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Stability analysis of historic underground quarries
Computers and Geotechnics 37 (2010) 476–486
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Stability analysis of historic underground quarries Anna Maria Ferrero a, Andrea Segalini a,*, Gian Paolo Giani b a b
Dept. of Civil, Environmental and Territory Engineering and Architecture, University of Parma, Italy Dept. of Geological Science, State University of Milan, Italy
a r t i c l e
i n f o
Article history: Received 26 June 2009 Received in revised form 26 January 2010 Accepted 28 January 2010 Available online 16 March 2010 Keywords: Underground quarries Rock mass numerical modeling Discontinuities monitoring
a b s t r a c t This work, carried out at the Department of Civil, Environmental and Territory Engineering and Architecture (DICATeA) of the University of Parma, analyzes the stability conditions of the ancient underground quarries of Viggiù (Varese, Italy). The objective of the study is to verify the actual structural predisposition to instability phenomena of the old Viggiù quarries, within the context of a historical and cultural valorization and recovery of the ancient ornamental stone quarries. These quarries, that are now completely abandoned, could be used as a tourist attraction and/or as a teaching environment. They are a wonderful example of industrial architecture by presenting an audacious composition of filled in trenches and room and pillar techniques. An experimental campaign based on in situ measurements and laboratory measurements has been carried out to characterize the rock mass and to determine rock mass mechanical features. A numerical model of the entire rock mass has been developed in order to analyze the stability of the entire underground openings. A preliminary monitoring phase has been realized, aimed at controlling abandoned rock structure movements at the most significant discontinuities. Some measurements of the vertical stress in the pillars and in the walls have been performed, as well, and used for the model calibration. Once the model has been calibrated, the analysis of the actual stress and deformation conditions has been evaluated, the stability condition of the entire structure computed and a forecasting analysis of any intervention that could be realized to guarantee the underground public access has been performed. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The two quarries examined are located on the southern side of the Monte Rosa Massif, near Piamo-Vallera (Viggiù village), and are named Cava Danzi and Cava Beltrami, respectively. The present study aims to verify the stability conditions of the rock mass– underground excavation system by evaluating the historical–cultural renewal of Viggiù’s old subterranean ornamental quarries. The stability analysis was carried out with different analytical and numerical approaches, which schematized the rock mass by the continuous equivalent or discontinuous schemes according to the scale of the problem examined and the aspect analyzed [8]. This choice arose from the need to analyze both the local and overall stability conditions of the pillars and roof of the quarries. A method of analysis that uses the discontinuous approach to verify the possible local formation of blocks, which come off and move on pre-existing discontinuities, was used in the roof stability analysis, while a stress–strain analysis of the entire room and pillars system was used in the stability analysis for individual pillars. In particu* Corresponding author. Address: Dept. of Civil, Environmental and Territory Engineering and Architecture, University of Parma, V.le G.P. Usberti, 181/a, 43124 Parma, Italy. Tel.: +39 0521 905952; fax: +39 0521 905924. E-mail address: [email protected] (A. Segalini). 0266-352X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compgeo.2010.01.007
lar, a stability analysis of the walls and the pillar located near the entrances was carried out using the key block method [12] to verify the possible movement of blocks along pre-existing discontinuities, and the entire rock mass was analyzed with the finite element method (FEM) [26].
2. Geological classification and geomechanical characterization of the rock mass Geological studies and geomechanical characterization of the rock mass have been developed at Politecnico di Milano [21]. The main results of these studies, which are essential for the stability analysis, are briefly reported below. The area of this study belongs to the Southern Alps tectonic unit; more specifically, it is located in the West Lombard Pre-alps sector usually known as the Zona del Varesotto Luganese. Cava Danzi is one of the largest quarries in this area, and it was used for the subterranean extraction of Saltrio limestone, which is a dominant calcareous formation, composed of light brown or whitish biocalcarenite. Fine solid limestones with flat parallel bedding are dominant. The geomechanical characterization of the rock mass required the execution of scanlines for a survey of discontinuities on the
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outcropping rocks, laboratory and site tests. All the discontinuities intercepting the scan lines were censored, and the orientation (dip and dip direction angle), spacing, persistence, wall strength, roughness, aperture, possible filling thickness and water presence were evaluated for each discontinuity according to the methods suggested by ISRM [15]. The interpretation of the discontinuity survey allowed for the individuation of five discontinuity systems (Fig. 1) in the rock mass in addition to a foliation plane, and the frequency and spacing values are reported in Table 2. Orientation data are reported in Table 1. Direct shear tests on natural discontinuities allowed for the evaluation of the peak and residual strength of natural discontinuities. A peak and residual failure envelope of the discontinuities was achieved with direct shear laboratory tests. The peak and residual angles are equal to 54° and 41°, respectively. Uniaxial and triaxial compression tests and direct tensile tests (Brazilian test) were conducted to determine the simple compression strength (rc), tensile strength (rr) and rock matrix shear strength parameters (c, /) according to the Hoek–Brown strength criterion linearized in the appropriate stress range (Table 3) using the Rocklab Code [20]. These tests were conducted on rock blocks cored in three orthogonal directions to analyze possible rock anisotropy. On the basis of the scanline surveys of discontinuities and laboratory test, the rock mass in the excavation zones, which is considered homogeneous from a geomechanical point of view, was classified. This allowed for the definition of the quality indexes: rock mass rating (RMR) [5], Q [3] and Palmstrom’s rock mass index (RMi). The indexes required to assess the Q value of the Barton classification are: rock quality designation (RQD), reported in Table 4 and calculated using the frequency value reported in Table 2, Jn, Jr, Ja, Jw, and SRF, which are, respectively, the number of discontinuity families, the surface roughness, the deterioration and filling of joints, the water presence and the stress ratio factor (SRT). The Palmstrom’s rock mass index RMi [18] is a volumetric parameter that indicates the uniaxial compression strength of the rock mass approximately. It is defined as the product of the uniaxial compression strength in intact rock rc and a reduction parameter Jp, which considers existing discontinuities. RMi indexes are 8.05 for the Danzi Quarry and 6.67 for the Beltrami Quarry.
Table 1 Main joint set orientation. Sets
Dip
Dip direction
1 2 3 4 5
74 ± 4 74 ± 10 67 ± 5 32 ± 5 83 ± 5
270 ± 30 323 ± 20 25 ± 20 159 ± 12 72 ± 20
Quality indexes values obtained for the rock mass according to classifications were used to calculate the rock mass bulk modulus. Several different empirical relations have been used within this scope [6,17,24,14,4,2,18,19,10,16,25]. A significant variation in values depending on the chosen correlation can be observed, with the difference ranging between two orders of magnitude; consequently, an average value was chosen. With regard to rock mass strength properties, RMR values locate the rock mass in class III, for which [5] we assume a cohesion value varying from 0.2 and 0.3 MPa and a friction angle varying in the 25–35° range. The non-linear Hoek–Brown strength envelope was found to have m and s values of 2.29 and 0.0205, respectively. 2.1. Flat jack tests A flat jack is a thin envelope-like bladder with inlet and outlet ports that may be pressurized with hydraulic oil. A flat jack may be manufactured in many shapes and sizes, determined by its function, the slot preparation technique and the properties of the rock mass being tested (Fig. 2). This test is based on the principle of partial stress release and involves the local elimination of stresses, followed by controlled stress compensation. The reference field of displacements is first determined by measuring the distances between gauge points fixed to the surface of the rock face. Then, a slot is cut in a plane normal to the direction of the measured stresses. This allows deformations in a direction normal to the slot. The distances between gauge points decrease because cutting the slot causes partial stress relief in the rock above and below (Fig. 3). Afterward, a thin flat jack is introduced into the slot. With the aid of this device, pressure
Fig. 1. Stereographic projection of discontinuity poles in the Danzi and Beltrami Quarries.
