Direct Shear Test of Silty Clay Based on Corrected Calculating Model

Abstract

Direct shear test is one of the common method to study the parameters of shear strength and shear strength of soil. However, the current standard of geotechnical test method does not consider the calculation error caused by the change of shear area during shear process. In this paper, the direct shear test corrected calculation model considering effective shear area is established. This model shows that the test values of shear stress and normal stress are lower than the corrected values with the decrease of effective shear area, and the errors between them will increase with the increase of relative shear displacement. The analysis of the direct shear test results of silty clay shows that the errors between the test and corrected shear stress values are also related to the normal stress. The errors will increase with the increase of the normal stress. The shear strength parameters after correction tends to decrease. The effect of the corrected model on the cohesion is more significant than internal friction angle, and the effect on internal friction angle can be neglected approximately. On the basis of Mohr-Coulomb criterion, a shear strength criterion based on the corrected calculation model is established, which can be used to calculate the true shear strength parameters more accurately.

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Direct Shear Test of Silty Clay Based on Corrected Calculating Model
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2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
1
Direct Shear Test of Silty Clay Based on Corrected
Calculating Model
Zhaohui Sun1, a, Hanbing Bian1, 2, 3, b, Chenyu Wang1, c, Saize Zhang1, 4, d and
Xiumei Qiu1, *
1College of Water Conservancy and Civil Engineering, Shandong Agricultural
University, Taian, China
2School of Civil Engineering, Changsha University of Science and Technology,
Changsha, China
3Polytech-Lille Institute, University of Lille, Lille, France
4State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-
Environment and Resources, Chinese Academy of Sciences, Lanzhou, China
*Corresponding author e-mail:qxmxr@126.com, amrsunzhaohui@163.com,
bhanbing.bian@univ-lille.fr, c18653835020@163.com, dzhangsaize@foxmail.com
Abstract. Direct shear test is one of the common method to study the parameters of
shear strength and shear strength of soil. However, the current standard of geotechnical
test method does not consider the calculation error caused by the change of shear area
during shear process. In this paper, the direct shear test corrected calculation model
considering effective shear area is established. This model shows that the test values of
shear stress and normal stress are lower than the corrected values with the decrease of
effective shear area, and the errors between them will increase with the increase of
relative shear displacement. The analysis of the direct shear test results of silty clay
shows that the errors between the test and corrected shear stress values are also related
to the normal stress. The errors will increase with the increase of the normal stress. The
shear strength parameters after correction tends to decrease. The effect of the corrected
model on the cohesion is more significant than internal friction angle, and the effect on
internal friction angle can be neglected approximately. On the basis of Mohr-Coulomb
criterion, a shear strength criterion based on the corrected calculation model is
established, which can be used to calculate the true shear strength parameters more
accurately.
1. Introduction
In the field of geotechnical engineering, the mechanical properties of soil, such as stress-strain
relationship and shear strength parameters, are the important basis of engineering investigation, and also
the key to the calculation of bearing capacity of foundation and subgrade. Therefore, how to quickly
and accurately determine the mechanical properties of soil is of great significance to geotechnical
engineering research.
Nowadays, there are many test methods to study the shear strength parameters of soil, such as triaxial
test, unconfined compressive strength test, direct shear test and so on. Among them, the direct shear test

