An integrated approach for the design of stable mine backfill sillmats

Transcription

1 An integrated approach for the design of stable mine backfill sillmats E. De Souza & A.P. Dirige Department of Mining Engineering Queen s University, Canada Abstract Sillmats are structural elements used to support backfill in large underground mining excavations. Failure of such support structures may be catastrophic and result in substantial economic losses. The traditional design of cemented sillmats has been based on experience and on analytical models derived from static equilibrium analysis. This approach offers inherent limitations and generally results in conservative designs and expensive mine support installations. This paper presents a novel integrated procedure in which centrifuge modeling techniques are combined with numerical and analytical models to provide accurate engineering structural designs of sillmats. 1 Introduction In order to maximize the recovery of ore in modem and highly productive mining methods, cemented backfill is normally placed in underground excavations to provide structural support. In order to save on costs, backfill of low cement content is used to fill the mined out stopes. This backfill mass is supported by a sillmat structure cast from cemented backfill of very high strength. Mining excavations progress under the sillmats, which must remain stable when exposed and subjected to mine induced stresses, The stability behavior of the sillmat elements must be carefully studied to provide very effective, safe and economic mining operations. Improper design of these support structures may result in fill mass failure, with consequent losses of production, ore dilution, and in safety problems.

2 304 Damage and Fracture Mechanics VII In a unique design approach, centifuge model studies are combined with analytical and numerical modeling analysis to describe and predict the behavior and potential failure modes of sillmats. In this novel approach, centrifuge modeling is the primary tool used to dynamically test sillmat performance. Analytical modeling was carried out using limiting equilibrium analysis, based on a method introduced by Mitchell and Roettger [1]. Numerical modeling was carried out using FLAC (Fast Lagrangian Analysis of Continua), a powerful two-dimensional elastic plastic-finite difference code [2]. Application of the design approach is demonstrated from an engineering design study conducted for an underground gold mine, aimed at minimizing backfill binder content and at producing cost efficient paste fill recipes for sillmat construction. The modeling study incorporated the effect of stope geometry and itope wall roughness on sillmat behaviour and stability performance, Models were developed to conform with two stope conditions applied underground: stopes 3 m wide, 15 m long, and 30 m high, and stopes m wide, 15 m long, and 40 m high. In all cases the stope walls were inclined at 75 and smooth, medium-rough and rough rock wall conditions were established for simulating typical excavation bounda~ modes encountered in the mine. Paste fill was prepared at 800/0 pulp density using unclassified tailings mixed with Type 10 Normal Portland cement (NPC) and Type C fly ash (FA). All recipes were prepared at 7~o binder content and cured at 14 and 28 days. 2 Sillmat design approaches 2.1 Centrifuge modeling Centrifuge modeling is based on the development of scaled models to study the complex behaviour of materials. When designing scaled models, a geometrically-equivalent model to the field situation (prototype) is first formed, scaled down at I/N, using the same materials of identical properties, including paste fill recipes and curing times, as that being used in the field. The scaling of the prototype must ensure that the model should observe conditions of similitude such as the same relative inclination, position, proportions, boundary conditions (wall roughness), values and structure, The model is, in essence, a small prototype, The scaled model is then placed in the centrifuge strongbox and accelerated to N gravities. During flight, a centnpetal force acceleration is experienced by the model, inducing self-weight forces in the test material, The inertial mass induced stresses at any point in the model will be identical to the gravitational mass induced stresses at any similar point in the prototype, provided that the boundary conditions are identical at all equivalent points [3]. Thus, the model accelerated in the centrifuge experiences analogous behaviour as the prototype. The centrifuge used is a 5.3 m diameter machine driven by a 45 kw hydraulic motor and speed control assembly. The centrifuge modeling facility is located in the Department of Mining Engineering, Queen s University, It is designed to rotate up to a maximum speed of 350 rpm and it is capable of

3 Damage and Fracture Mechanics VII 305 exerting up to 300 gravities on typical models, It is rated at 30g-tonne and can carry payloads of up to 300 kg, An aluminum swing strong box, 0.75 m long, 0,56 m wide and 0,42 m high, is used to house scaled models, The centrifuge has a total of 14 slip rings and a data acquisition system is utilized for model data transmission and storage, Models can be viewed and video taped during flight through a port in the centrifuge concrete pit, and with the aid of a high intensity strobe light, 2,2 Analytical modeling Mitchell and Roettger [1] developed an analytical solution on the basis that sillmats are normally of such length that the problem can be idealized as a twodimensional plane strain stability problem, The critical operational stage of a sill pillar after the underlying ore is removed is shown is Figure 1. The sill supports a non-uniform vertical stress, a,, of unknown magnitude, and a lateral closure stress, ac,resulting from rock deformations. Figure 1: Sill pillar loadings (after Mitchell and Roettger). Possible failure modes include sill pillar slippage, caving, sill pillar shear, rotational shear or flexural (bending) failure. For this case application, where the sillmat constitutes the entire cemented paste fill column in the stope, slippage and shear failure are of particular importance. Sill pillar slippage failure is likely to occur when, yh=d13# ( sin2~-0,15sin2~ ) (1)