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Table 2 Frequency and spacing values obtained from discontinuity surveys in the two sites examined used for rock mass classification. Frequency
fS
f K1
f K2
f K3
f K4
f K5
f global
Spacing (m)
Beltrami Quarry Danzi Quarry
3.255 2.477
3.571 2.787
2.645 2.566
1.913 2.573
3.690 1.429
1.546
16.620 11.832
0.06 0.085
Table 3 Rock matrix resistance properties considering three test directions (x, y, z).
Global X Y Z
mi ()
C (MPa)
/ (°)
rr (MPa)
rc (MPa)
9.03 10.24 8.21 15.47
17.63 15.29 17.06 14.89
47.92 49.27 46.42. 54.73
10.44 8.38 10.68 6.40
94.31 85.84 87.69 99.08
Table 4 Values considered in rock mass classification.
Danzi Quarry Beltrami Quarry
RQD
Jn
Jr
Ja
SRF
Jw
Q
75 60
15 15
3 3
1 1
2.5 2.5
1 1
6 4.8
260 mm
350 mm
Fig. 3. Measurement scheme during testing [1].
Fig. 2. The flat jack used.
(compressive stress) is applied to the rock. This pressure causes a partial restoration of the initial displacement field, which at some point reaches (approximately) the previously measured values. The necessary pressure can be related to the compressive stress in the direction normal to the slot. The hydraulic pressure in the flat jack necessary to restore the undamaged state is higher than the actual stress. This is caused by the inherent stiffness of the flat jack, which resists expansion when the jack is pressurized. Another factor that contributes to this effect is the difference between the area of the jack and the area of the slot (the latter being greater than the former). Both of these factors are taken into account when interpret-
ing the test results. The test, as described above, is based on the following assumptions: the stress in place of the test is compressive; the rock mass surrounding the slot is homogenous; the rock mass deforms symmetrically around the slot; the state of stresses in the place of the measurement is uniform; the stress applied to the rock mass by the flat jack is uniform; and the values of the stresses (compared to compressive strength) allow the rock to work in an elastic regime (see Fig. 4). Nine tests were performed in the pillars and in the boundary walls by allowing the estimation of the acting state of stresses (Table 5). These results were utilized for the model calibration discussed in the following sections. 2.2. Monitoring system A monitoring system of opening–closing movements of discontinuities was installed to control the evolution of movements that can warn of an incipient collapse in untended rock structures. Qualitative analysis of every collected discontinuity was carried out to define the positioning of the instrumentation. Overall,
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- TRASDUCER C13 -
SPOSTAMENTI RELATIVI (mm) RELATIVE DISPLACEMENTS(mm)
0.1
0
-0.1
Fig. 4. Example of test realization.
Table 5 Vertical stresses obtained by flat jack tests. Location
Flat jack tests (MPa)
Pillar 13 Pillar 23 Pillar 40 Pillar 54 Pillar 63 M Pillar 63 V Pillar 63 M FON 1–3 FON 2–4
1.74 2.14 0.0 5.00 2.16 0.00 5.57 2.02 7.68
fifteen displacement transducers were installed orthogonally to some selected discontinuities. These devices measured the linear movement along its axes and were wired to three different control units. The monitoring system controlled the discontinuities that are believed to be the most significant for the overall behavior of the whole rock mass. Nine of the 109 surveyed discontinuities were selected for monitoring in the Danzi Quarry, while the remaining transducers were located in the Beltrami Quarry: five were located in the north-central area, while the four remaining devices were located in the northern portion of the underground opening. It is possible to draw some general conclusions from the examination of the displacement measurements. A representative example of the results of discontinuity monitoring with a displacement transducer is shown in Fig. 5. This qualitative trend is similar to that registered in all other control units. During the observation period the movement was between 0.12 mm in opening and 0.12 in closure; the closure registered rate was around 0.04 mm/month in mean speed. We have now found a 0.1-mm relative closure with almost the same mean velocity as in the same period in 2007. The analysis refers to a cycle of readings made during three complete solar years. In fact, there is a tendency towards cyclic movements related to seasonal evolution (temperature, rainfall, etc.) with a natural return to the initial conditions. The system allowed us to assert that the movements measured were of the order of one tenth of a millimeter per year, with a seasonal trend caused by thermal variations. The recordings lead us to verify that the monitored blocks are currently stable.
3. Stability analysis using the key block theory 3.1. Key block theory The essential part of the key block theory [23] is the joint analysis of the discontinuity system with the excavation surfaces. The intersection of the discontinuities can originate solids of variable
18/07/06 23/08/06 28/09/06 03/11/06 09/12/06 14/01/07 19/02/07 27/03/07 02/05/07 07/06/07 13/07/07 18/08/07 23/09/07 29/10/07 04/12/07 09/01/08 14/02/08 21/03/08 26/04/08 01/06/08 07/07/08 12/08/08 17/09/08 23/10/08 28/11/08 03/01/09 08/02/09 16/03/09 21/04/09 27/05/09
-0.2
DATE Fig. 5. Displacement transducer readings between July 2006 and March 2008.
shape that, depending on available strengths, can be in critical stability conditions. The theory aims to identify the critical blocks that, in the absence of appropriate contrast, release other blocks near the voids and trigger the collapse of the rock structure. The block located in the most dangerous position, the first to be released, is defined as the ‘‘key block”. If the potentially dangerous block (key block) is identified before the movement begins, and if its stability is assured, then the other blocks will not move. The method can be implemented either with a vector calculus or a graphic process. The graphic process uses equiangular stereographic projection (Fig. 6). This kind of projection represents a particular perspective form, in which all points are projected from one of the sphere poles, in this case the lower pole on a horizontal projection plane. The main features of this method are that planes project as circles and lines projects as points, and that the projection also maintains the angles between the planes. The assumptions on which the method is based are that the discontinuity surfaces are perfectly plane and persistent at least inside the blocks and are characterized by a definite direction beforehand; the blocks are nondeformable; and the block movements are possible only without interference from adjoining blocks. The block method distinguishes rock mass blocks inside the rock mass (JB) from the blocks that overlook the excavation surfaces (JP). The finite blocks can either be removable or non-removable. Removable blocks are further divided into stable blocks independent of acting forces, stable blocks due to the shear strength effect on discontinuities and unstable blocks (key blocks). To define a finite and removable block stability condition, it is necessary to compare acting forces and available strengths. For this purpose, it is possible to apply either an analytic or a graphic procedure to define friction angle values able to maintain a stable joints pyramid, in connection with a potential sliding condition. The Rock 3D program [11] was used for the block analysis; the code recognizes possible kinematic mechanisms of blocks and estimates their stabilities with the limit equilibrium method. This analysis assumes that it is possible to associate a definite rock volume with every kinematic mechanism (fall, sliding on one or two planes), even if it has a complex shape or is bounded by different discontinuity
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Fig. 6. Example of equiangular projection utilized for key block application.
planes and excavation walls, if the discontinuity map geometry allows that. For a selected kinematic mechanism the program defines, according to the discontinuity tracks surveyed on the rock face, the maximum close boundaries that are not connected to each other, using only discontinuities compatible with the examined kinematic mechanism (Fig. 7). This analysis phase and the one that follows must be repeated for each possible kinematic mechanism and seek the greatest block instability conditions. The program optionally generates a pseudo-random discontinuities map that respects the statistical distribution of frequencies and persistence measured on the natural rock face. The following phase is directed to the complete geometrical reconstruction of complex blocks (Fig. 8). The program defines the solid derived from the union of all elemental polyhedrons contained within closed boundaries. For each complex block, Rock3D calculates volumes and surfaces.