2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
2
is easy to operate and calculate, and can quickly obtain the shear strength parameters of soil. Therefore,
it is widely used in scientific research and engineering practice. However, the direct shear test itself has
some shortcomings. For example, the traditional calculation method regards the shear area as a constant
value (πr2). Although it simplifies the calculation process, it ignores the change of shear area in the shear
process. However, the calculation of shear stress and shear strength parameters are all related to the
change of shear area. Therefore, it can be ascertained that the results calculated by traditional methods
will be difficult to accurately reflect the true mechanical properties of materials.
Many scholars have proposed the calculation method of effective shear area and stress [1]. Wang
obtained the equation of effective shear area and shear stress by calculating the integral of shear area. It
was found that when the shear displacement reached 4 mm, the difference of shear stress before and
after correction reached about 10% [2]. Zhan et al. studied the calculation error from the diameter of the
circular box and the shear stress, and proposed that the sample box should be made into a small upper
box and a large lower box to eliminate the error caused by the reduction of the shear area [3]. Xu et al.
established normal stress correction model which is to divide pressure by effective area. They believed
that the change of the shear area should be taken into account in the calculation of shear stress, and the
shear strength could be neglected in the calculation of shear strength [4]. Considering the change of
shear area, Ge et al. studied the variation of stress and strength parameters of rock mass structural plane
[5]. Yu et al. summarized the single-point area correction method and the multi-point area correction
method. On this basis, a single-point area stress correction method based on area correction and normal
stress correction was proposed. It was also found that the increase of shear displacement would make
the shear stress greater than the test value [6]. Dong and Wang considered the shear surface fluctuation
caused by the eccentricity of normal stress in the shear process. Based on the waveform shear surface
calculation model, the effective shear area was corrected. It was pointed out that the calculation results
of the model were closer to the true strength values of soil samples, but the fluctuation characteristics of
shear surface were difficult to obtain and could not be realized in practical application [7]. Zhang and
Wang deduced the equation for calculating effective shear area and processed the data by least square
method. It was found that the error of shear strength of soil decreased with the increase of shear area.
The results based on shear area correction showed that the true value of shear strength parameters was
larger than the test value [8].
In summary, many scholars have basically reached a consensus on the issue that the change of shear
area will affect the shear stress and normal stress [9, 10, 11, 12, 13]. However, due to the different
simplification of direct shear test calculation model, the calculation models of effective shear area and
stress are diverse, and the analysis of shear test results is also different. It is difficult to generalize the
results of standard direct shear tests to non-standard (arbitrary radius) tests. Therefore, this paper
deduces a direct shear test calculation model considering effective shear area by analytic equation, gives
a general corrected model of shear area, shear stress and normal stress. This paper combines the direct
shear test data of silty clay under the influence of multiple factors, studies and modifies the shear stress-
shear displacement relationship and shear strength of the model. Based on the corrected model of direct
shear test and the existing shear strength criterion, the shear strength criterion based on effective shear
area calculation is established.
2. Calculating models
2.1. Shear area correction model
In the process of shearing, the relative displacement of the upper and lower shear box is produced, and
the shear area decreases gradually. The calculation sketch is shown in Figure 1. When the shear
displacement is s, according to the symmetry, a quarter of the shear area can be calculated first.
Sector area:
2
1
2
S
dA r d

 (1)

2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
3
0
2
2
0
1 1
=
2 2 2
A r rd r



 
  

S（
）
(2)
0arcsin
2
s
r

 (3)
Triangular area:
2
0 0 0
1 1
cos sin = sin 2
2 4
T
A r r r
  
  (4)
Corrected shear area:
2 2 2
0 0
4 2 sin 2
S T
A A A r r r
  
    （ ） (5)
Figure 1. Calculation model of direct shear test.
The absolute error eA and relative error eA'of the corrected shear area are respectively:
2
0 0 0
( 2 sin 2 )
A
e A A r
 
     (6)
0 0 0
0
2 sin 2
'
A
A A
eA
 

  
  (7)
0
(1 ')
A
A A e
  (8)
In equation (8), its eA’ can also be called shear area correction factor. Fig. 2 shows the relationship
between the relative error of shear area before and after correction and relative shear displacement after
normalization. Fig. 2a is a integral curve, in which the relationship between relative error and relative
shear displacement is non-linear , and the relative error is always negative. This indicated that the
effective shear area decreases with the increase of shear displacement during shear process. For standard
direct shear test, the diameter of shear box is 61.8 mm, and the shear displacement is generally in the
range of 0-6 mm. Therefore, we should focus on the relationship between eA’ and relative shear
displacement in the range of 0-0.1. As shown in Fig. 2b, in the range of 0-0.1 relative shear displacement,
eA’ has a good linear relationship with relative shear displacement, and its linear fitting equation is as
follows:
1.27
y x
 
(9)
r
O
1
s
/2
x
y
r
r
O
2
O
1
θ
0
dA
S
s
A
A
1
z
x
O
2
F
σ
1
τ
σ
σ
0
P
P
s
/2
h/2
Shear direction
Shear direction
(a)
Shearing schematic
(b)
Area calculation schematic
h/2
(c)
Stress calculation schematic

