# Anchor Bolt Technology and Theoretical Research of Rock - PDF

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```					ROCK BOLTING MECHANISM AND DEVELOPMENT OF
QUANTITATIVE APPROACH IN TUNNELLING DESIGN

Introduction
Rock bolting design in tunnelling is still empirical, and its reinforcing mechanism has not been clarified yet. In order to achieve a safe and
economic solution, a quantitative assessment method is desirable. The interaction mechanism of rock bolt and rock mass is very important
to the quantitative assessment. Although the numerical analysis such as Finite Element Method (FEM) is often used, some problems are
still remaining, e.g, the determination of interface parameter.
The objective of this research is to establish a quantitative evaluation method for rock bolting design in tunnelling. Based on a refined
Shear-Lag theory, an interaction model of rock bolt and ground is proposed, and a quantitative approach is suggested according to the
convergence-confinement concept. A program named as Visual System of Tunnelling Aided Design(VSTAD) is developed further. As
an example, rock bolting effect in standard supporting pattern of Japan Highway Public Corporation (JH) is analyzed quantitatively.

Contents
Quantitative approach for evaluating rock bolting effect
Refined Shear-Lag model
Refined Shear-Lag model                                                                                                                                                                                                                                                                                                                      Mechanical behavior of reinforced rock mass
Mechanical behavior of reinforced rock mass
Original                                                                                                                                                                                                           Constitutive law
Shear-lag                                                                                                                                                               o
Sc=( σ 1 - σ 3 )                    σ1
+                ε1
e
αεe1          ε1
rb
theory
σ3             σ3
symmetric                                               Sc                                                                                                     εp1
dP ( x )
= H (u b − u m )                                                                                                                                                                                                                                         E`         σ1                                      h
dx                                                                                                                                                                                               Lz
Po                  E                       σ 3=Constant
Possible failure
(r,x)+d (r,x)                                                                                                                                                                                                                     position at Interface
Plastic flow
Sc*                                                           εp'
1

τ(rb,x)
zone                                                                                                                 f
σm(r,x)+ σ (r,x)

εe1              εp1             ε1                                 ε
σm(r,x)+dσm(r,x)

Soften zone                                                                                          p
ε
Shear strength                                                                                                                                                                                                                  p'
- ε3
3
σm(r,x)

P(x)+dP(x)                                                                                                                                         P(x)                                                                                                                                                                                                                                                                                               e                                                                            3
m

P(x)                                                                                                                                                                                                                                                                                                                                                                                                                                         Elastic zone                                 f
τm                                                                                    L
P(x)+dP(x)
ω
σm(r,x)

dx                                                                                                                                                                                                                                                                                                                   residual strength
Strain softening model and dilatantion characteristic
dx
τ mo                                                                                                                           r
dx                                                                                                                                                                                   O                 r        ρ Rf L1 Re
kini
(a) rock bolt                                                               (b) rock mass                                                                                                                                                                                                                                                                                                                                                                                                                                           Equilibrium equations
(c) rock bolt and
dP ( x )                                                                                                                                                                                                                                                                                                                      u max                                  displacement                                σr: radial stress
= −2πrbτ b                                                    mass                                                                                                                                                                                                                                                                                                                                                                                                    Axial force distribution
∂σ m (r , x ) ∂τ (r , x) τ (r , x )                                                                                                                                                                                                                                                                 Constitutive law                                                                         σt tangential stress
dx                              +          +           = 0 dP ( x)        R d
+ 2π ∫ r σ m (r , x)dr = 0                                                                                                                                                                                                                            of interface                                                                  σt                                            Ground                                           Neutral point                        dσ r σ r − (1 − β )σ t
∂x            ∂r         r
dx           rb dx
σr σr
+                  =0
Rock bolt                         dr          r
dr
+         opening
P max
dP

σr

=
b

dθ                   σt                    Interaction                                                                               ⎧+ 2πrb λra / Lz Lt     ra < r < ρ
Predicting axial force
Predicting axial force                                                                                                                                                                                           r                                shear stress       Pick up Anchor part                                               β =⎨
Pullout analysis
Pullout analysis                                                                                                                                                                                                                                                                                                                                                                                   ω             θ
part                                                                   ⎩− 2πrb λra / Lz Lt     ρ < r < L + ra
distribution
distribution                                                                                                                                                                         O                                        x
elastic zone
Shear stress
50                           Proposed approach
Oreste and Peila (1996)
Axial force (kN)

40                           In-situ measurements
Rock bolt
30
Modeling mechanical characters
Opening
Axial force
20
of reinforced rock mass based                                                   pir                              po              Boundary conditions
Opening
on interaction of rock bolt and
r=ra , σr=pir
Rock bolt                                    X
O                 r     Rf Re                                                    O                                                                                                  10
Po                                                                                                                                                                                                      strain soften zone                                                                                                                                                                                                                                                                           L
plastic flow zone                                                                                       elastic zone
0                                                                                       ground                                                                                    ra
, σr=pir
0.0          0.5           1.0                            1.5      2.0
d 2 P( x )    ⎡ P( x) P( x) ∂um ⎤
Interaction behavior is                                                                                                       dx 2
= H⎢      +
⎣ Eb Ab Em S
−    ⎥
∂x ⎦
Distance from tunnel wall (m)
r=
verified in pullout test.                                                                                                                    ⎧u p ( x ) in plastic region                                                                                               Comparison of theoretical
⎪                                                                                                                          prediction and measured data
um = ⎨us ( x ) in soften region
⎪u ( x ) in elastic region
⎩ e