3.2. Application of key block method to the Danzi Quarry The key block method was applied to the excavation roofs, paying attention to the entrance zones in particular. The details of the structural data for the rock mass are reported in Section 3. Removable blocks were identified for each entrance by determining the larger blocks formed by the observed discontinuities. This phase was performed for each block type in order to determine the worst possible conditions in terms of possible unstable volumes. A statistical variation of the discontinuity orientations was considered in order to analyze the influence of dip and dip direction variation on the block stability condition. The sliding directions, factors of safety and volumes of each removable block were then computed. Figs. 9 and 10 show the results obtained for the three Danzi Quarry entrances. At first, the friction angle assigned was relatively low and equal to the residual value measured by laboratory testing, and the cohesion was nil. Parametrical analysis was performed to evaluate the influence of the variation in strength on the stability conditions. In the parametric analysis, the high friction angle simulates a rough discontinuity, while the presence of cohesion can be due to rock bridges.
Fig. 7. Example of discontinuity traces on a rock face.
Results obtained by parametrical analysis on the central entrance roof, considering both the limit equilibrium condition (F = 1) and a safer condition determined by a factor of safety equal to 1.3, show that if the friction angle is lower than 53.7° instability occurs. If the friction angle is in the range of 53.7–68.6° and the cohesion is in the range of 8.10–13.56 kPa, the factor of safety varies in the range of 1–1.3. When the friction angle is above 68.6°, the
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3.3. Application of the key block method to the Beltrami Quarry The area analyzed was the quarry roof in an area with the dimension of 27 27 m2. The analysis was performed using the procedure that was described for the Danzi Quarry and by varying the orientation of the main joint sets according to the measured variability. Results show that the maximum computed (Table 6) block has a volume of 4.108 m3 and is near the entrance. The possible instability at the pillar sides was also investigated. Sliding phenomena along the intersection between joint set 1 and 2 of limited volumes (below 0.5 m3) as can be observed in the quarry corresponding to pillars 15 and 16.
Fig. 8. Example of a rock block identified for volume computation.
Safety Factor vs Cohesion (Friction angle = 25°) 2.5
4. FEM models
Safety Factor
2 1.5 block 1001
1
block 1000 block 1100
0.5
block 1001
0 0
20
40
60
Cohesion [kPa]
80
100
120
Fig. 9. Factor of safety trend as function of the cohesion. Friction angle fixed at 25°. Central entrance to Danzi Quarry.
The complex geometry of the excavations compelled us to use a numerical model to analyze the stress–strain behavior of the underground rock structure. The finite element method (FEM) [26] was used for this purpose. A three-dimensional model was set up to discretize the excavated rock mass by representing the pillars and slabs of the quarries. The medium was considered to be a continuous equivalent medium, and an elastic ideally plastic behavior was assigned to the rock mass. The strength and deformation features of the rock mass are given in Table 7. The mechanical parameters of the rock mass were calibrated with the geomechanical characterization data and compared with the in situ flat jack measurements. 4.1. 3D model features and results
Factor of Safety vs friction angle (Cohesion = 0) 2.5
Safety Factor
2 1.5 1
block 1001
0.5
block 1000
0
block1001 block 1100
0
20
40
60
80
100
Friction Angle [°] Fig. 10. Factor of safety trend as function of the friction angle. Cohesion fixed at zero. Central entrance to Danzi Quarry.
stability conditions are guaranteed by the higher safety factor values. The results for the lower entrance identified three possible unstable rock blocks with volumes of 11.8, 2.2 and 4.9 m3, respectively. Parametric results obtained for the lower entrance to the Danzi Quarry shows that if the friction angle is equal to 44.5°, then instability occurs. The factor of safety varies in the range of 1–1.3 when the friction angle is in the range of 44.5–56.6° and cohesion is in the range of 30.38–32.92 kPa. When the friction angle is above 56.6°, the safety factor is above 1.3. Comparing the parametric analysis results with the shear strength obtained with experimental tests, we can observe that friction does not guarantee a suitable stability condition, while a small cohesion value determined by rock bridges can strongly increase the overall stability.
The analyses were carried out using the FEM computer code Straus 7 [9]. Numerical simulations were carried out in different phases, starting from a gravitational analysis and proceeding with the room excavations. The FEM model contained 106,517 brick elements and 22,517 nodal points. The model was bounded by vertical and horizontal planes, where horizontal and vertical displacements were blocked, respectively, and by the existing gentle slope surface in its upper part. The initial stress state was determined by assigning the unit weight to the modeled rock mass and applying gravity forces. Subsequent FEM analyses were carried out by excavating the different rooms and by determining the vertical stress in pillars and slabs. The numerical stress results obtained in the pillars and walls where flat jack measurements were carried out are analyzed below. Fig. 11 shows the general 3D model layout with both the internal excavation geometry and the slope topography. Fig. 12 shows the 3D FEM mesh generated to simulate the geometry described above. A concentration of vertical stress is usually found at the pillar edges. Because the excavation levels are gently inclined and some pillars are relatively thin, some flexural and compression states of
Table 6 Computed geometry of blocks. Block
Volume (m3)
1 2 3 4 5 6 7
2.110 4.108 0.490 1.870 1.125 1.482 0.800
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Table 7 Mechanical and deformability features of the rock mass. Mechanical features Deformability modulus Poisson ratio Unit weight Constitutive model Shear strength criterion Friction angle Cohesion
7.83 109 (Pa) 0.35 () 27 (kPa/m) Elastoplastic Mohr–Coulomb 35 [°] 3.00 105 (Pa)
stress can occur. This is the case for pillar 13 (see Fig. 13) and for pillar 23. The vertical stress is, in fact, equal to 1.70 MPa at the edge of pillar 13, while it is equal to 2.40 MPa at the center of the same pillar. Analogously, the vertical stress in pillar 23 is equal to 2.46 MPa at the center of the pillar and 2.15 MPa at its edge. A strong effect of the combination of flexural and compression stress is shown in Fig. 15, which reports the vertical stress isocurves. For pillar 63 the vertical stress varies in the range of 1.2–2.0 MPa from one edge of the pillar to the opposite edge, and for pillar 54, where
Fig. 11. Slope and excavation geometry reproduced in the FEM model.
Fig. 12. 3D FEM mesh.
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483
Fig. 13. Computed vertical stresses in pillar 13 on Section 3.
Fig. 14. Computed vertical stresses in pillar 63.
the vertical stress varies in the range of 2.28–1.00 MPa from one pillar edge to the opposite edge. Analogously, for pillar 40 the vertical stress is in the range of 2.2–0.7 MPa from one edge to the opposite edge. The stress concentration effect is less obvious on the quarry walls. In the 1–3 wall, the vertical stress varies from 1.4 MPa at the roof wall and the foot wall contact up to 1.9 MPa in the center of the wall. Fig. 13 through Fig. 17 show the vertical stress isocurves in some relevant sections where flat jack measurements were carried out. Flat jack measurements were performed on five pillars and in two slope walls, and their results were compared with the values computed at the same points for model calibration. Since the geometry of the pillars is often very irregular and the excavation is inclined due to the ore inclination, most of the pillars are loaded by an inclined load that induces both compression and
bending stresses and a non-uniform stress distribution in the pillar section. This occurs in pillars 54 and 63 (see Fig. 14), where the vertical stress is in the range of 1.2–2.0 MPa on opposite sides in pillar 54, and in pillar 63, it is in the range of 2.28–1.0 MPa. In some pillars, such as pillar 40, the stress ranges from 2.2 MPa down to 0.7 MPa on the opposite corner, while on the quarry walls the state of stress reaches 1.9 in the center of the wall (see Fig. 16). Table 8 compares the computed and measured vertical stresses at the same measuring positions. The plasticization zones are limited to some small tension areas on the roofs and some very small shearing areas on a few pillar edges. The limited dimension of the plasticity zones located at the pillar corners does not compromise the global stability of the structures.