2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
4
0.0 0.2 0.4 0.6 0.8 1.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Relative error e'
Relative shear displacement
(a
) Integral curve
0.00 0.02 0.04 0.06 0.08 0.10
-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
Model curve
Fitting curve
y=-1.27x
Relative error e'
Relative shear displacement
(b)
Partial
curve
Figure 2. Relative error of shear area vs. relative shear displacement.
2.2. Shear stress correction model
The traditional method is to multiply the shear displacement and the stiffness coefficient of the force
ring to represent the shear stress, which is essentially the stress of the effective shear plane rather than
the true value. From above equations, it can be seen that the effective shear area is a function of shear
displacement, which decreases continuously during the shear process. Therefore, the shear stress
calculated according to the traditional method is smaller than the true value, so the original calculation
model needs to be corrected. The corrected shear stress value is τ, and the test shear stress value
calculated by the traditional method is τ0 The following relationship is established:
0
CR

 (10)
0 0
A A
 
 (11)
Corrected shear stress:
0 0
1
0 0
2 + sin 2
=(1+ ) =(1+ )
2 sin 2
CR CR
 
 
  
  (12)
0 0
1
0 0
2 + sin 2
=
2 sin 2
 

  
  (13)
Among them, C is the stiffness coefficient of the measuring ring, R is the displacement value of the
dial indicator, CR is the product of the stiffness coefficient of the measuring ring and the indication,
which is called the test value of shear stress. Among them, β1 is the shear stress correction factor. From
equation (13) and (5), it can be seen that β1 is a function of shear displacement and the size of the direct
shear box. Therefore, it is not universally applicable to study only the relationship between shear
displacement and β1. We also normalize the shear displacement.. It can be seen from Fig.3a that the
relationship between β1 and relative shear displacement is non-linear, and increases with the increase of
relative shear displacement, and the growth rate increases synchronously. From Fig.3b, it can be seen
that the increment of β1 is proportional to the increment of relative shear displacement in the range of 0-
0.1. When the relative shear displacement reaches 10%, the error of shear stress increases to 14.6%.
Through linear fitting of the original curve, the fitting linear equation is as follows:
1.4
y x

(14)

2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
5
0.0 0.2 0.4 0.6 0.8 1.0
0
20
40
60
80
100
Shear stress correction factor β
1
Relative shear displacement
(a
) Integral curve
0.00 0.02 0.04 0.06 0.08 0.10
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
y=1.4x
Model curve
Fitting curve
Shear stress correction factor β
1
Relative shear displacement
(b)
Partial
curve
Figure 3. Shear stress correction coefficient vs. relative shear displacement.
2.3. Normal stress correction model
During shearing process, the effective shear area decreases and the normal pressure keeps unchanged,
so the normal stress distribution on the shear plane will inevitably change. Therefore, it is necessary to
correct the normal stress calculation model. The forces acting on the shear process are shown in Figure
1, where σ0 is the normal stress applied, σ1 is the stress applied to the lower shear box, σ is the true
normal stress on the shear plane, and h is the thickness of the direct shear specimen. For strain-controlled
direct shear tests, the shear process can be regarded as uniform motion, which conforms to Newton's
second law. Static analysis of upper shear specimens was carried out:
1 0 1
0 0 1 1
0
0
0
=0
x
z
F A F
F A A A
M M M M
  

  
  

   

 


，
，
，
(15)
0
1
0 0
1 1
/ 4
2
P
M A h
s
M A
M A x






 



 


 


(16)
Among them, A0 is the area of the circle, xP is the distance between the equivalent force of σ1 1and
P, which can be calculated by following equation:
1 2
0
0
2
0
2
o
s
x x
s
A A
xA A

 



  



(17)
The corrected normal stress equation can be obtained from the simultaneous equation (15-17):
0 0 2
(2 +sin 2 )
= + = +
2 ( 2 -sin 2 )
CRh
CR
s
 
   
  
