# Apparent Deterioration Law and Shear Failure Mode of Rock–Mortar Interface Based on Topography-Sensing Technology

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## Abstract

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## 1. Introduction

_{N}to represent the peak dilatation angle and established the shear strength model. Through studying the fractal dimension of interface, Kulatilake et al. [14] proposed a shear strength model that could characterize the interface anisotropy. Homand et al. [15] defined multiple parameters to describe the characteristics of the three-dimensional interface, such as fluctuation, inclination, and curvature and deduced the shear strength model. Singh and Basu [16] collected 11 reasonable criteria for peak shear strength and found that the Tang model [17] and Yang model [18] based on Grasselli morphological parameters were superior to other models in form and prediction accuracy. In addition, the exploration of interface morphology cannot be separated from the corresponding equipment. The perspective of topography-sensing technology is macro and comprehensive [19], which is convenient for interface apparent topography investigation and model construction of rock mass, wherein the three-dimensional non-contact laser topography sensor is the most widely used surface shape measurement equipment currently [20]. The parameter estimation is very intelligent, and it is easy to obtain the data of fractal geometric parameters, statistical parameters, height parameters, and texture characteristics, which is conducive to the subsequent research on the mechanism of interface topography degradation. Xia and Sun [21,22] designed the RSP-1 type intelligent rock surface topography analyzer and the TJXW-3D type three-dimensional rock surface topography sensor successively to achieve better measurement of surface topography of rock interface. Cao and Fan [23] used Talysurf CLI 2000, a high-precision three-dimensional surface topography sensor, to scan the interface surface for realizing the three-dimensional visualization of interface. Grasselli et al. [24,25,26] proposed employing the maximum potential contact area ratio, maximum apparent angle, and roughness parameters to quantitatively describe the interface topography characteristics through high-precision three-dimensional scanning and sensing quantification method of interface topography. Gui et al. [27,28] studied the shear mechanical behavior and the deterioration characteristics of interface topography in different shear displacements on the basis of three-dimensional topography-sensing technology. Although these have greatly enriched the understanding of shear mechanical properties of rock interfaces, most are concentrated on the single shear performance of the interface.

## 2. Presentation of Test Strategy

#### 2.1. Test Apparatus

- (1)
- Topography-sensing test of rock–mortar interface

- (2)
- Cyclic direct shear tests on rock–mortar interface

- Before loading, the normal and tangential loading devices are moved close to the sample quickly and stopped at approximately 5 mm away from the sample.
- Normal loading is controlled by constant force, and the loading speed is 0.1 kN/s until the target value is reached. Tangential loading begins after the normal force remains stable for 10 s.
- Tangential loading is achieved by constant force and constant displacement: Firstly, tangential force control is adopted at 0.1 kN/s until the tangential force reaches 2 kN. Then, the tangential displacement control is manually started to load at a constant speed of 0.01 mm/s, and it ends when sample failure occurs.

#### 2.2. Rock–Mortar Interface Preparation

#### 2.3. Test Program

## 3. Strength Deterioration and Dilatancy Characteristics of Rock–Mortar Interface

#### 3.1. Deterioration of Interface Strength under Cyclic Shearing

#### 3.2. Dilatancy Characteristics of Interface under Cyclic Shearing

_{n}. Figure 10 shows the relationship between dilation angle, shear stress, and shear displacement of each shearing. The peak dilatation angle after first shearing is 27°, while the dilatancy angle corresponding to the peak shear stress is 11.33°, which shows a great difference. In the process of practical interface shearing, the maximum dilatancy effect is earlier than shear failure due to the different stiffnesses of mortar and rock. Thus, it is more appropriate to regard the the peak value of the real-time dilatancy angle curve as the peak dilatancy angle d

_{n}. Considering that there is no obvious peak shear stress in the shear-stress–shear-displacement curves of the second and third shearing, the maximum dilatancy angles are employed, which are 8.487° and 8.37°, respectively. With the increase of shear numbers, the values of d

_{n}decreases at a decreasing rate.