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Fig. 15. Computed vertical stresses in pillar 65.
Fig. 16. Computed vertical stresses in the slope wall (FON 2–4).
5. Pillar safety factors The design of the rock structures to be preserved as supports in a room and pillar mining exploitation is conventionally carried out by assessing the safety factor of individual pillars. The computation can be done using an empirical formulation that is able to evaluate the ratio between the assessed pillar strength and the acting pressure. The pressure acting on a pillar is usually evaluated by the tributary area method [7]. Because the FEM method allowed us to compute the vertical stresses in every FEM mesh element, the average vertical stress in the middle section of a pillar was therefore used to evaluate the acting pressure instead of using the area tributary method. The pillar strength was evaluated by using the formula proposed by Hedley [13]:0.5
Sp ¼ S 0
a0:5 p 0:75
hp
where: Sp is the pillar strength,S0 is the rock mass uniaxial compression strength, and ap is the pillar length. According to the suggestions of Sheory & Singh [22], S0 was assessed by taking the Bieniawski [6] RMR index into account as follows:
S0 ¼ r c e
RMR100 20
where rc is the intact rock uniaxial strength. In this case rc is, on average, equal to 110 MPa, and consequently the S0 value is 13.47. Therefore, the safety factor is F = S0/average rv. Table 9 reports some safety factors computed in pillars where flat jack measurements were taken.
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Fig. 17. Computed vertical stresses in pillars 20 and 23 in Section 4.
Legend Pillars with 15
Fig. 18. Quarry map reporting the safety factor range for each pillar.
Table 8 Comparison of measured (flat jack test) and computed (3D numerical model) stress states. Location
Flat jack tests (MPa)
Numerical model 3D (MPa)
State
Pillar 13 Pillar 23 Pillar 40 Pillar 54 Pillar 63 M Pillar 63 V FON 1–3 FON 2–4
1.74 2.14 0.0 5.00 2.16
1.70 2.46 0.7 2.0 2.28
Compression Compression Compression Compression Compression
0.00 2.02 7.68
1.00 1.9 1.9
Compression Compression Compression
The comparison between the vertical pressures measured and the average vertical stress computed can be used as evidence because the flat jack measurements were done on the pillar surface where flexural compression can be present and did not allow us to have a completely reliable value of the average vertical stress acting on the pillar.
Table 9 Comparison of computed stress by FEM models and pillar resistance. Pillar number
Sp (MPa)
Safety factor (SF)
Pillar Pillar Pillar Pillar Pillar Pillar Pillar
5.72 4.20 5.43 4.46 5.86 5.86 4.41
3.38 2.80 4.52 4.02 4.54 4.54 2.14
13 23 40 54 63 M 63 V 65 M
Fig. 18 shows the factor of safety computation for each pillar of the whole quarries. The graphical representation reported in Fig. 18 was used to identify an optimal visiting path in the light of the stability conditions of the pillars.
6. Conclusions This study allowed us to gather some important information on the stability of the ancient quarry excavations and indicated the
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possible consolidations works needed to achieve a safe condition that could allow for public visits of the underground complex. Different methods were applied with different aims: key block method analysis was used to find possible instabilities in blocks that could detached from the excavation roofs and from the sides of the pillars, and 3D FEM models were set up in order to determine and quantify the global stability of the excavations. The results indicate that in both quarries there is a serious risk of block instability at the roofs, and the volumes and shapes of the blocks were also determined. On this basis, consolidation work such as rock bolting can be quantified. These phenomena are particularly evident at the quarry entrances where the rock mass is more damaged, and unstable blocks can reach a volume of a few cubic meters and are only supported by rock bridges. Rock block instabilities can also occur at the sides of the pillars as well as at the quarry walls, where the presence of vertical joint sets can determine the formations of vertical slabs at the pillars and wall surfaces. These phenomena can be observed in some of the pillars in the Beltrami Quarry. In terms of the global stability of the excavations, the voids are globally safe, but pillars show different degrees of stability depending on the actual state of stress. The safety factor map (see Fig. 18) helped to determine the possible path that visitors might take in order to avoid the more hazardous zones and to point out the pillars where consolidation works are needed. The excavation roofs are mostly within the elastic field, but in some cases, the FEM model indicates a tensile state that could increase block detachments and, therefore, needs to be considered in the design of the restoration works.
References [1] ASTM D 4729-87. Standard test method for in-situ stress and modulus of deformation using the flatjack method. 1993 annual book of ASTM standards, vol. 04–08, 1993. [2] Barton N, Bandis S. Effect of block size on the shear behaviour of jointed rock joints (Keynote lecture) issues in rock mechanics. In: 23rd US symposium on rock mechanics. Berkeley, California: Society of Minino Engineers of AIME; 1982. [3] Barton N, Lien R, Lunde J. Engineering classification of rock masses for design of tunnel support. Rock Mech 1974:186–236. [4] Barton N, Løset F, Lien R, Lunde J. Application of the Q-system in design decision concerning dimensions and appropriate support for underground
[5] [6] [7] [8]
[9] [10]
[11] [12] [13] [14] [15] [16] [17]
[18]
[19]
[20] [21]
[22] [23]
[24] [25] [26]
installations. In: Proceeding of international conference subsurface space, vol. 2. Stockholm: Rockstar; 1980. p. 553–61. Bieniawski ZT. Engineering classification of jointed rock masses. Trans, South Africa Inst Civil Eng 1973:335–44. Bieniawki ZT. Determining rock mass deformability: experience from case histories. Int J Rock Mech Min Sci Geomech Abstr 1978;15:237–47. Brady BH, Brown ET. Rock mechanics for underground mining. London: Kluwer Academic Publisher; 2004. Ferrero AM, Migliazza M, Giani G. Analysis of the stability condition of tunnels: comparison between continuous and discontinuous approaches. Int J Rock Mech 2004:483–90. G+D Computing, Straus7. In: Using Strand7, Sydney. NSW 2000, Australia; May 1999. Gardner WS. Design of drilled piers in the Atlantic Piedmont. Foundations and excavations in decomposed rock of the piedmont province. GSP ASCE 1987:62–86. Geo&Soft. Key block theory based three dimensional rock block analysis. Rock3D. Manual. Tratto da Geo&Soft; 2008.. Goodman RE, Shi GH. Block theory and its application to rock engineering. London: Prentice Hall; 1985. Hedley D, Grant F. Stope-and-pillar design for the elliot lake uranium mines. Bull Can Inst Min Metall 1972:37–44. Hoek E, Carranza Torres C, Corkum B. Heok–Brown failure criterion. In: Proceedings of North American rock mechanics society, Toronto; 2002. ISRM Commission for Standardization of Laboratory and Field Tests. Int J Rock Mech 1978;5:319–368. Kayabasi A, Gokceoglu C, Ercanoglu M. Estimating the deformation modulus of rock masses: a comparative study. Int J Rock Mech Min Sci 2003;40:55–63. Mitri HS, Edrissi R, Henning J. Finite element modelling of cable-bolted stopes in hard rock ground mines. SME Annual Meeting, Albuquerque; 1994. p. 94116. Palmstrøm A. Characterization of rock masses by the RMi for use in practical rock engineering. Tunn Undergr Sp Tech 1996; 11:175-86 [Part 1], 287–303 [Part 2]. Palmstrøm A, Singh R. The deformation modulus of rock masses – comparison between in situ tests and indirect estimates. Tunn Undergr Sp Tech 2001:115–31. Rocscience Inc. RocLab user’s guide. Toronto, Ontario, Canada; 2007. Scesi L. Studio geologico, idrogeologico e geologito tecnico delle antiche cave sotterranee di pietra di Viggiù, Saltrio e Brenno. Milano: Politecnico di Milano; 2000. Sheory P, Singh B. Estimation of pillar loads in single and continuous seam workings. Int J Rock Mech Min Sci 1974;5:97–102. Shi G, Goodman R. A new concept for support of underground and excavations in discontinuous rocks based on keystone principle. Rock mechanics from research to applications. In: XXII American rock mechanics conference. Cambridge (MA): MIT; 1981. p. 290–6. Verman M, Singh B, Viladkar MN, Jethua JL. Effect of tunnel depth on modulus of deformation of rock mass. Rock Mech Rock Eng 1997;30:121–7. Zhang L, Einstein HH. Using RQD to estimate the deformation modulus of rock masses. Int J Rock Mech Min Sci 2004;41:337–41. Zienkiewicz O. The finite element method. Oxford: Butterworth–Heinemann; 2000.