 (18)
2
(2 +sin 2 )
=
2 ( 2 -sin 2 )
h
s
 

  
 (19)
In the above equations, β2 is a normal stress correction factor, and β2 is also a function of shear
displacement and shear box size. Similarly, it is normalized and the relationship between β2 and relative
shear displacement is obtained as shown in Fig. 4. Comparing with FIG. 3, it can be found that β2 and

2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
6
β1 have similar change rules, both increase with the increase of relative shear displacement, and the
increasing rate is accelerating. In the range of 0-0.1, the increment of β2 is also positively correlated with
the increment of relative shear displacement. When the relative shear displacement reaches 10%, the
correction coefficient of normal stress will reach 23.55%. The same is true, the product of β2 and shear
stress will also be enlarged, reflecting that the difference between the true value of normal stress and the
test value of direct shear will gradually increase with the increase of shear displacement.
0.3 +0.205
y x

(20)
0.0 0.2 0.4 0.6 0.8 1.0
0
20
40
60
80
100
Shear stress correction factor β
2
Relative shear displacement
(a
) Integral curve
0.00 0.02 0.04 0.06 0.08 0.10
0.20
0.21
0.22
0.23
0.24
y=0.3x+0.205
Shear stress correction factor β
2
Relative shear displacement
Model curve
Fitting curve
(b)
Partial
curve
Figure 4. Normal stress correction coefficient vs. relative shear displacement.
3. Test introduction
The soil samples were taken from Weishan Irrigation District, Shandong Province. According to the
Standard of Geotechnical Test Method (GB/T 2023-1999), particle size analysis test and liquid-plastic
limit test were carried out. The test results show that the maximum dry density of silty clay is 1.67 g/cm3,
the optimum water content is 16.7%, the plastic limit WP is 21.38%, the liquid limit WL is 33.53%, and
the plastic index IP is 12.15. The test process is as follows: firstly, the soil sample is dried after 2 mm
sieve, secondly, it is prepared according to the water content of the test design and treated overnight.
Thirdly, direct shear specimens with diameter of 61.8 mm and height of 20 mm are pressed by a die
press. In the process of sample preparation, the water content is controlled by spraying the deionized
water through the sprayer, the dry density is controlled by weighing soil samples quantitatively and
pressing moulding machine, the freeze-thaw cycle uses freezer constant temperature freezing (-15 ℃)
and freezer constant temperature thawing (-20 ℃). The minimum cycle of freeze-thaw cycle is 24 hours,
freezing and thawing are 12 hours each. In order to avoid the loss of water during freezing and thawing,
all the samples were wrapped with fresh-keeping film. The shear rate of the test was 2.4 mm/min. The
specific testl scheme is shown in Table 1.
Table 1. Direct shear test scheme.
Water content /%
Dry density / g·cm
-3
Number of freeze
-
thaw cycles
Normal stress /kPa
12.7
1.47
,
1.57
,
1.67
0
,
1
,
2
,
3
0
,
50
,
100
,
200
16.7
1.47
,
1.57
,
1.67
0
,
1
,
2
,
3
0
,
50
,
100
,
200
20.7
1.47
,
1.57
,
1.67
0
,
1
,
2
,
3
0
,
50
,
100
,
200
4. Results
Based on the above calculation model, the second development of EXCEL is carried out by using VBA
(Visual Basic for Applications), and a set of data correction program is established. The program can
complete the correction of the test data, automatically generate shear stress-displacement diagram and
shear strength envelope diagram, etc., which greatly improves the speed and authenticity of data
processing. It can be popularized in future research

