friction coefficient shear displacement
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Friction coefficient – shear displacement curve of kaolinite in different slip rate
Presenter : Yi-Chia Chiang
Advisor : Prof. Jia-Jyun Dong
Date : 2020.03.27
Outline
1. Introduction
2. Methodology
3. Preliminary results
4. Preliminary conclusions
5. Future works
Introduction
• The strength of sliding surface will be strongly affected by the slip rate and the sliding distance when the landslide occurs. (e.g., Tika and Hutchinson, 1999; Yang et al., 2014; Alonso et al., 2016).
Introduction Methodology Results Conclusions Future work
1
Introduction
• Slip-dependence friction law
Introduction Methodology Results Conclusions Future work
2
Slip-strengthening
Slip-weakening
Lowslip rate
Intermediate slip rate
High slip rate
Introduction
• Shear rate-dependence friction law
Introduction Methodology Results Conclusions Future work
3
Displacement (m)
Fric
tio
n c
oef
fici
en
t (-
)
Rate-strengthening
Rate-weakening
Shear rate V
The steady-state friction coefficient
𝝁𝒔𝒔
The steady-state friction coefficient
𝝁𝒔𝒔
Shear rate
𝒗
Shear rate
𝒗
Shear rate V
𝑉1
𝑉2
𝑉3
𝑽𝟏 > 𝑽𝟐 > 𝑽𝟑𝑽𝟑 > 𝑽𝟐 > 𝑽𝟏
Purpose
1. Find out the reason that makes the difference of the strength measurement by rotary shear test.
2. Investigate the friction coefficient - shear displacement curve under different shear rate, and try to define the friction coefficient in more.
Introduction Methodology Results Conclusions Future work
4
Rotary shear test
Introduction Methodology Results Conclusions Future work
Rotational side
Stational side
𝜎𝑛
• A low to high rotary-shear frictional testing apparatus
5
Experiment conditions
• Pre-consolidated : 1MPa
• Normal stress : 1MPa (shear tests)
0.5~2MPa (Teflon calibration)
• Shear rate : 10−7 ~ 1 m/s
• Material : Kaolinite clay
• Water condition : Room humidity
Introduction Methodology Results Conclusions Future work
6
Introduction Methodology Results Conclusions Future work
7
The reasons that make the difference of the strength measurement by rotary shear test.
Is shear displacement enough?
The way used to calculate 𝝁𝒔𝒔 ?
Shear rate : 𝟏𝟎−𝟕m/s
Introduction Methodology Results Conclusions Future work
8
𝝁𝒔𝒔= 0.39𝝁𝒔𝒔= 0.28𝝁𝒔𝒔= 0.29
Is it steady-state ?
Shear rate : 𝟏𝟎−𝟔m/s
Introduction Methodology Results Conclusions Future work
9
𝝁𝒔𝒔= 0.59 𝝁𝒔𝒔= 0.40 𝝁𝒔𝒔= 0.40
Shear rate : 𝟏𝟎−𝟓m/s
Introduction Methodology Results Conclusions Future work
10
𝝁𝒔𝒔= 0.49 𝝁𝒔𝒔= 0.41 𝝁𝒔𝒔= 0.48
Shear rate : 𝟏𝟎−𝟒m/s
Introduction Methodology Results Conclusions Future work
11
𝝁𝒔𝒔= 0.60 𝝁𝒔𝒔= 0.46 𝝁𝒔𝒔= 0.79
Shear rate : 𝟏𝟎−𝟑m/s
Introduction Methodology Results Conclusions Future work
12
𝝁𝒔𝒔= 0.81 𝝁𝒔𝒔= 0.57 𝝁𝒔𝒔= 0.70
Shear rate : 𝟏𝟎−𝟐m/s
Introduction Methodology Results Conclusions Future work
13
𝝁𝒔𝒔= 0.82 𝝁𝒔𝒔= 0.74 𝝁𝒔𝒔= 0.90
Steady-state friction coefficient
Introduction Methodology Results Conclusions Future work
14
Introduction Methodology Results Conclusions Future work
15
𝝁- Displacement Curve pattern
Lowslip rate
Intermediate slip rate
High slip rate
Displacement (m)
Fric
tio
n c
oef
fici
ent
(-)
𝟏𝟎−𝟕, 𝟏𝟎−𝟔m/s 𝟏𝟎−𝟐, 𝟏𝟎−𝟏, 𝟏 m/s
Increase to 1st peak and weaken to residual value
𝟏𝟎−𝟕, 𝟏𝟎−𝟔m/s𝟏𝟎−𝟕, 𝟏𝟎−𝟔m/s
Shear rate V
Rate-strengthening
Displacement (m)
Fric
tio
n c
oef
fici
en
t (-
)
Increase to 1st peak and weaken to residual value
Rate-strengthening
Rate-weakening
𝟏𝟎−𝟐~𝟏𝟎−𝟏m/s
𝟏𝟎−𝟏~𝟏 m/s
𝟏𝟎−𝟐, 𝟏𝟎−𝟏, 𝟏 m/s𝟏𝟎−𝟐, 𝟏𝟎−𝟏, 𝟏 m/s𝟏𝟎−𝟐, 𝟏𝟎−𝟏, 𝟏 m/sShear rate V
Shear rate V
Displacement (m)
Fric
tio
n c
oef
fici
ent
(-)
𝟏𝟎−𝟓, 𝟏𝟎−𝟒, 𝟏𝟎−𝟑m/s
Shear rate V
Two peaks appear before the friction coefficient reaches a steady state value
Rate-strengthening
Introduction Methodology Results Conclusions Future work
16
What is the reason that we need much longer shear displacement to reach the steady-state?