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Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo
Stability analysis of historic underground quarries Anna Maria Ferrero a, Andrea Segalini a,*, Gian Paolo Giani b a b
Dept. of Civil, Environmental and Territory Engineering and Architecture, University of Parma, Italy Dept. of Geological Science, State University of Milan, Italy
a r t i c l e
i n f o
Article history: Received 26 June 2009 Received in revised form 26 January 2010 Accepted 28 January 2010 Available online 16 March 2010 Keywords: Underground quarries Rock mass numerical modeling Discontinuities monitoring
a b s t r a c t This work, carried out at the Department of Civil, Environmental and Territory Engineering and Architecture (DICATeA) of the University of Parma, analyzes the stability conditions of the ancient underground quarries of Viggiù (Varese, Italy). The objective of the study is to verify the actual structural predisposition to instability phenomena of the old Viggiù quarries, within the context of a historical and cultural valorization and recovery of the ancient ornamental stone quarries. These quarries, that are now completely abandoned, could be used as a tourist attraction and/or as a teaching environment. They are a wonderful example of industrial architecture by presenting an audacious composition of filled in trenches and room and pillar techniques. An experimental campaign based on in situ measurements and laboratory measurements has been carried out to characterize the rock mass and to determine rock mass mechanical features. A numerical model of the entire rock mass has been developed in order to analyze the stability of the entire underground openings. A preliminary monitoring phase has been realized, aimed at controlling abandoned rock structure movements at the most significant discontinuities. Some measurements of the vertical stress in the pillars and in the walls have been performed, as well, and used for the model calibration. Once the model has been calibrated, the analysis of the actual stress and deformation conditions has been evaluated, the stability condition of the entire structure computed and a forecasting analysis of any intervention that could be realized to guarantee the underground public access has been performed. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The two quarries examined are located on the southern side of the Monte Rosa Massif, near Piamo-Vallera (Viggiù village), and are named Cava Danzi and Cava Beltrami, respectively. The present study aims to verify the stability conditions of the rock mass– underground excavation system by evaluating the historical–cultural renewal of Viggiù’s old subterranean ornamental quarries. The stability analysis was carried out with different analytical and numerical approaches, which schematized the rock mass by the continuous equivalent or discontinuous schemes according to the scale of the problem examined and the aspect analyzed [8]. This choice arose from the need to analyze both the local and overall stability conditions of the pillars and roof of the quarries. A method of analysis that uses the discontinuous approach to verify the possible local formation of blocks, which come off and move on pre-existing discontinuities, was used in the roof stability analysis, while a stress–strain analysis of the entire room and pillars system was used in the stability analysis for individual pillars. In particu* Corresponding author. Address: Dept. of Civil, Environmental and Territory Engineering and Architecture, University of Parma, V.le G.P. Usberti, 181/a, 43124 Parma, Italy. Tel.: +39 0521 905952; fax: +39 0521 905924. E-mail address: [email protected] (A. Segalini). 0266-352X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compgeo.2010.01.007
lar, a stability analysis of the walls and the pillar located near the entrances was carried out using the key block method [12] to verify the possible movement of blocks along pre-existing discontinuities, and the entire rock mass was analyzed with the finite element method (FEM) [26].
2. Geological classification and geomechanical characterization of the rock mass Geological studies and geomechanical characterization of the rock mass have been developed at Politecnico di Milano [21]. The main results of these studies, which are essential for the stability analysis, are briefly reported below. The area of this study belongs to the Southern Alps tectonic unit; more specifically, it is located in the West Lombard Pre-alps sector usually known as the Zona del Varesotto Luganese. Cava Danzi is one of the largest quarries in this area, and it was used for the subterranean extraction of Saltrio limestone, which is a dominant calcareous formation, composed of light brown or whitish biocalcarenite. Fine solid limestones with flat parallel bedding are dominant. The geomechanical characterization of the rock mass required the execution of scanlines for a survey of discontinuities on the
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outcropping rocks, laboratory and site tests. All the discontinuities intercepting the scan lines were censored, and the orientation (dip and dip direction angle), spacing, persistence, wall strength, roughness, aperture, possible filling thickness and water presence were evaluated for each discontinuity according to the methods suggested by ISRM [15]. The interpretation of the discontinuity survey allowed for the individuation of five discontinuity systems (Fig. 1) in the rock mass in addition to a foliation plane, and the frequency and spacing values are reported in Table 2. Orientation data are reported in Table 1. Direct shear tests on natural discontinuities allowed for the evaluation of the peak and residual strength of natural discontinuities. A peak and residual failure envelope of the discontinuities was achieved with direct shear laboratory tests. The peak and residual angles are equal to 54° and 41°, respectively. Uniaxial and triaxial compression tests and direct tensile tests (Brazilian test) were conducted to determine the simple compression strength (rc), tensile strength (rr) and rock matrix shear strength parameters (c, /) according to the Hoek–Brown strength criterion linearized in the appropriate stress range (Table 3) using the Rocklab Code [20]. These tests were conducted on rock blocks cored in three orthogonal directions to analyze possible rock anisotropy. On the basis of the scanline surveys of discontinuities and laboratory test, the rock mass in the excavation zones, which is considered homogeneous from a geomechanical point of view, was classified. This allowed for the definition of the quality indexes: rock mass rating (RMR) [5], Q [3] and Palmstrom’s rock mass index (RMi). The indexes required to assess the Q value of the Barton classification are: rock quality designation (RQD), reported in Table 4 and calculated using the frequency value reported in Table 2, Jn, Jr, Ja, Jw, and SRF, which are, respectively, the number of discontinuity families, the surface roughness, the deterioration and filling of joints, the water presence and the stress ratio factor (SRT). The Palmstrom’s rock mass index RMi [18] is a volumetric parameter that indicates the uniaxial compression strength of the rock mass approximately. It is defined as the product of the uniaxial compression strength in intact rock rc and a reduction parameter Jp, which considers existing discontinuities. RMi indexes are 8.05 for the Danzi Quarry and 6.67 for the Beltrami Quarry.