2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
7
4.1. Shear stress-displacement relationship
Taking the direct shear test results of silty clay with the optimum water content of 16.7%, maximum dry
density of 1.67 g/cm3 and freeze-thaw cycles of 0 times as an example, the corrected shear stress-shear
displacement relationship (hereinafter referred to as τ-μ curve) is shown in Fig. 5. When the normal
stress is 0 kPa, 50 kPa and 100 kPa, the peak shear stress of τ-μ curves are strain-softening. When the
normal stress is 200 kPa, the τ-μ curve has no peak stress and is strain-hardening. It can be found that
the type of τ-μ curve will not be changed before and after correction. When the normal stress is 0 kPa,
the τ-μ curve almost coincide before and after the correction. When the normal stress is 50 kPa, 100 kPa
and 200 kPa, the corresponding maximum shear stress errors are - 5.567 kPa, - 9.948 kPa and - 17.97
kPa, respectively. It is confirmed again that the test shear stress is less than the true value, and the error
between them is related to the normal stress. The greater the normal force, the greater the error.
0 1 2 3 4 5 6
0
20
40
60
80
100
120
140
160
200 kPa
100 kPa
50 kPa
0 kPa
Shear stress
（
kPa
）
Shear displacement (mm)
Experimental data
Corrected fitting curve
Figure 5. Shear stress vs. shear displacement.
4.2. Shear stress-displacement relationship
According to the shear stress-displacement relationship, the corrected τ-μ curves can be divided into
strain softening and strain hardening. For strain softening, the peak shear stress is shear strength, and
for strain hardening curve, the shear stress corresponding to 6 mm shear displacement is shear strength.
At present, Mohr-Coulomb criterion is commonly used in solving shear strength parameters. The
equation for calculating shear strength is as follows.
tan
C
  
 
(21)
In the above equation, τ is shear stress, σ is normal stress, φ is internal friction angle, and C is cohesive
force. It is used to fit the relationship between shear strength and normal stress linearly, as shown in
Fig.6. The fitting results show that the Mohr-Coulomb criterion has good applicability for both test and
corrected values. Therefore, the Mohr-Coulomb criterion is selected to describe the shear strength in
this paper. The shear strength parameters of silty clay are calculated according to the traditional method
and the model modification algorithm respectively. The results of internal friction angle and cohesion
C are obtained as shown in Table 2.

2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
8
Table 2. Calculation results of shear strength parameters.
Number
Test values
Correction value
Number
Test values
Correction value
φ
0
/°
C
0
/
kPa
φ
/°
C
/
kPa
φ
0
/°
C
0
/
kPa
φ
/°
C
/
kPa
1
31.467
5.23
31.716
4.702
19
32.005
4.999
31.881
4.076
2
32.005
4.422
31.758
4.356
20
31.675
4.616
31.467
4.48
3
32.579
3.499
32.252
3.507
21
32.005
11.8
31.964
8.543
4
32.943
2.115
32.538
2.241
22
31.964
10.15
30.922
8.945
5
30.541
9.576
30.795
7.731
23
31.675
9.653
31.716
6.904
6
32.538
6.769
32.088
6.538
24
32.005
7.268
31.964
5.439
7
31.142
6.499
31.088
6.245
25
32.66
4.115
32.252
3.92
8
32.293
5.384
32.047
5.135
26
32.293
3.846
32.005
3.855
9
32.456
12.15
32.005
8.999
27
32.375
3.615
32.088
3.584
10
31.84
10.73
31.132
7.905
28
32.334
3.422
32.046
3.549
11
32.293
9.651
31.882
6.722
29
32.619
5.653
32.334
5.585
12
31.84
8.768
31.592
6.812
30
32.375
5.461
32.129
5.185
13
33.024
4.346
32.66
4.301
31
32.782
4.884
32.456
4.795
14
32.375
3.422
32.088
3.454
32
31.758
3.999
31.55
4
15
32.334
3.23
32.047
3.265
33
32.782
8.422
32.619
6.541
16
31.84
2.999
31.633
3.074
34
33.544
6.269
33.225
5.033
17
32.86
5.615
32.619
4.421
35
33.064
6.115
32.741
5.525
18
31.592
5.192
31.425
5.102
36
32.822
5.969
32.538
4.843
The relationship of the relative error between the corrected shear strength parameters and the test
values is shown in Fig.7, and the calculation equation is equation (22). In the picture, it can be seen that
the calculated results of the corrected shear strength parameters are mostly negative, that is, the test
shear strength parameters are larger than the true values. The maximum relative error of internal friction
angle is 0.008317, the minimum value is -0.0326, and the average value is -0.00808. The maximum
relative error of cohesion is 0.059574, the minimum value is -0.30349 and the average value is -0.09885.
Thus it can be seen that the influence of the corrected model on the calculation results of internal friction
angle and cohesion is different. Among them, the relative error of internal friction angle has good
constancy. The change of internal friction angle before and after the correction is about 1%, reflecting
that the change of shear area has little effect on the internal friction angle. The relative error of cohesion
is higher discreteness, the maximum error is more than 30%, which reflects that the change of shear area
has a significant impact on cohesion.
0 50 100 150 200 250
0
20
40
60
80
100
120
140
160
y=0.632x+9.651 y=0.622x+6.722
Test values
Correction values
Test fitting curve
Corrected fitting curve
Shear strength(kPa)
Normal stress(kPa)
Figure 6. Shear strength vs. normal stress.
0 4 8 12 16 20 24 28 32 36
-0.4
-0.3
-0.2
-0.1
0.0
0.1
Relative Error
Test Number
Internal Friction Angle
Cohesion
Figure 7. Relative error of shear strength
parameters.