_{n}of the first shearing ranges between 15° and 50°, d

_{n}of the second shear is distributed in the intervel from 5° to 15°, and d

_{n}of the third shear changes from 0° to 10°. With the increase of shear times, the peak dilatancy angle decreases, and the interface with larger normal stress has a greater reduction of peak dilatancy angle. Meanwhile, the differences between the peak dilatancy angles of each interface are getting smaller, indicating that its sensitivity to the normal stress, the interface material, and the roughness is decreasing. However, by comparing the peak dilatancy angle of the first shearing, it can be found that the dilatancy angle corresponding to malmstone is generally larger, followed by red sandstone and blue sandstone.

## 4. Apparent Evolution Characteristics of Rock–Mortar Interface

#### 4.1. Introduction of Three-Dimensional Topography Parameters

- (1)
- Description of height characteristic parameters of surface topography.
- a.
- Maximum interface height S
_{p}: The vertical distance between the lowest point and the highest point of the interface; - b.
- Interface height root mean square S
_{q}: The square root of the mean distance from each point on the measured surface to the datum. The expression is$${S}_{q}=\sqrt{\frac{1}{\mathrm{A}}{\displaystyle \underset{A}{\iint}{\mathrm{z}}^{2}(x,y)dxdy}}$$ - c.
- Arithmetic mean deviation Sa: The arithmetic mean of the distance from each point on the measured surface to the datum in the sampling area, which can be calculated by$${S}_{a}=\frac{1}{\mathrm{A}}{\displaystyle \underset{A}{\int}\left|\mathrm{z}(x,y)\right|}dxdy$$
- d.
- Skewness coefficient of surface height distribution function S
_{sk}: The ratio of the cubic moment of the height distribution density function to the third power of the root mean square of height. It describes the symmetry of the surface topography and can be expressed by Equation (3).$${S}_{sk}=\frac{1}{{S}_{q}^{3}}\left(\frac{1}{A}{\displaystyle \underset{A}{\iint}{\mathrm{z}}^{3}(x,y)dxdy}\right)$$ - e.
- The peak coefficient of the surface height distribution function S
_{ku}: Description of the steepness of the interface surface topography. The calculation formula is$${S}_{ku}=\frac{1}{{S}_{q}^{4}}\left(\frac{1}{A}{\displaystyle \underset{A}{\iint}{\mathrm{z}}^{4}(x,y)dxdy}\right)$$

- (2)
- Surface morphology texture feature parameters
- a.
- Texture topography ratio S
_{tr}: Characterizing the degree of interface anisotropy and anisotropy. Its values range from 0 to 1. The larger the value, the greater the degree of isotropy. - b.
- Texture direction angle S
_{td}: Describing the main tilt direction of the surface texture. The value is the angle between the main tilt direction and the tilt direction of the least square surface.

- (3)
- Surface peak morphology characteristics
- a.
- Peak point density S
_{pd}: Number of peak points per unit area, which can characterize the complexity of the surface. - b.
- Arithmetic mean curvature at peak point S
_{pc}: Arithmetic mean of curvature of all peaks, which reflects the surface peak’s sharpness or roundness.

- (4)
- Surface topography mixed parameters
- a.
- Fractal dimension D
_{s}: The box-counting method is used to calculate fractal dimension of the surface, and the slope of the regression line is the fractal dimension, which can describe the complexity of the interface. - b.
- Root mean square of slope of interface S
_{dq}: Characterizing the tilt degree of the interface to a certain extent, which can be obtained by$${S}_{dq}=\sqrt{\frac{1}{A}{\displaystyle \underset{A}{\iint}{\left(\frac{\partial \mathrm{z}(x,y)}{\partial x}\right)}^{2}+{\left(\frac{\partial \mathrm{z}(x,y)}{\partial y}\right)}^{2}dxdy}}$$ - c.
- Interface area ratio S
_{dr}: Used to represent the complexity of the interface, the expression of which is

#### 4.2. Morphology Parameter Evolution of Rock–Mortar Interface Subjected to Cyclic Shearing

_{p}decreases with the increase of shear times, as in the four groups of interfaces with 4 MPa normal stress (AD-1, AD-2, AD-3 and BD-1); however, S

_{p}corresponding to first shearing is greater than that before the test and then shows a decreasing trend with the increase of shear times. The reason is that mortar and rock bond more closely under greater normal stress, and the two materials share the shear resistance in the shearing process. During the first shearing, the two materials are not completely separated, and part of the mortar remained bonded to the rock surface. In other words, a new failure surface occurred (see Figure 13), producing greater roughness. In the second and third shearing, the micro-convex is cut off, causing the decrease of S

_{p}. For the other interfaces (BD-2, CD-1, CD-2, and CD-3), the bonding between mortar and rock is relatively weak [66]. Under the action of shear stress, the interface is worn and damaged after separation, as shown in Figure 14.