Table 1 Main joint set orientation. Sets
Dip
Dip direction
1 2 3 4 5
74 ± 4 74 ± 10 67 ± 5 32 ± 5 83 ± 5
270 ± 30 323 ± 20 25 ± 20 159 ± 12 72 ± 20
Quality indexes values obtained for the rock mass according to classifications were used to calculate the rock mass bulk modulus. Several different empirical relations have been used within this scope [6,17,24,14,4,2,18,19,10,16,25]. A significant variation in values depending on the chosen correlation can be observed, with the difference ranging between two orders of magnitude; consequently, an average value was chosen. With regard to rock mass strength properties, RMR values locate the rock mass in class III, for which [5] we assume a cohesion value varying from 0.2 and 0.3 MPa and a friction angle varying in the 25–35° range. The non-linear Hoek–Brown strength envelope was found to have m and s values of 2.29 and 0.0205, respectively. 2.1. Flat jack tests A flat jack is a thin envelope-like bladder with inlet and outlet ports that may be pressurized with hydraulic oil. A flat jack may be manufactured in many shapes and sizes, determined by its function, the slot preparation technique and the properties of the rock mass being tested (Fig. 2). This test is based on the principle of partial stress release and involves the local elimination of stresses, followed by controlled stress compensation. The reference field of displacements is first determined by measuring the distances between gauge points fixed to the surface of the rock face. Then, a slot is cut in a plane normal to the direction of the measured stresses. This allows deformations in a direction normal to the slot. The distances between gauge points decrease because cutting the slot causes partial stress relief in the rock above and below (Fig. 3). Afterward, a thin flat jack is introduced into the slot. With the aid of this device, pressure
Fig. 1. Stereographic projection of discontinuity poles in the Danzi and Beltrami Quarries.
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Table 2 Frequency and spacing values obtained from discontinuity surveys in the two sites examined used for rock mass classification. Frequency
fS
f K1
f K2
f K3
f K4
f K5
f global
Spacing (m)
Beltrami Quarry Danzi Quarry
3.255 2.477
3.571 2.787
2.645 2.566
1.913 2.573
3.690 1.429
1.546
16.620 11.832
0.06 0.085
Table 3 Rock matrix resistance properties considering three test directions (x, y, z).
Global X Y Z
mi ()
C (MPa)
/ (°)
rr (MPa)
rc (MPa)
9.03 10.24 8.21 15.47
17.63 15.29 17.06 14.89
47.92 49.27 46.42. 54.73
10.44 8.38 10.68 6.40
94.31 85.84 87.69 99.08
Table 4 Values considered in rock mass classification.
Danzi Quarry Beltrami Quarry
RQD
Jn
Jr
Ja
SRF
Jw
Q
75 60
15 15
3 3
1 1
2.5 2.5
1 1
6 4.8
260 mm
350 mm
Fig. 3. Measurement scheme during testing [1].
Fig. 2. The flat jack used.
(compressive stress) is applied to the rock. This pressure causes a partial restoration of the initial displacement field, which at some point reaches (approximately) the previously measured values. The necessary pressure can be related to the compressive stress in the direction normal to the slot. The hydraulic pressure in the flat jack necessary to restore the undamaged state is higher than the actual stress. This is caused by the inherent stiffness of the flat jack, which resists expansion when the jack is pressurized. Another factor that contributes to this effect is the difference between the area of the jack and the area of the slot (the latter being greater than the former). Both of these factors are taken into account when interpret-
ing the test results. The test, as described above, is based on the following assumptions: the stress in place of the test is compressive; the rock mass surrounding the slot is homogenous; the rock mass deforms symmetrically around the slot; the state of stresses in the place of the measurement is uniform; the stress applied to the rock mass by the flat jack is uniform; and the values of the stresses (compared to compressive strength) allow the rock to work in an elastic regime (see Fig. 4). Nine tests were performed in the pillars and in the boundary walls by allowing the estimation of the acting state of stresses (Table 5). These results were utilized for the model calibration discussed in the following sections. 2.2. Monitoring system A monitoring system of opening–closing movements of discontinuities was installed to control the evolution of movements that can warn of an incipient collapse in untended rock structures. Qualitative analysis of every collected discontinuity was carried out to define the positioning of the instrumentation. Overall,
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- TRASDUCER C13 -
SPOSTAMENTI RELATIVI (mm) RELATIVE DISPLACEMENTS(mm)
0.1
0
-0.1
Fig. 4. Example of test realization.
Table 5 Vertical stresses obtained by flat jack tests. Location
Flat jack tests (MPa)
Pillar 13 Pillar 23 Pillar 40 Pillar 54 Pillar 63 M Pillar 63 V Pillar 63 M FON 1–3 FON 2–4
1.74 2.14 0.0 5.00 2.16 0.00 5.57 2.02 7.68
fifteen displacement transducers were installed orthogonally to some selected discontinuities. These devices measured the linear movement along its axes and were wired to three different control units. The monitoring system controlled the discontinuities that are believed to be the most significant for the overall behavior of the whole rock mass. Nine of the 109 surveyed discontinuities were selected for monitoring in the Danzi Quarry, while the remaining transducers were located in the Beltrami Quarry: five were located in the north-central area, while the four remaining devices were located in the northern portion of the underground opening. It is possible to draw some general conclusions from the examination of the displacement measurements. A representative example of the results of discontinuity monitoring with a displacement transducer is shown in Fig. 5. This qualitative trend is similar to that registered in all other control units. During the observation period the movement was between 0.12 mm in opening and 0.12 in closure; the closure registered rate was around 0.04 mm/month in mean speed. We have now found a 0.1-mm relative closure with almost the same mean velocity as in the same period in 2007. The analysis refers to a cycle of readings made during three complete solar years. In fact, there is a tendency towards cyclic movements related to seasonal evolution (temperature, rainfall, etc.) with a natural return to the initial conditions. The system allowed us to assert that the movements measured were of the order of one tenth of a millimeter per year, with a seasonal trend caused by thermal variations. The recordings lead us to verify that the monitored blocks are currently stable.
3. Stability analysis using the key block theory 3.1. Key block theory The essential part of the key block theory [23] is the joint analysis of the discontinuity system with the excavation surfaces. The intersection of the discontinuities can originate solids of variable
18/07/06 23/08/06 28/09/06 03/11/06 09/12/06 14/01/07 19/02/07 27/03/07 02/05/07 07/06/07 13/07/07 18/08/07 23/09/07 29/10/07 04/12/07 09/01/08 14/02/08 21/03/08 26/04/08 01/06/08 07/07/08 12/08/08 17/09/08 23/10/08 28/11/08 03/01/09 08/02/09 16/03/09 21/04/09 27/05/09
-0.2
DATE Fig. 5. Displacement transducer readings between July 2006 and March 2008.
shape that, depending on available strengths, can be in critical stability conditions. The theory aims to identify the critical blocks that, in the absence of appropriate contrast, release other blocks near the voids and trigger the collapse of the rock structure. The block located in the most dangerous position, the first to be released, is defined as the ‘‘key block”. If the potentially dangerous block (key block) is identified before the movement begins, and if its stability is assured, then the other blocks will not move. The method can be implemented either with a vector calculus or a graphic process. The graphic process uses equiangular stereographic projection (Fig. 6). This kind of projection represents a particular perspective form, in which all points are projected from one of the sphere poles, in this case the lower pole on a horizontal projection plane. The main features of this method are that planes project as circles and lines projects as points, and that the projection also maintains the angles between the planes. The assumptions on which the method is based are that the discontinuity surfaces are perfectly plane and persistent at least inside the blocks and are characterized by a definite direction beforehand; the blocks are nondeformable; and the block movements are possible only without interference from adjoining blocks. The block method distinguishes rock mass blocks inside the rock mass (JB) from the blocks that overlook the excavation surfaces (JP). The finite blocks can either be removable or non-removable. Removable blocks are further divided into stable blocks independent of acting forces, stable blocks due to the shear strength effect on discontinuities and unstable blocks (key blocks). To define a finite and removable block stability condition, it is necessary to compare acting forces and available strengths. For this purpose, it is possible to apply either an analytic or a graphic procedure to define friction angle values able to maintain a stable joints pyramid, in connection with a potential sliding condition. The Rock 3D program [11] was used for the block analysis; the code recognizes possible kinematic mechanisms of blocks and estimates their stabilities with the limit equilibrium method. This analysis assumes that it is possible to associate a definite rock volume with every kinematic mechanism (fall, sliding on one or two planes), even if it has a complex shape or is bounded by different discontinuity
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Fig. 6. Example of equiangular projection utilized for key block application.
