Risk assessment of collapse in shallow caverns using numerical modeling ...in.bgu.ac.il/teva/geological/eng/hatzor/Site Assets/Pages/Research... · caverns using numerical modeling

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:

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 18 2012 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. 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:

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 18 2012 Wuhan China 3

h

B

The modeled rock mass in our simulations is a typicalblocky 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 0/0 0.70 m 1.0 0 m

2 88/182 5 m 0.96 m 0.5 2.5 m

3 88/102 5 m 0.78 m 0.5 2.5 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 (0.7m).


To estimate the mechanical stability of each structural configuration, we measure the vertical displacement (v) and the horizontal stress (sx) 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.


The results of forward modeling with DDA are classified into three categories of structural response, depending on the vertical displacement (v) and horizontal stress (sx) 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


-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0 2 4 6 8 10 12

Time, sec.

v,m

Measurement Point 1

Measurement Point 2

Measurement Point 3

Measurement Point 4

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

0 2 4 6 8 10 12

Time, sec.

sx ,kN/m2

Measurement Point 1

Measurement Point 2

Measurement Point 3

Measurement Point 4

10 m.

h/B = 0.78


Example of Stable configuration

10 m.

h/B = 1.0

-6

-5

-4

-3

-2

-1

0

0 5 10 15 20

Time, sec.

v,mMeasurement Point 1 Measurement Point 2

Measurement Point 3 Measurement Point 4 -1400

-1200

-1000

-800

-600

-400

-200

0

0 5 10 15 20

Time, sec.

sx ,kN/m2

Measurement Point 1

Measurement Point 2

Measurement Point 3

Measurement Point 4


Extension of Stable definition

10 m

h/B = 0.76

-6

-5

-4

-3

-2

-1

0

0 5 10 15

Time, sec.


Measurement Point 3 Measurement Point 4

B

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

0 5 10 15

Time, sec.

sx ,kN/m2

Measurement Point 1

Measurement Point 2

Measurement Point 3

Measurement Point 4


Marginally stable configuration

-6

-5

-4

-3

-2

-1

0

0 5 10 15 20

Time, sec.


Measurement Point 3 Measurement Point 4-1400

-1200

-1000

-800

-600

-400

-200

0

0 5 10 15 20

Time, sec.

sx ,kN/m2

Measurement Point 1

Measurement Point 2

Measurement Point 3

Measurement Point 4

10 m.

h/B = 0.5


Unstable configuration

As we know, per a given cover height (here h ~ 20 m) the span width adversely affects stability:

h/B = 0.76

10 m. B = 25 m

10 m.

h/B = 0.73

B = 30 m

10 m.

h/B = 0.5

B = 40 m


Similarly, per given cavern span ( here B = 25 m) the cover height positively affects stability:

10 m.

h/B = 1.2 h = 30 m

10 m.

h/B = 1.0h = 25 m

10 m.

h/B = 0.5h = 12.5 m


The final resulting relationship between B and h required for stability however proves to be not linear:

0

5

10

15

20

25

30

35

0 10 20 30 40 50

h , m

B , m

1(6) 2(6)

3(11)

4(6) 5(6)

6(10)

7(14) 8(15)

9(20)

10(25)

13(30) 17(30)

19(22)

18(11)

Legend: Safe Marginal Unsafe

Safe

Marginal

Unsafe

11(15)

12(22)

14(12.5)

16(19)

15(25)

h

B

Ayalon Cave

Zedekiah Cave

Tel Beer Sheva

h/B = 1

h/B = 0.5


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 2000 year old Zedekiah quarry -underneath the old city of Jerusalem

3. The Tel Beer Sheva 3000 year old underground water storage system –southern Israel.


Case 1: Ayalon Cave – a present day 40 meter span karstic cavern underneath an active open pit mine with 30 meters of rock cover:


Statistical joint survey results:

J2

J2

J3

J3

J2

J2

J3

J3

J1

0

5

10

15

20

25

30

35

40

45

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3

Thickness (m)

Fre

qu

ency

J2

0

5

10

15

20

25

30

35

0.0 0.3 0.6 0.9 1.3 1.6 1.9 2.2 2.5 2.8 3.1 3.4 3.8 4.1 4.4 4.7

Spacing (m)

Fre

qu

ency

J3

0

5

10

15

20

25

30

35

0.0 0.3 0.6 0.9 1.3 1.6 1.9 2.2 2.5 2.8 3.1 3.4 3.8 4.1 4.4 4.7

Spacing (m)

Fre

qu

ency


Current configuration of explored cavern underneath the mine:

No. of Blocks A mean

15,011 1.07 m2


Results of forward analysis with DDA:

-7

-6

-5

-4

-3

-2

-1

0

0 10 20 30 40

Point 1

Point 2

Point 3

Point 4

t, sec

v, m-600

-500

-400

-300

-200

-100

0

0 10 20 30 40

Point 1

Point 2

Point 3

Point 4

t, sec

s x , kPa

No. time

steps

90,000

Real Time 35.04 s

Mean no.

it. pts.

5.26

CPU time 361 hr.