Rotary shear test vs Ring shear test
V=0 Vmax Vmin Vmax
Introduction Methodology Results Conclusions Future work
17
(Doung et al.,2018)
STEP 1
•Defined the curve of shear stress versus shear displacement
•Get 𝜏𝑝, 𝜏𝑟, 𝐷𝑝, 𝐷𝑟
Introduction Methodology Results Conclusions Future work
18
Introduction Methodology Results Conclusions Future work
19
STEP 1
•Defined the curve of shear stress versus shear displacement
•Get 𝜏𝑝, 𝜏𝑟, 𝐷𝑝, 𝐷𝑟
Shear rate V
STEP 2
•Cut the shear plane into 5 rings
•Calculate the shear rate of each ring
Introduction Methodology Results Conclusions Future work
20
V=0 Vmax
The shear rate and shear displacementon the shear plane are not uniformly
distributed from the outside to the inside
𝐑𝟏
𝐑𝟐
𝐑𝟒
𝐑𝟑
𝐑𝟓
𝐕𝟏 𝑽𝟐 𝑽𝟒𝑽𝟑 𝑽𝟓
STEP 2
•Cut the shear plane into 5 rings
•Calculate the shear rate of each ring
Introduction Methodology Results Conclusions Future work
21
Shear rate V
Set 𝑉𝑒𝑞 = 10−4m/s
𝑉𝑚𝑎𝑥 = 10−4m/s 𝑉0 = 0m/s
V1 9.0 × 10−5m/s
V2 7.0 × 10−5m/s
V3 5.0 × 10−5m/s
V4 3.0 × 10−5m/s
V5 1.0 × 10−5m/s𝐕𝟏 𝑽𝟐 𝑽𝟒𝑽𝟑 𝑽𝟓
STEP 3
•Calculate the shear stress of each ring
•Transform to the shear stress of the whole plane
Introduction Methodology Results Conclusions Future work
22
𝜏𝑎𝑙𝑙 =𝑖=1𝑖=5
𝜏𝑅𝑖 × 𝐴𝑅𝑖
𝐴𝑎𝑙𝑙
𝜏𝑟𝑎𝑙𝑙 =𝑖=1𝑖=5
𝜏𝑟𝑅𝑖 × 𝐴𝑅𝑖
𝐴𝑎𝑙𝑙τRi : Shear stress of RiARi : Area of Ri
𝑨𝟏
𝑨𝟐
𝑨𝟒
𝑨𝟑
𝑨𝟓
Preliminary conclusions1. At the low (10−7, 10−6m/s) and high (10−2~1m/s) shear rates, the
friction coefficient increases with the increasing shear displacement
to a peak and then weakens to a steady state.
Introduction Methodology Results Conclusions Future work
23Displacement (m)
Fric
tio
n c
oef
fici
ent
(-)
𝟏𝟎−𝟕, 𝟏𝟎−𝟔m/s𝟏𝟎−𝟕, 𝟏𝟎−𝟔m/s𝟏𝟎−𝟕, 𝟏𝟎−𝟔m/s
Shear rate V
𝟏𝟎−𝟐, 𝟏𝟎−𝟏, 𝟏 m/s
Displacement (m)
Fric
tio
n c
oef
fici
ent
(-)
𝟏𝟎−𝟐, 𝟏𝟎−𝟏, 𝟏 m/s𝟏𝟎−𝟐, 𝟏𝟎−𝟏, 𝟏 m/s𝟏𝟎−𝟐, 𝟏𝟎−𝟏, 𝟏 m/sShear rate V
Shear rate V
Preliminary conclusions2. The friction coefficient-shear displacement curve obtained from the
rotary shear test actually reflects the results of the weighted
average of different shear rates and displacements covered by the
sliding surface.
The complexity of the obtained results under medium shear rate is related to
this limitation of the rotary shear test.
Introduction Methodology Results Conclusions Future work
24Displacement (m)
Fric
tio
n c
oef
fici
ent
(-)
𝟏𝟎−𝟓, 𝟏𝟎−𝟒, 𝟏𝟎−𝟑m/s
Shear rate V
𝐕𝟏𝑽𝟐 𝑽𝟒𝑽𝟑 𝑽𝟓
Future works
• To do more calculation using the strength measurement results by
ring shear test at different slip rate.
• To discuss the reasons that make the complexity of the obtained
results under medium shear rate .
Introduction Methodology Results Conclusions Future work
25
Thank you
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