planes and excavation walls, if the discontinuity map geometry allows that. For a selected kinematic mechanism the program defines, according to the discontinuity tracks surveyed on the rock face, the maximum close boundaries that are not connected to each other, using only discontinuities compatible with the examined kinematic mechanism (Fig. 7). This analysis phase and the one that follows must be repeated for each possible kinematic mechanism and seek the greatest block instability conditions. The program optionally generates a pseudo-random discontinuities map that respects the statistical distribution of frequencies and persistence measured on the natural rock face. The following phase is directed to the complete geometrical reconstruction of complex blocks (Fig. 8). The program defines the solid derived from the union of all elemental polyhedrons contained within closed boundaries. For each complex block, Rock3D calculates volumes and surfaces.
3.2. Application of key block method to the Danzi Quarry The key block method was applied to the excavation roofs, paying attention to the entrance zones in particular. The details of the structural data for the rock mass are reported in Section 3. Removable blocks were identified for each entrance by determining the larger blocks formed by the observed discontinuities. This phase was performed for each block type in order to determine the worst possible conditions in terms of possible unstable volumes. A statistical variation of the discontinuity orientations was considered in order to analyze the influence of dip and dip direction variation on the block stability condition. The sliding directions, factors of safety and volumes of each removable block were then computed. Figs. 9 and 10 show the results obtained for the three Danzi Quarry entrances. At first, the friction angle assigned was relatively low and equal to the residual value measured by laboratory testing, and the cohesion was nil. Parametrical analysis was performed to evaluate the influence of the variation in strength on the stability conditions. In the parametric analysis, the high friction angle simulates a rough discontinuity, while the presence of cohesion can be due to rock bridges.
Fig. 7. Example of discontinuity traces on a rock face.
Results obtained by parametrical analysis on the central entrance roof, considering both the limit equilibrium condition (F = 1) and a safer condition determined by a factor of safety equal to 1.3, show that if the friction angle is lower than 53.7° instability occurs. If the friction angle is in the range of 53.7–68.6° and the cohesion is in the range of 8.10–13.56 kPa, the factor of safety varies in the range of 1–1.3. When the friction angle is above 68.6°, the
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3.3. Application of the key block method to the Beltrami Quarry The area analyzed was the quarry roof in an area with the dimension of 27 27 m2. The analysis was performed using the procedure that was described for the Danzi Quarry and by varying the orientation of the main joint sets according to the measured variability. Results show that the maximum computed (Table 6) block has a volume of 4.108 m3 and is near the entrance. The possible instability at the pillar sides was also investigated. Sliding phenomena along the intersection between joint set 1 and 2 of limited volumes (below 0.5 m3) as can be observed in the quarry corresponding to pillars 15 and 16.
Fig. 8. Example of a rock block identified for volume computation.
Safety Factor vs Cohesion (Friction angle = 25°) 2.5
4. FEM models
Safety Factor
2 1.5 block 1001
1
block 1000 block 1100
0.5
block 1001
0 0
20
40
60
Cohesion [kPa]
80
100
120
Fig. 9. Factor of safety trend as function of the cohesion. Friction angle fixed at 25°. Central entrance to Danzi Quarry.
The complex geometry of the excavations compelled us to use a numerical model to analyze the stress–strain behavior of the underground rock structure. The finite element method (FEM) [26] was used for this purpose. A three-dimensional model was set up to discretize the excavated rock mass by representing the pillars and slabs of the quarries. The medium was considered to be a continuous equivalent medium, and an elastic ideally plastic behavior was assigned to the rock mass. The strength and deformation features of the rock mass are given in Table 7. The mechanical parameters of the rock mass were calibrated with the geomechanical characterization data and compared with the in situ flat jack measurements. 4.1. 3D model features and results
Factor of Safety vs friction angle (Cohesion = 0) 2.5
Safety Factor
2 1.5 1
block 1001
0.5
block 1000
0
block1001 block 1100
0
20
40
60
80
100
Friction Angle [°] Fig. 10. Factor of safety trend as function of the friction angle. Cohesion fixed at zero. Central entrance to Danzi Quarry.
stability conditions are guaranteed by the higher safety factor values. The results for the lower entrance identified three possible unstable rock blocks with volumes of 11.8, 2.2 and 4.9 m3, respectively. Parametric results obtained for the lower entrance to the Danzi Quarry shows that if the friction angle is equal to 44.5°, then instability occurs. The factor of safety varies in the range of 1–1.3 when the friction angle is in the range of 44.5–56.6° and cohesion is in the range of 30.38–32.92 kPa. When the friction angle is above 56.6°, the safety factor is above 1.3. Comparing the parametric analysis results with the shear strength obtained with experimental tests, we can observe that friction does not guarantee a suitable stability condition, while a small cohesion value determined by rock bridges can strongly increase the overall stability.
The analyses were carried out using the FEM computer code Straus 7 [9]. Numerical simulations were carried out in different phases, starting from a gravitational analysis and proceeding with the room excavations. The FEM model contained 106,517 brick elements and 22,517 nodal points. The model was bounded by vertical and horizontal planes, where horizontal and vertical displacements were blocked, respectively, and by the existing gentle slope surface in its upper part. The initial stress state was determined by assigning the unit weight to the modeled rock mass and applying gravity forces. Subsequent FEM analyses were carried out by excavating the different rooms and by determining the vertical stress in pillars and slabs. The numerical stress results obtained in the pillars and walls where flat jack measurements were carried out are analyzed below. Fig. 11 shows the general 3D model layout with both the internal excavation geometry and the slope topography. Fig. 12 shows the 3D FEM mesh generated to simulate the geometry described above. A concentration of vertical stress is usually found at the pillar edges. Because the excavation levels are gently inclined and some pillars are relatively thin, some flexural and compression states of
Table 6 Computed geometry of blocks. Block
Volume (m3)
1 2 3 4 5 6 7
2.110 4.108 0.490 1.870 1.125 1.482 0.800
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Table 7 Mechanical and deformability features of the rock mass. Mechanical features Deformability modulus Poisson ratio Unit weight Constitutive model Shear strength criterion Friction angle Cohesion
7.83 109 (Pa) 0.35 () 27 (kPa/m) Elastoplastic Mohr–Coulomb 35 [°] 3.00 105 (Pa)
stress can occur. This is the case for pillar 13 (see Fig. 13) and for pillar 23. The vertical stress is, in fact, equal to 1.70 MPa at the edge of pillar 13, while it is equal to 2.40 MPa at the center of the same pillar. Analogously, the vertical stress in pillar 23 is equal to 2.46 MPa at the center of the pillar and 2.15 MPa at its edge. A strong effect of the combination of flexural and compression stress is shown in Fig. 15, which reports the vertical stress isocurves. For pillar 63 the vertical stress varies in the range of 1.2–2.0 MPa from one edge of the pillar to the opposite edge, and for pillar 54, where
Fig. 11. Slope and excavation geometry reproduced in the FEM model.
Fig. 12. 3D FEM mesh.
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483
Fig. 13. Computed vertical stresses in pillar 13 on Section 3.
