Risk assessment of collapse in shallow caverns using numerical modeling of block interactions with DDA: Suggested approach and case studies

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Harold Gaines
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1 Risk assessment of collapse in shallow caverns using numerical modeling of block interactions with DDA: Suggested approach and case studies Yossef H. Hatzor Professor and Chair in Rock Mechanics, BGU, Israel Visiting Professor, CAS, Wuhan, China International Top-level Forum on Engineering Science and Technology Development Strategy Safe Construction and Risk Management of Major Underground Engineering May 17 19, Wuhan, China.

Shallow caverns, typically of Karstic origin, may pose great risk to surface civil engineering structures, but are quite difficult to detect, therefore exploration drilling is often employed:

2 Shallow caverns, typically of Karstic origin, may pose great risk to surface civil engineering structures, but are quite difficult to detect, therefore exploration drilling is often employed: Research Question: What is the limiting relationship between cavern span (B) and cover height (h) that will ensure stability? The answer will constrain the required drilling length (D) and distance (d) in the exploration effort. Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 2

One way to answer this question is to study it numerically with discrete element methods, by generating, synthetically, Blocky rock masses and then running forward modeling.

3 One way to answer this question is to study it numerically with discrete element methods, by generating, synthetically, Blocky rock masses and then running forward modeling. Here we keep the rock mass structure constant and change in each simulation the span width (B) and cover height (h) to obtain the structural response with DDA: h B An example of a blocky rock mass structure with a synthetic jointing pattern as generated with DDA Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 3

4 The modeled rock mass in our simulations is a typical blocky rock mass as found in central Israel, with a horizontal bedding planes set and two sub-vertical and sub-orthogonal joint sets: Joint Set Dip/Direction Trace Length Mean Spacing Degree of Randomness Rock Bridge Length 1 /.7 m 1. m 2 88/182 5 m.96 m m 3 88/12 5 m.78 m m These structural parameters represent mean values obtained from a number of joint surveys in central Israel where the problem of karstic cavern collapse exists The large value of assigned rock bridge length (2.5m) is used to simulate the phenomena of mechanical layering, where the extent of joint trace length is conditioned by bed thickness The same effect is obtained by using a relatively small value of trace length (5m) with respect to bed thickness (.7m). Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 4

5 To estimate the mechanical stability of each structural configuration, we measure the vertical displacement (v) and the horizontal stress (s x ) components as obtained with forward DDA at four measurement points evenly distributed at the roof of the modeled excavation: The lateral boundaries are set at a distance of b = 3B to ensure the decay of stress concentrations near the boundaries of the modeled domain. Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 5

6 The results of forward modeling with DDA are classified into three categories of structural response, depending on the vertical displacement (v) and horizontal stress (s x ) component outputs at the measurement point locations: Stable Configuration: the 3 upper measurement points exhibit static stability Marginally Stable: the 2 upper measurement points exhibit static stability Unstable: Only the upper measurement point or no measurement point exhibit static stability Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 6

h/b =.78 Example of Stable configuration 1 m. -.1 2 4 6 8 1 12 Time, sec. Measurement Point 1-5 -1 2 4 6 8 1 12 Time, sec. Measurement Point 1 Measurement Point 2 -.

7 h/b =.78 Example of Stable configuration 1 m Time, sec. Measurement Point Time, sec. Measurement Point 1 Measurement Point Measurement Point 2 Measurement Point 3 Measurement Point Measurement Point 3 Measurement Point v,m -45 s x,kn/m 2 Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 7

h/b = 1. Extension of Stable definition 1 m. 5 1 15 2 5 1 15 2 Time, sec.

