Surface groove morphology of structure and particle distribution of soil had a significant effect on the surface friction of structure. In order to investigate the interface shear stress-shear displacement curves, interface model and interface shear strength index when normal stress, groove width, and groove angle change, the interface shear tests of standard sand with steel plates are performed using an improved direct shear apparatus. Test results indicate that the peak shear stress increases with normal stress and the intersection angle between groove direction and shear direction. When the angle increases by 45°, the peak shear stress increases range from 4% to 13%. The peak shear stress increases with groove width, for every 1 mm increase in groove width, and the increasing extent of peak shear stress ranges from 4% to 22%, 3% to 13%, and 1% to 6%, respectively. When the groove angle is 45° and 90°, the increasing extent of peak shear stress decreases with groove width, but when the groove angle is 0°, the decrease regularity of peak shear stress increasing extent is not obvious. The hyperbolic model and Gompertz-C model are used to study the shear stress-shear displacement curves of sand-steel interface. The ratio of the interface peak shear stress of the hyperbolic model and Gompertz-C model to that of the shear test ranges from 0.90 to 1.03 and 0.88 to 0.98, respectively. The interface friction angle at the sand-steel interface ranges from 22° to 29°, and the friction angle of the rough interface is larger than that of the smooth interface. The interface friction angle increases with the intersection angle between the groove direction and the shear direction, the largest at 90°, the second at 45°, and the smallest at 0°. Under the same groove angle, the interface friction angle increases with the groove width, for every 1 mm increase in groove width, and the increasing extent of interface friction angle ranges from 4% to 15%, 4% to 7%, and 2% to 3%, respectively. The increasing extent of interface friction angle decreases with groove width, and this change rule is more obvious at the groove angle of 45° and 90° than at 0°.
The interaction at the interface between a structural surface and the surrounding soil surface is often seen in geotechnical engineering applications. A comprehensive understanding of interfacial shear behavior is very important for more accurate analysis and design of different geotechnical structures, such as pile foundation, tunnels, retaining wall, and other structures [
The direct shear test has become an important approach to study the basic laws of shear properties at the interface between structure and soil. The influencing factors and mechanical properties of the interfaces have been studied by a large number of scholars. Potyondy [
In the above research, the shape, width, and depth are mainly considered in the fabrication of structure surface groove, and the groove direction is mostly perpendicular to the cutting direction. However, in the actual engineering, the direction of the structure surface groove is disordered, and the angle between groove direction and shear direction can be any angle. Under the same groove volume, it is worth to further study on the characteristics of shear strength and shear index of the interface with different groove directions. Wang et al. [
The direct shear device used in the test is transformed from the strain-controlled direct shear apparatus, as shown in Figure
Improved direct shear apparatus sketch.
(a) ① Steel ring; ② connecting bolts for fixing the steel ring and lower shear box; ③ circular hole at the bottom of the lower box; ④ bolts for fixing the structure in the lower box; ⑤ bolt hole for connecting the upper shear box. (b) Lower shear box for direct shear apparatus.
The standard sand used in the test is produced by the Xiamen ISO Standard Sand Co., Ltd. company, which manufactured according to GB/T 17671-1999. The particle size distribution curve of standard sand in the test is shown in Figure
Particle size distribution curve of sand in the test.
Sand used in the test.
Physical and mechanical properties of sand.
Φ (°) | ||||||
---|---|---|---|---|---|---|
0.11 | 0.647 | 0.886 | 0.808 | 2.64 | 1.46 | 31.6 |
The steel plate used in the test is made up of stainless steel by mechanical processing. Front and elevation view of the steel plate are shown in Figures
Front view of the steel plate used in the test. (a) Int-A; (b) Int-B; (c) Int-C; (d) Int-D.
Elevation of the steel plate used in the test. (a) Int-A; (b) Int-B; (c) Int-C; (d) Int-D.