Fig. 14. Computed vertical stresses in pillar 63.
the vertical stress varies in the range of 2.28–1.00 MPa from one pillar edge to the opposite edge. Analogously, for pillar 40 the vertical stress is in the range of 2.2–0.7 MPa from one edge to the opposite edge. The stress concentration effect is less obvious on the quarry walls. In the 1–3 wall, the vertical stress varies from 1.4 MPa at the roof wall and the foot wall contact up to 1.9 MPa in the center of the wall. Fig. 13 through Fig. 17 show the vertical stress isocurves in some relevant sections where flat jack measurements were carried out. Flat jack measurements were performed on five pillars and in two slope walls, and their results were compared with the values computed at the same points for model calibration. Since the geometry of the pillars is often very irregular and the excavation is inclined due to the ore inclination, most of the pillars are loaded by an inclined load that induces both compression and
bending stresses and a non-uniform stress distribution in the pillar section. This occurs in pillars 54 and 63 (see Fig. 14), where the vertical stress is in the range of 1.2–2.0 MPa on opposite sides in pillar 54, and in pillar 63, it is in the range of 2.28–1.0 MPa. In some pillars, such as pillar 40, the stress ranges from 2.2 MPa down to 0.7 MPa on the opposite corner, while on the quarry walls the state of stress reaches 1.9 in the center of the wall (see Fig. 16). Table 8 compares the computed and measured vertical stresses at the same measuring positions. The plasticization zones are limited to some small tension areas on the roofs and some very small shearing areas on a few pillar edges. The limited dimension of the plasticity zones located at the pillar corners does not compromise the global stability of the structures.
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Fig. 15. Computed vertical stresses in pillar 65.
Fig. 16. Computed vertical stresses in the slope wall (FON 2–4).
5. Pillar safety factors The design of the rock structures to be preserved as supports in a room and pillar mining exploitation is conventionally carried out by assessing the safety factor of individual pillars. The computation can be done using an empirical formulation that is able to evaluate the ratio between the assessed pillar strength and the acting pressure. The pressure acting on a pillar is usually evaluated by the tributary area method [7]. Because the FEM method allowed us to compute the vertical stresses in every FEM mesh element, the average vertical stress in the middle section of a pillar was therefore used to evaluate the acting pressure instead of using the area tributary method. The pillar strength was evaluated by using the formula proposed by Hedley [13]:0.5
Sp ¼ S 0
a0:5 p 0:75
hp
where: Sp is the pillar strength,S0 is the rock mass uniaxial compression strength, and ap is the pillar length. According to the suggestions of Sheory & Singh [22], S0 was assessed by taking the Bieniawski [6] RMR index into account as follows:
S0 ¼ r c e
RMR100 20
where rc is the intact rock uniaxial strength. In this case rc is, on average, equal to 110 MPa, and consequently the S0 value is 13.47. Therefore, the safety factor is F = S0/average rv. Table 9 reports some safety factors computed in pillars where flat jack measurements were taken.
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Fig. 17. Computed vertical stresses in pillars 20 and 23 in Section 4.
Legend Pillars with 1
Fig. 18. Quarry map reporting the safety factor range for each pillar.
Table 8 Comparison of measured (flat jack test) and computed (3D numerical model) stress states. Location
Flat jack tests (MPa)
Numerical model 3D (MPa)
State
Pillar 13 Pillar 23 Pillar 40 Pillar 54 Pillar 63 M Pillar 63 V FON 1–3 FON 2–4
1.74 2.14 0.0 5.00 2.16
1.70 2.46 0.7 2.0 2.28
Compression Compression Compression Compression Compression
0.00 2.02 7.68
1.00 1.9 1.9
Compression Compression Compression
The comparison between the vertical pressures measured and the average vertical stress computed can be used as evidence because the flat jack measurements were done on the pillar surface where flexural compression can be present and did not allow us to have a completely reliable value of the average vertical stress acting on the pillar.
Table 9 Comparison of computed stress by FEM models and pillar resistance. Pillar number
Sp (MPa)
Safety factor (SF)
Pillar Pillar Pillar Pillar Pillar Pillar Pillar
5.72 4.20 5.43 4.46 5.86 5.86 4.41
3.38 2.80 4.52 4.02 4.54 4.54 2.14
13 23 40 54 63 M 63 V 65 M
Fig. 18 shows the factor of safety computation for each pillar of the whole quarries. The graphical representation reported in Fig. 18 was used to identify an optimal visiting path in the light of the stability conditions of the pillars.
6. Conclusions This study allowed us to gather some important information on the stability of the ancient quarry excavations and indicated the
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possible consolidations works needed to achieve a safe condition that could allow for public visits of the underground complex. Different methods were applied with different aims: key block method analysis was used to find possible instabilities in blocks that could detached from the excavation roofs and from the sides of the pillars, and 3D FEM models were set up in order to determine and quantify the global stability of the excavations. The results indicate that in both quarries there is a serious risk of block instability at the roofs, and the volumes and shapes of the blocks were also determined. On this basis, consolidation work such as rock bolting can be quantified. These phenomena are particularly evident at the quarry entrances where the rock mass is more damaged, and unstable blocks can reach a volume of a few cubic meters and are only supported by rock bridges. Rock block instabilities can also occur at the sides of the pillars as well as at the quarry walls, where the presence of vertical joint sets can determine the formations of vertical slabs at the pillars and wall surfaces. These phenomena can be observed in some of the pillars in the Beltrami Quarry. In terms of the global stability of the excavations, the voids are globally safe, but pillars show different degrees of stability depending on the actual state of stress. The safety factor map (see Fig. 18) helped to determine the possible path that visitors might take in order to avoid the more hazardous zones and to point out the pillars where consolidation works are needed. The excavation roofs are mostly within the elastic field, but in some cases, the FEM model indicates a tensile state that could increase block detachments and, therefore, needs to be considered in the design of the restoration works.
References [1] ASTM D 4729-87. Standard test method for in-situ stress and modulus of deformation using the flatjack method. 1993 annual book of ASTM standards, vol. 04–08, 1993. [2] Barton N, Bandis S. Effect of block size on the shear behaviour of jointed rock joints (Keynote lecture) issues in rock mechanics. In: 23rd US symposium on rock mechanics. Berkeley, California: Society of Minino Engineers of AIME; 1982. [3] Barton N, Lien R, Lunde J. Engineering classification of rock masses for design of tunnel support. Rock Mech 1974:186–236. [4] Barton N, Løset F, Lien R, Lunde J. Application of the Q-system in design decision concerning dimensions and appropriate support for underground
[5] [6] [7] [8]
[9] [10]
[11] [12] [13] [14] [15] [16] [17]
[18]
[19]
[20] [21]
[22] [23]
[24] [25] [26]
installations. In: Proceeding of international conference subsurface space, vol. 2. Stockholm: Rockstar; 1980. p. 553–61. Bieniawski ZT. Engineering classification of jointed rock masses. Trans, South Africa Inst Civil Eng 1973:335–44. Bieniawki ZT. Determining rock mass deformability: experience from case histories. Int J Rock Mech Min Sci Geomech Abstr 1978;15:237–47. Brady BH, Brown ET. Rock mechanics for underground mining. London: Kluwer Academic Publisher; 2004. Ferrero AM, Migliazza M, Giani G. Analysis of the stability condition of tunnels: comparison between continuous and discontinuous approaches. Int J Rock Mech 2004:483–90. G+D Computing, Straus7. In: Using Strand7, Sydney. NSW 2000, Australia; May 1999. Gardner WS. Design of drilled piers in the Atlantic Piedmont. Foundations and excavations in decomposed rock of the piedmont province. GSP ASCE 1987:62–86. Geo&Soft. Key block theory based three dimensional rock block analysis. Rock3D. Manual. Tratto da Geo&Soft; 2008.