Friction coefficient shear displacement

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

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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

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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