Groove angle of interface
Four kinds of steel plates are put with different surface morphology into the lower shear box, respectively, the sand after oven drying and permeable stone are placed into the upper shear box, and in turn, the quality of standard sand and prepressing time is the same for each test. The vertical dial indicator is zeroed after prepressing 10 min at normal stress for each test, and then shear tests were carried out under normal stress of 50 kPa, 100 kPa, 150 kPa, and 200 kPa. There are 40 groups of interfacial shear tests. The displacement control loading method is adopted in the test, and the shear rate is set at 0.8 mm/min.
The shear stress-shear displacement curves for the steel-sand interfaces are shown in Figure
Shear stress-shear displacement curves for the steel-sand interfaces. (a) Int-A. (b) Int-B-0°. (c) Int-B-45°. (d) Int-B-90°. (e) Int-C-0°. (f) Int-C-45°. (g) Int-C-90°. (h) Int-D-0°. (i) Int-D-45°. (j) Int-D-90°.
Peak shear stress-groove width relationship for the steel-sand interfaces. (a) 50 kPa. (b) 100 kPa. (c) 150 kPa. (d) 200 kPa.
Increasing extent of peak shear stress with groove angle.
Interface | Groove angle (°) | |||||
---|---|---|---|---|---|---|
0 | 45 | 90 | ||||
Int-B | 50 | 22.06 | 23.49 | 25.55 | 6.5 | 8.8 |
100 | 43.80 | 46.98 | 49.99 | 7.2 | 6.4 | |
150 | 69.03 | 72.84 | 75.38 | 5.5 | 3.5 | |
200 | 87.76 | 92.20 | 97.12 | 5.1 | 5.3 | |
Int-C | 50 | 23.49 | 25.55 | 28.41 | 8.8 | 11.2 |
100 | 45.86 | 51.74 | 56.34 | 12.8 | 8.9 | |
150 | 71.26 | 77.45 | 80.62 | 8.7 | 4.1 | |
200 | 93.00 | 97.92 | 103.00 | 5.3 | 5.2 | |
Int-D | 50 | 24.28 | 26.34 | 29.36 | 8.5 | 11.4 |
100 | 47.77 | 53.48 | 59.51 | 12.0 | 11.3 | |
150 | 73.16 | 78.56 | 83.48 | 7.4 | 6.3 | |
200 | 96.01 | 100.46 | 104.74 | 4.6 | 4.3 |
Increasing extent of peak shear stress with groove width.
Groove angle (°) | Groove width (mm) | |||||||
---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | |||||
50 | 0 | 21.11 | 22.06 | 23.49 | 24.28 | 4.5 | 6.5 | 3.4 |
45 | 21.11 | 23.49 | 25.55 | 26.34 | 11.3 | 8.8 | 3.1 | |
90 | 21.11 | 25.55 | 28.41 | 29.36 | 21.1 | 11.2 | 3.4 | |
100 | 0 | 41.74 | 43.80 | 45.86 | 47.77 | 4.9 | 4.7 | 4.2 |
45 | 41.74 | 46.98 | 51.74 | 53.48 | 12.5 | 10.1 | 3.4 | |
90 | 41.74 | 49.99 | 56.34 | 59.51 | 19.8 | 12.7 | 5.6 | |
150 | 0 | 66.34 | 69.03 | 71.26 | 73.16 | 4.1 | 3.2 | 2.7 |
45 | 66.34 | 72.84 | 77.45 | 78.56 | 9.8 | 6.3 | 1.4 | |
90 | 66.34 | 75.38 | 80.62 | 83.48 | 13.6 | 6.9 | 3.5 | |
200 | 0 | 82.84 | 87.76 | 93.00 | 96.01 | 5.9 | 6.0 | 3.2 |
45 | 82.84 | 92.20 | 97.92 | 100.46 | 11.3 | 6.2 | 2.6 | |
90 | 82.84 | 97.12 | 103.00 | 104.74 | 17.2 | 6.0 | 1.7 |
It is an important research aspect to find a reasonable mathematical model to describe the shear stress-shear displacement relationship of the soil-structure interface. The correct and reasonable interface mathematical model is of great significance to the simulation of soil-structure interaction. At present, the existing interface mathematical models include hyperbolic model [
The mathematical equation of Gompertz curve was first proposed by British mathematician and statistician B. Gompertz in 1825. The equation is as follows:
In the above formula,
The schematic diagram of the Gompertz-C model is shown in Figure
Schematic diagram of the interface model.