Application examples
Application examples                                                                                                                                                                                                                                                                                                                  Visual System of Tunnel Aided Design
Visual System of Tunnel Aided Design
(1) Modifying rock bolting design during                                                                                                                                                                                                                                    (2) Verifying rock bolting effect in                                                                                                                                                                                                                                      Input sheet
tunnelling construction                                                                                                                                                                                                                                             standard supporting pattern (JH)                                                                                                                              Main interface                                  Predicting axial force and         Pre-processor            Database of soft rock
Parameter Checker
V b -w   W e a th e re d v o lc a n ic b re c c ia                                 L t L a v a tu ff                                                                                                                                                                                                                                                                                                                                                                                        shear stress distribution
150
Tb     T u ff b re c c ia                                                          A n 1 A n d e s ite
A n 2 F ra c tu re d a n d e s ite
Vb                                                                                               Rock mass in class B                                                                 Srp:                                                                      Data sheet for input,                          Assessing                                                        Charting results

w a t e r le v e l                                                                                                                                          competency factor of rock
100                                                                                                                                Vb
A n1
Tb                                                                                                                    JH-Pt1,     =0.095                                        mass.                                                                     import, save                                   reinforcement effect
Control panel
Control panel                   Design panel
T u n n e l e n tra n c e         V b -w                                     Vb
Lt
Srp = σ c /( H ⋅ γ )
50
F H 8 .3 0 3                                                                                                   T un nel T b
A n2
Ground-Support
σc--- compress rock mass                                                                                                           Calculation core                                Post-processor
Predicted axial force and measured results                                                                                                                                                                                                                                                                                                     strength;                                                                      interaction curve
D II                                                      70                          measured data
40% disp released                                                                                                                                                                                        Rock bolting density,                                                      γ --- density of rock mass;                                                                                                                     Structure of the system
C II                                                      60
H --- covering depth of
Pressure on tunnel wall (MPa)

80% disp released                                                             0.7                               Pattern 2 (β=0.197)
Stress distribution
Axial force (kN)

D II                                                      50                          40% disp released, L=3.0m

DI
40
0.6
JH-Pt1:                                                                                                      tunnel.
0.5

C II

DI
30

20
0.4
0.3
No rock bolt
uo / umax= 40%
Standard supporting pattern
for the rock mass in class B                                                                          Rock mass in class DII
around opening
10
0.2
Data

0
uo / umax= 90%
0.1
DI
0       1          2
Rock bolt length (m)
3           4
0.0
0
uo / umax= 20%

20         40        60        80       100
JH-Pt5:                                                                                                                                                                                                       Axial force                                  processor
Post-                            Visual panel
Standard supporting pattern
70

60
L=1.0m
Displacement u / umax (%)

for the rock mass in class DII
JH-Pt5,   =0.242
distribution of bolt                                      processor                        for optimal
L=1.5m
tunneling
Axial force (kN)

50                                       L=3.0m
Study section                                                       40                                       L=4.0m
L=6.0m
Fenner-Pacher curve                                                                                                                                                                                                                                                                                                                                                                                      design
30
of bolted rock mass                                                                                                                                                                                                                                                                                                                      Stress around tunnel                   Charting
Different                                            20

10

bolting length                                              0
0   1         2        3        4       5        6                                                                                                                                                                                                                                                           Rock bolting density,                                                                                                            Rock bolt axial force                  results
Rock bolt length (m)
Fenner-Pacher Curve

Published paper
Cai Y., Esaki T., Jiang,Y., Predicting Axial Load of Grouted Rock Bolt in Soft Rocks for NATM Tunneling, Tunnelling and Underground Space Technology, Vol. 19/6 pp.607-618, 2004.
Cai Y., Esaki T., Jiang,Y., An interaction model for rock bolt, International Journal of Rock Mechanics and Mining Sciences, Vol. 41/7 pp.1055-1067, 2004.

Conclusions
Based on interaction behavior of rock bolt and ground, a quantitative approach is proposed to evaluate the rock bolting effect for
tunnelling design. The rock bolting effect in standard supporting pattern of JH is analyzed quantitatively. It is found that the rock bolt
does not always works as expected. It is valid for the ground with a low competency factor, however, its effect is not significant for the
ground in a good condition.

Institute of Environmental System, Faculty of Engineering, Kyushu University, Fukuoka, Japan
Contact: Tetsuro ESAKI, Yue CAI                                                                                                                                                                                                                                                                                      E-mail esaki@, cai@ies.kyushu-u.ac.jp

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