8 h/b = 1. Extension of Stable definition 1 m Time, sec. Time, sec v,m -12 Measurement Point 1 Measurement Point 2 Measurement Point 3 Measurement Point 4-14 s x,kn/m 2 Measurement Point 1 Measurement Point 2 Measurement Point 3 Measurement Point 4 Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 8

9 h/b =.76 Marginally stable configuration 1 m Time, sec Time, sec v,m Measurement Point 1 Measurement Point 2-18 Measurement Point 3 Measurement Point 4 s x,kn/m 2 Measurement Point 1 Measurement Point 2 Measurement Point 3 Measurement Point 4 B Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 9

h/b =.5 Unstable configuration 1 m. 5 1 15 2 5 1 15 2 Time, sec.

10 h/b =.5 Unstable configuration 1 m Time, sec. Time, sec v,m -12 Measurement Point 1 Measurement Point 2 Measurement Point 3 Measurement Point 4-14 s x,kn/m 2 Measurement Point 1 Measurement Point 2 Measurement Point 3 Measurement Point 4 Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 1

11 As we know, per a given cover height (here h ~ 2 m) the span width adversely affects stability: h/b =.76 B = 25 m 1 m. h/b =.73 1 m. B = 3 m h/b =.5 1 m. Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China B = 4 m 11

Similarly, per given cavern span ( here B =

stability: h = 3 m h/b = 1.2 1 m. h/b = 1. h = 25 m 1 m.

12 Similarly, per given cavern span ( here B = 25 m) the cover height positively affects stability: h = 3 m h/b = m. h/b = 1. h = 25 m 1 m. h/b =.5 h = 12.5 m 1 m. Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 12

13 The final resulting relationship between B and h required for stability however proves to be not linear: h, m h/b = 1 35 Ayalon Cave h 17(3) 13(3) 3 B Zedekiah Cave h/b =.5 15(25) 25 Safe 1(25) 19(22) 12(22) 2 16(19) 9(2) 15 7(14) Marginal 11(15) 8(15) 3(11) 6(1) 14(12.5) 1 18(11) 1(6) 2(6) 4(6) Unsafe 5(6) 5 Tel Beer Sheva B, m Legend: Safe Marginal Unsafe Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 13

14 The above was shown for the same, synthetically generated, rock mass structure. Results from three different case studies in different rock masses support our concluding chart: 1. The Ayalon cave underneath Ramle open pit mine central Israel 2. The 2 year old Zedekiah quarry - underneath the old city of Jerusalem 3. The Tel Beer Sheva 3 year old underground water storage system southern Israel. Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 14

15 Case 1: Ayalon Cave a present day 4 meter span karstic cavern underneath an active open pit mine with 3 meters of rock cover: Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 15

16 Statistical joint survey results: J1 J 3 J 2 J 2 J 3 Frequency Thickness (m) J2 J3 Frequency Spacing (m) Frequency Spacing (m) Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 16

Current configuration of explored cavern underneath the mine: No. of Blocks A mean 15,11 1.7 m 2 Y.

17 Current configuration of explored cavern underneath the mine: No. of Blocks A mean 15, m 2 Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 17

18 Results of forward analysis with DDA: Marginally stable configuration No. time steps Real Time 9, 35.4 s t, sec t, sec Mean no. it. pts. CPU time hr Point 1 Point 2 Point 3 Point Point 1 Point 2 Point 3 Point 4-7 v, m -6 s x, kpa Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 18

19 Case 2: Zedekiah cave a 2 years old 3 meter span cavern with 25 meter cover under the old city of Jerusalem: Maximum Length 23 m Maximum Width 1 m Average Height 15m Estimated Area - 9 m 2 Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 19

20 Cross section through main chamber A A 5m 1m 15m Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 2

79 3 Shears 67/231 1.48 4 Joints 75/155 1.39 Y.