In this paper, the hyperbolic model and Gompertz-C model are used to study the shear stress-shear displacement curves of sand-steel interfaces, and the parameters and fitting data of the two models are compared. Limited by the length of this paper, only In-A and Int-D are selected for research.
Table
Parameters of the interface mathematical model.
Interface | Normal stress (kPa) | Hyperbolic model | Gompertz-C model | ||
---|---|---|---|---|---|
Int-A | 50 | 0.0054 | 0.0467 | −20.20 | 4.882 |
100 | 0.0034 | 0.0229 | −40.65 | 4.177 | |
150 | 0.0029 | 0.0139 | −65.23 | 3.282 | |
200 | 0.0022 | 0.0112 | −81.18 | 3.508 | |
Int-D (0°) | 50 | 0.0039 | 0.0431 | −22.12 | 5.764 |
100 | 0.0027 | 0.0207 | −45.25 | 4.541 | |
150 | 0.0020 | 0.0132 | −70.19 | 4.158 | |
200 | 0.0016 | 0.0100 | −92.22 | 4.101 | |
Int-D (45°) | 50 | 0.0044 | 0.0400 | −23.90 | 4.896 |
100 | 0.0022 | 0.0189 | −49.91 | 5.030 | |
150 | 0.0016 | 0.0126 | −74.33 | 4.775 | |
200 | 0.0013 | 0.0096 | −96.38 | 4.854 | |
Int-D (90°) | 50 | 0.0033 | 0.0368 | −25.91 | 5.871 |
100 | 0.0021 | 0.0168 | −55.72 | 4.852 | |
150 | 0.0016 | 0.0115 | −80.85 | 4.657 | |
200 | 0.0015 | 0.0091 | −100.60 | 4.022 |
Interface pear shear stress of the mathematical model and test (kPa).
Interface | Normal stress (kPa) | ||||||
---|---|---|---|---|---|---|---|
Int-A | 50 | 21.11 | 20.76 | 20.20 | 0.98 | 0.96 | 1.03 |
100 | 41.74 | 41.92 | 40.65 | 1.00 | 0.97 | 1.03 | |
150 | 66.34 | 68.00 | 65.23 | 1.03 | 0.98 | 1.04 | |
200 | 82.84 | 84.54 | 81.18 | 1.02 | 0.98 | 1.04 | |
Int-D (0°) | 50 | 24.28 | 22.59 | 22.12 | 0.93 | 0.91 | 1.02 |
100 | 47.77 | 46.59 | 45.25 | 0.98 | 0.95 | 1.03 | |
150 | 73.16 | 72.67 | 70.19 | 0.99 | 0.96 | 1.04 | |
200 | 96.01 | 95.56 | 92.22 | 1.00 | 0.96 | 1.04 | |
Int-D (45°) | 50 | 26.34 | 24.51 | 23.90 | 0.93 | 0.91 | 1.03 |
100 | 53.48 | 51.47 | 49.91 | 0.96 | 0.93 | 1.03 | |
150 | 78.56 | 76.63 | 74.33 | 0.98 | 0.95 | 1.03 | |
200 | 100.46 | 100.20 | 96.38 | 1.00 | 0.96 | 1.04 | |
Int-D (90°) | 50 | 29.36 | 26.52 | 25.91 | 0.90 | 0.88 | 1.02 |
100 | 59.51 | 57.46 | 55.72 | 0.97 | 0.94 | 1.03 | |
150 | 83.48 | 83.65 | 80.85 | 1.00 | 0.97 | 1.03 | |
200 | 104.74 | 104.78 | 100.60 | 1.00 | 0.96 | 1.04 |
Model curves for sand-steel interfaces. (a) Int-A. (b) Int-D-0°. (c) Int-D-45°. (d) Int-D-90°.