4 306 Damage and Fracture Mechanics VII where, y is the unit weight of the uncemented fill (kn/m3); H is the height of the uncemented fill (m); 6 is the estimated wall closure; E is the stiffness modulus of fill (kpa); L is the sill pillar width (HW to FW distance, m); p is the coefficient of friction at the fill rock walls interface; 1 is the total contact length between sill and wall rocks (m); and ~ is the HW/FW dip, Sill pillar caving or crushing occurs if the closure stress, o,, exceeds the uniaxial compressive strength (UCS) of the cemented sill material. If the expected wall closure, ~ is estimated, then the cemented sill can be engineered, where the lateral prestress is considered the design condition, giving UC= EdL, The order of magnitude of the sill pillar stiffness modulus, E, can be controlled by the cement content used, Mitchell and Roettger [1] suggested that o, should be less than 50% of the UCS of the sill pillar, Wall rock interface conditions play an important role on fill stability, Irregular stope walls provide sill pillar and wall rock interlocking, thus preventing sill slippage. The rougher the wall conditions the lower the vertical stress due to arching of the fill mass, specially in narrow orebodies. Theoretical considerations, model studies and field measurements indicate that arching between the HW/ FW rocks reduces the vertical stress, crv (kn/m3) to, Crv = yl 2K tan@ (2) where, y is the fill unit weight (kn/m3) and K is a constant often taken to be unity. Although it is more likely that the footwall supports a considerable portion of the adjacent stress, it is prudent to assume that this stress acts uniformly on the sill. For equilibrium, block sliding of the sill due to side shear failure occurs when, Tf d [ sinz 13)() L W>2 where, w is the uniform loading (kpa) which include the self-weight of the sill (i.e., w = a,+ dy), d is the sill depth (m), ~f is the shear strength in the fill-wall rock contact zone (kpa), and ~ is the HW/FW dip. 2.3 Numerical modeling Numerical modeling was carried out using FLAC, an explicit finite difference program for engineering mechanics computation. The program simulates the behaviour of structures built of soil, rock or other materials that may undergo plastic flow when their yield limits are reached. The materials are represented by elements, or zones, which form a grid that can be adjusted to fit the shape of the object to be modeled. Each element behaves according to a prescribed linear or (3)

5 Damage and Fracture Mechanics VII 3 () 7 non-linear stresslstrain law in response to the applied forces or boundary restraints. The material can yield and flow, and the grid can deform (in largestrain mode) and move with the material that is represented [2]. FLAC program offers a wide range of capabilities to solve complex problems in mechanics; for this particular application, the program was used to validate the centrifuge modeling work, Two-dimensional elastic-plastic models were constructed and the stope walls were modeled as fixed boundaries, Because sillmat stability is dependent on the strength of the fill and fill-wall rock interface, the interface strength was simulated in three different scenarios. The smooth wall rock boundary condition was simulated with very low or no interface strength, The medium-rough wall rock condition was simulated by reducing the interface strength until sill failure would occur. For the rough wall rock condition, the interface strength was considered to be the same as the fill strength, defined by cohesion and friction angle, 3 Case application of sillmat design 3,1 Centrifuge modeling Eighteen centrifuge models were designed to represent prototype conditions consisting of paste filled stopes, 3 m, 5 m, and 7.5 m wide and 30 m to 40 m high, detailed in Table 1. All models were prepared using unclassified tailings supplied by an underground gold mine, mixed with 7% binder, The binder recipe consisted of 4% NPC and 3% FA. Treated form ply was used to construct the paste fill curing molds, which formed the scaled models, Prototype stopes 3 m wide by 15 m long by 30 m high were represented by models 6 cm by 30 cm by 60 cm high, scaled at 50 gravities, Prototype stopes m wide by 15 m long by 40 m high were represented by models cm by 23 cm by 61,5 cm high, scaled at 65 gravities. All model walls were sloped at 75 degrees from horizontal. Paste was poured at 80 % pulp density and models were cured for 14 and 28 days, under controlled conditions. The simulated boundary conditions were smooth (surface of form ply), medium-rough (O.15 m breakage for every 2 m vertical spacing at 50 g) and rough (0,19 m breakage for every 1 m spacing at 65g). Figure 2 shows a typical model ready for testing. After curing, the paste fill column was spray painted with white stripes to facilitate visual observation of deformation behaviour during flight, Each cured specimen was placed in a model box, and secured in the centrifuge swing strongbox, During test, the model was conditioned for minutes at a centrifuge speed of 60 rpm (producing accelerations of 10 g). The centrifuge speed was then increased at a rate of approximately 2-3 rpm per minute until either sillmat failure or the design scale was achieved, Six tests, Al -A6, were performed to simulate stopes with smooth wall conditions, Models A1-A3 were cured for 14 days. All three models exhibited total collapse of the complete fill mass (slip failure) prior to achieving the design scales; the gravity at failure is shown in Table 1. The failure process did not develop suddenly; it responded to increases in acceleration and stress loading.