_{a}decreases with the increase of shear times under 2 MPa normal stress, but it irregularly fluctuates under 4 MPa normal stress, which can be attributed to the great changes of interface morphology. Compared with S

_{a}, the interface height deviation root mean square S

_{q}is not only related to the relative foundation surface but also more sensitive to the interface points, which can better reflect the volatility and dispersion of interface. The variation pattern of S

_{q}is similar to that of S

_{p}, that is, with the increase of shear times, S

_{q}shows a decreasing trend. This indicates that the dispersion of the interface height distribution is weakened due to the damage of micro-convex. The higher micro-convex are worn or cut off, while the lower micro-convex show little changes.

_{sk}is less than 0, there are more thin and deep valleys on the surface, and vice versa. While the peak coefficient of the surface height distribution function is greater than 3, the height distribution is more concentrated, whereas the height distribution is more discrete. There is no obvious regularity in the changes of S

_{sk}in Table 4 because most of S

_{sk}tends to 0, which means the peaks and the troughs of interface tend to be symmetrical. However, the crest is constantly worn in the tests, while the number of troughs is almost constant, resulting in more discrete height distribution of interface. In other words, S

_{ku}shows a downward trend. Considering that there is a fourth power term in the S

_{ku}calculation formula, it is not sensitive to the distinction between peaks and troughs. Therefore, the validity of this parameter in describing the uneven surface remains to be further investigated. It is suggested to avoid employing the above two parameters in the topography description of interface subjected to cyclic shearing.

_{tr}approaches 1, the interface topography has a high degree of isotropy. While S

_{tr}is close to 0, it is highly anisotropic. In Table 5, the values of S

_{tr}before the tests are all less than 0.5, indicating that the anisotropy of texture morphology at the interface is obvious in the process of cyclic shearing. Since the irregular interface before tests is obtained by the intact rock shear tests, the corresponding S

_{tr}are also less than 0.5. In addition, S

_{tr}increases with the increase of shear timess, which means that the differences on the interface morphology in different directions gradually decrease. In cyclic shearing, due to the gradual wear of the micro-convex, the elevation difference of each point is gradually loaded. In addition, due to extrusion, the convex and concave parts gradually merge to form a micro-surface with fluctuation. The original tiny folds on the interface are also smoothed out or formed into small curved surfaces with low undulation angles. All these decrease the anisotropy of the interface, causing the increase of S

_{tr}. However, when the normal stress is 4 MPa, S

_{tr}of AD-1 and AD-2 interface after the first shearing is smaller than that before the tests, indicating that the first shearing raises the interface anisotropy and produces more complex interfaces.

_{td}decreases with the increase of shear times, and the decreasing amplitude is related to the normal stress. The protruding parts on the interface are gradually worn down during the cyclic shearing process, resulting in gradual decreases in the height, which is the main cause of S

_{td}reduction. Under low normal stress, the decreasing amplitude is relatively small. This is due to the weak extrusion between rock and mortar under 2 MPa normal stress. In the shearing process, the failues that occurred most often are slips along the direction of texture angle and wear damage to the small sharp convex body on the texture body, while the wear on the texture body is very weak. As a result, S

_{td}is less sensitive to changes in the texture features of the interface.

_{pd}can describe the complexity of the surface in the mesoscopic dimension. It ranges from 0 to 1 and decreases with the increase of shear times shown in Table 5. The decrease of S

_{pd}is attributed mainly to the fact that high peaks on the measured surface are smoothed out in the process of cyclic shearing, resulting in a flatter surface. Especially in the case of large normal stress, higher peak points are mostly cut off or worn down during the first and second shearing, and there is less change of S

_{pd}after the third shearing.

