mass in-duced by the blasting and deconfinement associ-ated with mining.

The numerical models gave the average mag-nitudes of the deviator stresses, S1 - S3, acting on the cave back. For a given S3, the maximum ma-jor principal stress that the rock mass can sustain is given by:

(5)

Therefore, the maximum deviatoric stress that the rock mass can sustain is given by:

(6)

where S3 is known from the results of the model-ling. The modelling assumes a dry rock mass so that the effective and total stresses are equal.

It is then possible to define the caving propagation factor, CPF, as the ratio between the average deviatoric stress acting in the cave back and the maximum deviatoric stress that the rock mass can sustain:

(7)

The caving propagation factor, CPF, can be re-garded as the inverse of the strength factors or factors of safety commonly used in geotechnical engineering. It can be interpreted as follows: If CPF < 1, the deviatoric stresses acting in the

cave back are not large enough to induce fail-ure of the rock mass, and the break-up of the rock mass ceases, arresting caving propagation.

If CPF = 1, the deviatoric stresses acting in the cave back are equal to the strength of the rock mass. This represents a local equilibrium con-dition in which cave propagation could cease, generating a metastable cavity.

If CPF > 1, the deviatoric stresses acting in the cave back are large enough to induce failure of the rock mass, allowing the upward propaga-tion of caving and the vertical growth of the cave.

Figure 5: Diagram illustrating the zones that define the likelihood of caving propagation in terms of the caving propagation factor, CPF, its variation with the relative height of the cave, h/B, and the concept of the minimum permissible value for the caving propaga-tion factor, CPFMIN.

If CPF is slightly larger than unity, caving will not necessarily propagate because of the inevit-able geotechnical uncertainties. Therefore, it be-comes necessary to define a minimum permiss-ible value of the caving propagation factor, CP-FMIN, such that if CPF is equal to or larger than this value, the likelihood of propagation will be high. This concept is illustrated in Figure 5 which, depending on the value of CPF, defines three zones:

Zone of No Caving Propagation (CPF < 1): In this zone the rock mass will not break-up, no cav-ing propagation will occur, the cave will stop growing upwards, and connection with the sur-face will not occur.

Transitional Zone (1 ≤ CPF < CPFMIN): In this zone failure or break-up of the rock mass and caving propagation are uncertain.

Zone of Caving Propagation (CPF CPFMIN): In this zone the stresses are large enough to fail the rock mass, allowing the upward propagation of caving and the connection of the cave with the surface.

Of course, the magnitude and the variation of the CPF with h/B depend on the strength of the rock mass. The better the geotechnical quality of

the rock mass the lower the position of the curve, and the less likely the propagation of caving.

The definition of the value of CPFMIN is not really a geotechnical issue but an economic de-cision, related to the degree of risk that the man-agement is willing to take in order to optimize the net present value (NPV) of the project. Ideally, the determination of CPFMIN should be based on the company’s permissible risk policy.

5 VALIDATION CASES

To validate the applicability of the CPF in en-gineering practice, some documented case histor-ies and mining projects were analyzed: Andina’s Rio Blanco Panel I (Chile), Finsch’s Block 4 (South Africa), Salvador’s Inca Oeste (Chile), Northparkes’ Lift 1 (Australia) and Palabora (South Africa). In all cases, the CPF results showed good agreement with the observed beha-vior (Flores and Karzulovic 2003). Three of these cases will be outlined here.

The Inca Oeste sector of Salvador mine suffered a caving arrest in July 1999. The arch failed in December 1999, generating an air blast and causing damage in the underground mine (de Nicola and Fishwick 2000).

The available data indicate that, for this case, HT = 600 m, HC = 180 to 210 m, B = 150 m (min-imum width of the footprint), K = 1.0, mi = 20 (estimated from typical values), ci = 100 to 150 MPa and GSI = 50 to 70 (estimated from RMR-

LAUBSCHER data).Figure 6 shows the location of this case on the

CPF chart. This location suggests that the cave will not propagate through the 200 m block height, because for h/B = 1.3 the CPF is slightly above 1. This is in good agreement with the ac-tual caving performance in this case.

Figure 6: Caving propagation chart showing the case of Salvador’s Inca Oeste sector.

Northparkes’ Lift 1 suffered a caving arrest in June 1997. Following cave induction, the arch failed in November 1999, generating an air blast and causing damage in the underground mine (van As and Jeffrey 2000).

The available data indicate that HT = HC = 480 m, B = 180 m (minimum width of the footprint), K = 1.5, mi = 20 (estimated), ci = 150 MPa and GSI = 50 to 70 (estimated from RMRLAUBSCHER

data).

Palabora mine is developing a transition from open pit to underground mining by panel caving. Pit’s operation ended in 2003. The underground begun in 2000 (Flores and Karzulovic 2002).

Figure 7: Caving propagation chart showing the case of Northparkes’ Lift 1.

Figure 7 shows the location of this case on the CPF chart. This suggests that the cave will not propagate through the 480 m block height, be-cause for h/B = 2.7 the CPF is 0.9. This is in very good agreement with the actual performance of caving in this case.

The Palabora mine is developing a transition from open pit to underground block cave mining. Development of the underground mine began in 2000. Mining operations in the open pit ceased early in November 2003. The first wedge failure at the bottom of the open pit wall was observed in late November 2003 (Glazer and Hepworth 2004).