6 308 Damage and Fracture Mechanics VII *r..,, Centrifuge lvloael i- Lure-- Design Test Boundary Gravity at Dimensions Times Gravity Comments No. (cm) (D!!!?! - g) conditions M%%iEf= - L3111UU1U Ad 1 allbu Smooth 28 Failed..- --, _ Smooth 13 Failed A4 6x30x Smooth 39 Failed A5 7.7 x23 x Smooth 23 Failed A6 11.5x 23x \ 65 Smooth 19 Failed B1 6x30x60 14 not fail B2 7.7x 23x B3 11.5x 2#av..< 1 I 1A.8 B4 6x30x60 28 B5 7.7 x23 X Rough 70 ldid not fail B6 11.5x 23x Rough 69 Failed cl 6x30x lmedium roughl 48 Failed C2 7.7-X23X ]Medium rough] 69 ldid not fail < ~ C3 11.5x 23x lmedium roughl 51 Failed C4 6x30x IMedium roughl 38 Failed C5 7.7 x_23 X [Medium roughl 55 Failed ~C6111.5x23x6L [Medium roughl 28 Failed The first indication of failure was manifested by the dislodgement of the entire fill mass from the hanging wall contact. In most cases, shear separation started from the bottom of the fill mass and propagated upwards at increased acceleration and then followed by a sudden collapse of the complete fill mass. Failure took place at the hanging wall-fill and footwall-fill contacts; no internal failure of the fill mass was noted, It is interesting to note that the gravity at

7 Damage and Fracture Mechanics VII 309 failure increased with decreasing model weight. This indicated the significance of fill self-weight on the failure mode of models with smooth wall conditions, Models A4, A5 and A6 were cured for 28 days. These models also exhibited collapse of the complete fill mass (slip failure). However, failure developed suddenly without any warning. The equivalent prototype dimensions at failure were below the design dimensions, thus indicating the inappropriateness of the paste design, The failure of model A4 is shown in Figure 3a, a b c Figure 3: Typical model failures, a. model A4; b. model B6; c, model C5, Models B 1, B2 and B3 were constructed with rough stope walls and cured for 14 days, Model B 1 could not be brought to failure at the design gravity of 50 g. Acceleration was increased to 60 g and no signs of failure were exhibited by the fill mass, thus indicating the significant contribution of wall roughness to fill stability. Models B2 and B3 failed below the design scale of 65 g, Failure of model B2 occurred at approximately 50 g, with a 19 m high fill mass plunging into the undercut. The first indication of failure propagation, in which the entire fill mass dislodged along the hanging wall contact, occurred at around 38 g, The mechanism was followed by the development of a sub-horizontal rupture plane at the hanging wall, then extending to the footwall, and leading to the eventual failure of the fill mass, A similar failure mechanism was developed for model B3, which failed at60g, with a31,2 m high fill mass sliding into the undercut, Models B4, B5 and B6 were designed with rough walls and cured for 28 days, Model B4 was not tested as it was not expected to fail. Model B5 was not brought to failure at the design gravity of 65 g, Model B6 was not brought to failure at the design gravity of 65 g. The acceleration was increased and failure of the model occurred at 69 g. The failure mechanism was first evidenced by the dislodging of the entire fill mass along the hanging wall contact at 58 g. The mechanism was followed by the development of a rupture plane at a height of approximately 31.2 m, followed by collapse of fill mass into the undercut, The failure of model B6 is shown in Figure 3b,