Marginally stable configuration


Case 2: Zedekiah cave – a 2000 years old 30 meter span cavern with 25 meter cover under the old city of Jerusalem:

Maximum Length – 230 m

Maximum Width – 100 m

Average Height – 15m

Estimated Area - 9000 m2


Cross section through main chamber

0 5m 10m 15m

A’ A


Rock Mass Structures

Bedding planes Vertical Joints

Set Type Dip Spacing

1 Bedding 08/091 0.85

2 Shears 71/061 0.79

3 Shears 67/231 1.48

4 Joints 75/155 1.39


Roof stability assuming bedding planes only

Free span (L) 30 m

Beam thickness (t) 0.85 m

Unit weight (g ) 19.8 kN/m3

Elastic modulus (E') 8*103 MPa

Uniaxial compressive strength (sc) 16.4 MPa (bedding parallel)

Tensile strength (st) 2.8 MPa

Maximum deflection at

centerline (η)

8.67 cm

Maximum shear stress

at abutments (tmax)

0.445 MPa

Maximum axial stress

(s)

10.5 MPa

The roof should have failed in tension…


Roof stability assuming the Voussoir analogue

S

tT

T

Mid-Span Crackfc

n

fc

Z

S

tT

T

Mid-Span Crackfc

n

fc

Z

With the given dimensions the roof should undergo buckling

culminating in a “snap – through” mechanics (Z < 0).

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, 2004):

So, what is keeping the roof stable?...


Results of forward modeling with DDA:

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

Ver

tica

l D

ispla

cem

ent

(m)

0

0 0.5

-0.025

a

m point 1m point 2m point 3m point 4

Time (sec)

-800

-700

-600

-500

-400

-300

-200

-100

0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Ho

rizo

nta

l C

om

pre

ssiv

e

Str

ess

( k

Pa)

b

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

Ver

tica

l D

ispla

cem

ent

(m)

0

0 0.5

-0.025

aVer

tica

l D

ispla

cem

ent

(m)

0

0 0.5

-0.025

0 0.5

-0.025

a

m point 1m point 2m point 3m point 4

Time (sec)

-800

-700

-600

-500

-400

-300

-200

-100

0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Ho

rizo

nta

l C

om

pre

ssiv

e

Str

ess

( k

Pa)

b m point 1m point 2m point 3m point 4

m point 1m point 1m point 2m point 2m point 3m point 3m point 4m point 4

Time (sec)

-800

-700

-600

-500

-400

-300

-200

-100

0

-800

-700

-600

-500

-400

-300

-200

-100

0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Ho

rizo

nta

l C

om

pre

ssiv

e

Str

ess

( k

Pa)

b

10MPa10MPa10MPa

1

2

3

4

10m

1

2

3

4

1

2

3

4

10m10m

Stable Configuration

24

Surprisingly, the jointing patterns keeps the

roof stable…Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May 18 2012 Wuhan China

Case 3: Tel Beer-Sheva – a 3000 years old underground water storage system


Underground System Layout: a a

b b

Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May 18 2012 Wuhan China26

The collapse which occurred during time of construction was supported by the

ancient engineers with a massive stone pillar.

Joint spacing, orientation, and friction angle:

0 2000 4000 6000 8000

Normal Stress (kPa)

0

10

20

30

40

50

(

de

g.)

27For the estimated level of normal stress the friction angle is assumed to be 35o

Y. Hatzor: Risk assessment of collapse in shallow caverns. CAE Top Level Forum. May 18 2012 Wuhan China

Kinematics of a Jointed Beam (Voussoir)

=30o=45o=75o=80o

Initial Geometry

Deformed state

S = 8m, t = 0.5m, Sj = 0.25m


Forward DDA modeling results proves to be a function of vertical joint spacing and friction angle:

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600 700 800

Vertical joint spacing (cm)

Fri

ctio

n a

ngle

req

uir

ed f

or

stab

ilit

y

For the attempted opening span the existing spacing between vertical joints dictates an Unstable configuration


DDA vs. UDEC

0

10

20

30

40

50

60

70

80

90

0 100 200 300 400 500 600 700

Mean joint spacing [cm]

Req

uir

ed

fri

cti

on

an

gle

fo

r sta

bil

ity

[Deg

ree]

DDA Element size 0.1 m Element size 10 m

Beam span = 7m Beam thickness = 2.5m Layer thickness = 0.5m

Barla, Monacis, Perino, and Hatzor (2010), Rock Mechanics & Rock Engineering.


The numerically obtained relationship between B and h with the case studies shown:

0

5

10

15

20

25

30

35

0 10 20 30 40 50

h , m

B , m

1(6) 2(6)

3(11)

4(6) 5(6)

6(10)

7(14) 8(15)

9(20)

10(25)

13(30) 17(30)

19(22)

18(11)

Legend: Safe Marginal Unsafe

Safe

Marginal

Unsafe

11(15)

12(22)

14(12.5)

16(19)

15(25)

h

B

Ayalon Cave

Zedekiah Cave

Tel Beer Sheva

Bakun-Mazor, Hatzor and Dershowitz (2009), IJRMMS.

Hatzor and Benari (1998), IJRMMS.

Hatzor, Wainshtein, and Bakun-Mazor (2010), IJRMMS.


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 Stableand 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.


Documents

Risk assessment of collapse in shallow caverns using numerical modeling ...in.bgu.ac.il/teva/geological/eng/hatzor/Site Assets/Pages/Research... · caverns using numerical modeling