The available data indicate that HT = 1200 m, HP = 815 m, HC = 385 m, B = 120 m (minimum width of the footprint), K = 1.5, mi = 20 (estim-ated), ci = 160 MPa and GSI = 70 to 90 (estim-ated from data presented by Calder et al 2000).

Figure 8 shows the location of this case on the CPF chart, indicating that caving should propag-ate through the 385 m block height, because for h/B = 3.2 the CPF is 1.5. The connection of the cave with the open pit appears to have been achieved (Glazer and Hepworth 2004).

6 DESIGN CHARTS

For a given set of conditions, the magnitude of CPF depends on the strength of the rock mass. For practical purposes, the following types of rock masses were considered:mi 20 (porphyries, quartzites, peridotites)

30 (granitic rocks)ci 100 MPa (medium to high strength)

150 MPa (high strength)

Figure 8: Caving propagation chart showing the case of the Palabora mine.

GSI 30 to 50 (poor to fair quality)50 to 70 (fair to good quality)70 to 90 (good to very good quality)

These parameters were used to compute CPF values from the results of the numerical analyses carried out for different problem geometries and stress conditions. The resulting CPF values showed that it was possible to simplify data presentation by normalizing the CPF values with respect to the magnitude of the stress ratio, K. Hence, the normalized caving propagation factor, NCPF, is given by:

(8)

Using this concept, design charts were de-veloped for evaluating the likelihood of caving propagation under a range of conditions. The cases considered in these design charts are:Cases: without an open pit

with an open pitUCL centred below the pit bottomUCL extreme below the slope’s toe

UCL depth: shallow (100 to 500 m)moderate (500 to 900 m)deep (900 to 1300 m)very deep (1300 to 1700 m)

Pit depth: 400, 800, 1200 mIn situ stresses: Vertical stress is lithostatic

K = 0.5, 1.0, 1.5, 2.0 and 2.5(along footprint width)

K = 1.0 (along footprint length)Rock masses: mi 20 and 30

ci 100 and 150 MPaGSI 30 to 50

50 to 70

70 to 90

Figure 9: Caving propagation chart for the case of a 800 m open pit, UCL centred below the pit floor, HT in the range 900 to 1300 m, and a hard rock mass of good geotechnical quality.

Figure 9 shows an example of a design chart. Such charts are intended to be indicative only and should be used with extreme care. If, as is to be preferred, a specific chart is developed for a given case study, it will not be necessary to nor-malize CPF by K.

Hence, the following methodology is sugges-ted for the evaluation of the likelihood of caving propagation:1. Define the geometry of the case to be studied

(eg with or without an open pit, HP, HC, HT, B), and the stress ratio K along the footprint width.

2. Assuming an isotropic and linearly elastic rock mass, compute the average deviatoric stress acting in the cave back by using PHASE2 or another software package. This should be done for different ratios, h/B, from say 0.1 to HC/B, and for different values of HC if required.

3. Estimate the values of the rock mass proper-ties mi, ci, and GSI required to define the rock mass strength.

4. Using these values and the results from (2) compute the CPF for the range of values of h/B being considered (eg by using an Excel© spreadsheet), and construct a caving propaga-tion chart such as that shown in Figure 9.

5. Establish the minimum permissible value of the caving propagation factor, CPFMIN.

6. If the block height, HC, is known, compute the ratio HC /B and, using the curve corres-ponding to HC, determine the CPF. If CPF is equal to or larger than CPFMIN, the likelihood of caving propagation is high, and

connection with the ground surface will prob-ably occur.If CPF lies between 1 and CPFMIN, then the likelihood of caving propagation and of a connection to surface are uncertain.If CPF is smaller than 1, then the likelihood of caving is low, and a connection to surface is unlikely to occur.

7. If HC has to be defined, use the value of CP-FMIN and determine the relative block height, HC /B, for caving propagation through differ-ent block heights. As B is known, the value of HC can be computed from the ratio HC/B. Indeed, it can take more than one value. For example, if CPFMIN is set at 1.4, K = 1, and B is 250 m, using the chart of Figure 9 the fol-lowing results are obtained:

Curve HC /B HC

HC = 300 m 2.0 500 m > 300 mHC = 400 m 1.8 450 m > 400 mHC = 500 m 1.4 350 m < 500 m

Hence, it is possible to cave 300 and 400 m block heights. Therefore, the block height used would probably be 400 m, unless other factors result in the choice of a lower block height.

If the likelihood of caving propagation through an ore column of height HC is not suffi-ciently high, it can be improved by increasing the minimum width of the footprint, B, and/or by pre-conditioning the rock mass to be caved.

This methodology for evaluating the likeli-hood of caving propagation does not take into account the effects of major geological struc-tures.

7 CONCLUSIONS

A method has been developed for evaluating the likelihood of caving propagation in strong rock masses. This method is based on widely used concepts, including the Hoek-Brown failure criterion, and commercially available software.

The concept of the caving propagation factor, CPF, has been introduced and used in the evalu-ation method. This method has been validated by back analysing five documented case histories. Although the methodology does not take into ac-count the effects of major geological structures, it can be used in the scoping and pre-feasibility stages of a mining project by caving methods.

ACKNOWLEDGEMENTS

The authors wish to thank the JKMRC and the sponsors of ICS-II for having given them the op-portunity to undertake this study: Codelco, De Beers, LKAB, Newcrest Mining, Northparkes, Rio Tinto, Sandvik-Tamrock and WMC. They also wish to thank Codelco’s El Teniente and Codelco Norte Divisions for providing informa-tion and support.

REFERENCES

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