21 Rock Mass Structures Bedding planes Vertical Joints Set Type Dip Spacing 1 Bedding 8/ Shears 71/ Shears 67/ Joints 75/ Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 21

22 Roof stability assuming bedding planes only Free span (L) 3 m Beam thickness (t).85 m Unit weight (g ) 19.8 kn/m 3 Elastic modulus (E') 8*1 3 MPa Uniaxial compressive strength (s c ) 16.4 MPa (bedding parallel) Tensile strength (s t ) 2.8 MPa Maximum deflection at centerline (η) Maximum shear stress at abutments (t max ) Maximum axial stress (s) 8.67 cm.445 MPa 1.5 MPa The roof should have failed in tension Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 22

23 Roof stability assuming the Voussoir analogue Since the tensile strength of the material is exceeded in at the lowermost layers of the roof a vertical crack may propagate and decompose the continuous roof slab into two blocks, thus forming the so called Voussoir Bean (See Ray Sterling PhD thesis and Brady and Brown, 24): S f c n T Z T t f c Mid-Span Crack With the given dimensions the roof should undergo buckling culminating in a snap through mechanics (Z < ). So, what is keeping the roof stable?... Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 23

24 Results of forward modeling with DDA: 1m 1MPa Vertical Displacement (m) Horizontal Compressive Stress ( kpa) a m point 4 m point 3 m point 2 b m point Time (sec) Stable Configuration Surprisingly, the jointing patterns keeps the roof stable Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 24

25 Case 3: Tel Beer-Sheva a 3 years old underground water storage system Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 25

26 Underground System Layout: a a b b The collapse which occurred during time of construction was supported by the ancient engineers with a massive stone pillar. Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 26

stress the friction angle is assumed to be 35 o Y.

27 Joint spacing, orientation, and friction angle: 5 4 (deg.) Normal Stress (kpa) For the estimated level of normal stress the friction angle is assumed to be 35 o Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 27

28 Kinematics of a Jointed Beam (Voussoir) S = 8m, t =.5m, S j =.25m Initial Geometry = 45 = 3 = 8 = 75 o Deformed state Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 28

29 Forward DDA modeling results proves to be a function of vertical joint spacing and friction angle: 1 9 Friction angle required for stability For the attempted opening span the existing spacing between vertical joints dictates an Unstable configuration Vertical joint spacing (cm) Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 29

30 Required friction angle for stability [Degree] DDA vs. UDEC Beam span = 7m Beam thickness = 2.5m Layer thickness =.5m Mean joint spacing [cm] DDA Element size.1 m Element size 1 m Barla, Monacis, Perino, and Hatzor (21), Rock Mechanics & Rock Engineering. Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 3

31 The numerically obtained relationship between B and h with the case studies shown: h, m Hatzor, Wainshtein, and Bakun-Mazor (21), IJRMMS. 35 Ayalon Cave h 17(3) 13(3) 3 B Zedekiah Cave 15(25) 25 Safe 1(25) 19(22) 12(22) 2 16(19) 9(2) 15 7(14) Marginal 11(15) 8(15) 3(11) 6(1) 14(12.5) 1 18(11) 1(6) 2(6) 4(6) Unsafe 5(6) 5 Hatzor and Benari (1998), IJRMMS. Tel Beer Sheva B, m Legend: Safe Marginal Unsafe Bakun-Mazor, Hatzor and Dershowitz (29), IJRMMS. Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 31

32 Summary Sinkhole collapse can pose a significant risk for people and surface civil engineering operations. We develop here, using the numerical DDA method, a function that marks the boundary between Stable and Unstable shallow cavern geometries, for blocky rock masses consisting of horizontal bedding planes and vertical joints. Our results are confirmed by three independent stability analyses of underground openings in blocky rock masses possessing different mechanical properties for intact rock elements as well as different joint friction and spacing. Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May Wuhan China 32

THE VOUSSOIR BEAM REACTION CURVE

THE VOUSSOIR BEAM REACTION CURVE Yossef H. Hatzor Ben-Gurion University, Department of Geological and Environmental Sciences Beer-Sheva, Israel, 84105 ABSTRACT: The influence of joint spacing (s) on the