8 310 Damage and Fracture Mechanics VII Models C 1, C2 and C3 represented medium-rough stope walls conditions and the fill was cured for 14 days, Models Cl and C3 failed below the design scales of 50 g and 65 g, respectively, and model C2 did not fail. Models C4, C5 and C6 were designed with medium-rough walls and cured for 28 days. All three models exhibited collapse of the fill mass (slip failure) below the design g scale, with fill masses of different heights plunging into the undercut. Model C4 failed with a 21 m high fill mass plunging into the undercut, model C5 failed with 12.4 m of fill collapse, and model C6 failed with 26 m of fill collapsing into the undercut. In all three models, the failure process did not develop suddenly. It was initiated with the dislodging of the entire fill mass along the hanging wall contact, immediately followed by the formation of sub-horizontal rupture plane and followed by the plunging of the fill mass at certain heights. This indicates the significance of fill self-weight in the failure mode of models with medium-rough wall conditions, The failure of model C5 is shown in Figure 3c. 3,2 Analytical modeling The limit equilibrium analysis assumed that sillmats are stable when the factor of safety against failure is more than 1. Application of the model described by equation (3) was based on a series of parametric calculations as follows. The fill shear strength parameters were obtained from triaxial tests and calculated from, ~ = c + o, tan$, where c is the cohesion, IS. is the normal stress the friction angle. The calculated shear strength, L of the fill was 551 kpa. The surcharge stress was calculated from equation (2), with y= kn/m3, L = 3 m, 5 m and 7.5 m, K = 1, and ~= 33, to be 44,74 kpa, 74,57 kpa and kpa. The values of dy were kpa for the 40 m high fill, and kpa for the 30 m high fill, The values of the uniform loading, w, were kpa, kpa and 886,60 kpa for 3, 5 and 7.5 m wide stopes, respectively. Trial calculations showed that sillmats of varying stope widths and heights would remain stable with the shear resistance at the rock wall-fill interface being as low as 2$%0 of the fill shear strength. Rock wall interfaces with shear strengths above this threshold value might thus be considered rough. Smooth rock wall conditions are assumed when the factor of safety against failure is less than 1, in which slippage failure occurs due to the self-weight of the till material, Smooth rock wall interface conditions would thus be characterized by having a shear resistance at the rock wall-fill interface below approximately 27?40 of the fill shear strength. The analytical model results indicated that this modeling approach may be used to provide some approximate parameters that can be used for predicting the behaviour of a sillmat. 3.3 Numerical modeling A series of two-dimensional elastic-plastic models were constructed using FLAC in an attempt to validate the physical models, The stope geometry and equivalent planar representation are illustrated in Figure 4. The fill was discretized into

9 Damage and Fracture Mechanics VII 311 square elements with an area of 0.25 m2. The fill was modeled as a Mohr- Coulomb material using effective shear strength parameters obtained from consolidated-undrained triaxial tests. The model input parameters are shown in Table 2. Figure 4: 3-D mining under fill geometry and equivalent fill 2-D representation. Table 2. Material properties of the fill and rock. Parameters Fill Rock Density (p) 1,975 kg/m3 2,700 kg/m3 Bulk Modulus (K) 80 MPa 310MPa Shear Modulus (G) 37 MPa 230 MPa Cohesion (c) MPa 0.01 MPa Friction Angle (@) 33 Tensile Strength MPa Two-dimensional interface elements were placed between the fill and the fixed stope wall boundaries to represent the fill-rock interface, Both the y- displacement and y-velocity histones were used to evaluate whether the system was reaching equilibrium at each step. Increased steps were continued until active collapse of fill occurred or the model reached equilibrium. Models were developed for 5 m and 7.5 m wide stopes, and considering the three different wall rock conditions, Numerical model results corresponded well with centrifuge models, Figure 5,a shows displacement vectors in a 5 m wide stope with rough rock wall conditions. In this case, the model came to equilibrium indicating stable mining conditions, Displacement vectors indicated a rotational response of the sill about the footwall contact. Figure 5.b shows histories of y-displacement at the bottom of the 5 m wide fill, a maximum displacement of approximately m was determined when equilibrium was attained at 5,915 steps,

10 312 Damage and Fracture Mechanics VII : > FI-AC 4.00 Steo S91S.0. Soo HISTORY l=l_ol- Y.axis Y C41.spl=ee.rnellt< a, 21) x-axle, Numb-r 0? t-p ~.600.+? s S 20 2S SS (-? 0---0=) a b Figare 5: Displacement vectors (a) and history of y-displacement (b) in a 5 m wide stope of rough wall conditions. 4 Conclusions A paste fill sillmat design methodology based on centrifuge, analytical and numerical modeling methods was successfully developed. For the materials tested and mining conditions modeled, although the three methods exhibited comparable results for smooth and rough wall rock conditions, centrifuge modeling seemed to be more effective in treating complex behaviour such as the modeling of medium-rough wall rock conditions. Different modes of sill failure were exhibited by the physical and numerical modeling techniques, Centrifuge modeling indicated that approximately one-half to three-quarters of the fill column would plunge into the undercut (slip failure) when subjected to failure stresses, In contrast, numerical modeling indicated a rotational failure about the footwall contact, References [1] Mitchell, R, J. and Roettger, J,J., Analysis and modeling of sill pillars. Innovations in Mining Backjlll Technolo~, Balkema:Rotterdam, [2] Itasca Consulting Group, FLAC-2D Version 4, Online User s Manual, [3] Mitchell, R. J., Centrifuge modeling as a consulting tool. Canadian Geotechnical Journal. 28(1), pp , 1991.