2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
9
0
0
0
0
'
'
C
e
C C
eC

 









(22)
4.3. Shear strength criterion
The linear regression equation of the standard Mohr-Coulomb criterion is:
1
1
2 2
1
1tan
1
i
i
C


 



 
 
 
   
 
  
 
 
   
 
 
 
 
 
M M
M
(23)
According to the calculation equation of shear stress and normal stress correction model, equation
(23) is corrected:
1 11
1 1 21
2 2 22 2 12
21
(1 )
+ 1
+ 1 (1 )
tan
+ 1
(1 )
i i i i i
CR
CR
C
CR
 
 
   

   

 
 
 
  
 
 
  
 
 
   
 
  
 
 
 
M M M (24)
When the normal stress is σi , the normal stress correction coefficients, shear stress correction
coefficients and percentile displacement meters are represented by β1i, β2i and Ri respectively. The
corrected shear strength criterion is obtained from the simultaneous equation (14) and equation (20):
1 1
1 1 1
2 22 2 2
(1 1.4 )
+(0.3 0.205) 1
(1 1.4 )
+(0.3 0.205) 1 tan
+(0.3 0.205) 1
(1 1.4 )
i i i i i
x
x
x
x
C
x
x

 

  
  


 
 
 
  
 
 
  
 
 
   
 
 

 
 
 
M M M (25)
In the above equation, σi and τi represent the test values of normal stress and shear strength
respectively. When the normal stress is σi, xi is a relative shear displacement which is dimensionless.
The relative shear displacement xi is added to the equation, so that the corrected shear strength criterion
can effectively calculate the true internal friction angle and cohesion.
5. Conclusion
On the basis of previous studies, this paper theoretically deduces corrected models suitable for (non)
standard circular box direct shear test, develops a set of data correction program, and analyses the data
of silty clay direct shear test. The main conclusions are as follows:
1. According to the corrected calculation model, it is concluded that the test values of shear stress
and normal stress are lower than the corrected true values due to the decrease of shear area in shear
process. The error of true value increases with the increase of relative shear displacement.
2. The characteristics of shear stress-displacement curve of silty clay are related to normal stress:
under low normal stress, the strain softening type is the dominant one, while under high normal stress,
the strain hardening type is the dominant one. In addition, the error between the test shear stress and the
true value is also related to the normal stress, which will increase with the increase of the normal stress.
3. Mohr-Coulomb criterion has good applicability to the corrected direct shear test data. After
correction, the change of internal friction angle is small and can be neglected approximately, but the
change of cohesion is discrete and the corrected model has a significant influence on cohesion.
4. The corrected model of shear stress and normal stress are substituted into the Mohr-Coulomb
linear regression equation, in which the relative shear displacement is added. The corrected shear
strength criterion can calculate the true shear strength parameters more accurately according to the test

2019 International Conference on Oil & Gas Engineering and Geological Sciences
IOP Conf. Series: Earth and Environmental Science 384 (2019) 012172
IOP Publishing
doi:10.1088/1755-1315/384/1/012172
10
shear strength, shear displacement and normal stress.
Acknowledgments
This work was financially supported by the Shandong key research and development plan project (Grant
No. 2017GSF16104) and the National Natural Science Foundations of China (Grant NO. 51678074).
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