Three stages of the interface model.
The shear strength failure formula of Mohr–Coulomb is applied to the linear fitting of the relationship between peak shear stress and the normal stress, and the shear strength index of the interface is obtained, as shown in Figure
Relationship between normal stress and peak shear strength for steel-sand interfaces. (a) Int-A. (b) Int-B. (c) Int-C. (d) Int-D.
Interface friction angle and fitting formula.
Interface | Interface friction angle (°) | Fitting formula | |
---|---|---|---|
Int-A | 22.94 | 0.995 | |
Int-B-0° | 24.00 | 0.997 | |
Int-B-45° | 25.17 | 0.997 | |
Int-B-90° | 26.27 | 0.998 | |
Int-C-0° | 25.05 | 0.999 | |
Int-C-45° | 26.66 | 0.996 | |
Int-C-90° | 27.92 | 0.992 | |
Int-D-0° | 25.74 | 0.999 | |
Int-D-45° | 27.20 | 0.996 | |
Int-D-90° | 28.60 | 0.984 |
Relationship between interface friction angle and groove width for steel-sand interfaces.
Increasing extent of interface friction angle with groove width.
Groove angel (°) | Groove width (mm) | ||||||
---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | ||||
0 | 22.94 | 24.00 | 25.05 | 25.74 | 4.6 | 4.4 | 2.8 |
45 | 22.94 | 25.17 | 26.66 | 27.20 | 9.7 | 5.9 | 2.0 |
90 | 22.94 | 26.27 | 27.92 | 28.60 | 14.5 | 6.3 | 2.4 |
In this paper, the shear behaviors of standard sand with steel plates are studied using an improved direct shear apparatus. The conclusions are as follows: The peak shear stress increases with normal stress and the angle between groove direction and shear direction. When the angle increases by 45°, the peak shear stress increases range from 4% to 13%. The peak value of shear stress increases with groove width, for every 1 mm increase in groove width, and the increasing extent of peak shear stress ranges from 4% to 22%, 3% to 13%, and 1% to 6%, respectively. When the groove angle is 45° and 90°, the increasing extent of peak shear stress decreases with the groove width, but when the groove angle is 0°, the decrease regularity of peak shear stress increasing extent is not obvious. The hyperbolic model and Gompertz-C model are used to study the shear stress-shear displacement curves of sand-steel interface. The ratio of the interface peak shear stress of the hyperbolic model to that of the Gompertz-C model ranges from 1.02 to 1.04. The ratio of the interface peak shear stress of the hyperbolic model and Gompertz-C model to that of the shear test ranges from 0.90 to 1.03 and 0.88 to 0.98, respectively. The model curves are divided into three stages. The interface friction angle at the sand-steel interface ranges from 22° to 29°, and the friction angle of rough interface is larger than that of the smooth interface. The interface friction angle increases with the intersection angle between the groove direction and the shear direction, the largest at 90°, the second at 45°, and the smallest at 0°. Under the same groove angle, the interface friction angle increases with groove width, for every 1 mm increase in groove width, and the increasing extent of interface friction angle ranges from 4% to 15%, 4% to 7%, and 2% to 3%, respectively. The increasing extent of interface friction angle decreases with groove width, and this change rule is more obvious at the groove angle of 45° and 90° than at 0°.
The data of the research conclusions in this paper are included within the article.
The authors declare that there are no conflicts of interest for this paper.
This work was funded by the National Natural Science Foundation of China (no. 51879246), the Natural Foundation of Shandong Province (no. ZR2019MEE056), the Science and Technology Project of Tibet Autonomous Region (no. XZ202001ZY0013G), the Science and Technology Development Plan Project of Weifang City (no. 2019GX087), and the Transportation Technology Project of Shandong Province (no. 2020B23).