_{pc}is similar to that of S

_{pd}. The reduction of S

_{pc}indicates that in the process of cyclic shearing, shear failure or friction failure occurs to the steep and sharp convex on the interface under the normal and shear stress, lowering the height difference between the peak point and surrounding area. Moreover, the steepness of local areas decreases, forming a smoother and more rounded peak point.

_{dr}approaches 0, it indicates that the tested surface is almost completely flat. In Table 6, the value of S

_{dr}decreases with the increase of shear times. Under the action of cyclic shearing, the uneven parts of the interface are constantly worn and cut off, and the wrinkles and the expansion area are reduced. Under the large normal stress, S

_{dr}decreases faster. This is because the normal stress promotes the contact between rock and mortar, which makes the shearing wear effect more obvious.

_{s}of the three-dimensional topography obtained by scanning before and after interface shearing is also calculated, as shown in Table 6. D

_{s}is distributed between 2.2 and 2.5, and most are approximately 2.3, indicating that the most shearing interfaces are not complex and are closer to flat two-dimensional planes. Under the normal stress, the interface occludes tightly, and the complex bumps, textures, and folds on the interface are all cut off or substantially worn. D

_{s}decreases with the increase of shear times, which is more obvious under the low normal stress. Considering the interface morphology has been seriously degraded after the first shearing under large normal stress, D

_{s}changes little in the subsequent shearing. By contrast, the interface fluctuation gradually degenerates in the process of cyclic shearing due to the shear separation effect between two materials when the normal stress is small. In this case, the reduction of D

_{s}is more distinct.

#### 4.3. Discussions

## 5. Conclusions

- (1)
- The failure mode of the rock–mortar interface changes from brittle fracture to interfacial friction in cyclic shearing. The shear strength decreases continuously, and the reduction amplitude decreases gradually. The shear performance of malmstone–mortar interface is better than that of red sandstone–mortar interface, and blue sandstone–mortar interface is the lowest. With the increase of shearing times, the peak dilatancy angle decreases. The greater the normal stress, the greater the drop of peak dilatancy angle. The interface dilatancy angle corresponding to malmstone is larger, followed by red sandstone and blue sandstone.
- (2)
- As the time of shearing increases, both maximum interface height S
_{p}and interface height root mean square S_{q}decrease. The arithmetic mean difference of surface height S_{a}also decreases only under the 2 Mpa normal stress, and it fluctuates greatly when the normal stress is 4 Mpa. The variation laws of skew coefficient S_{sk}and peak coefficient S_{ku}are not obvious. For more shearing times, the value of the aspect ratio of texture topography ratio S_{tr}is greater, representing the anisotropy of the rock–mortar interface decreases. Meanwhile, texture direction angle S_{td}is reduced, especially in the case of high normal stress. - (3)
- All the surface topography mixed parameters used in this study, including fractal dimension D
_{s}, root mean square of slope of interface S_{dq}, and interface area ratio S_{dr}, decrease with the shearing times, wherein when the normal stress is small, the redution of fractal dimension D_{s}is greater. The increase in shearing times lowers the surface complexity and the the peak curvature, which produces a more rounded peak. Based on the contour map, the interface steepness decreases and the sag continuously expands. According to the Abbot–Firestone curve, it is judged that the height of bearing shear body gradually decreases.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 8.**Normalized relationship between shear strength and shear times. (

**a**) Normal stress = 4 MPa; (

**b**) Normal stress = 2 MPa.

**Figure 10.**The relationship between shear displacement, dilatancy angle, and shear stress. (

**a**) First shearing; (

**b**) Second shearing; (

**c**) Third shearing.

**Figure 12.**The three-dimensional scanning of CD-3 interface for each shearing. (

**a**) Before shearing; (

**a**) Before shearing; (

**c**) Second shearing; (

**d**) Third shearing.

**Figure 16.**Contour map of CD-3 in cyclic shearing. (

**a**) Before test; (

**b**) First shearing; (

**c**) Second shearing; (

**d**) Third shearing.

**Figure 17.**Abbott–Firestone curve of CD-3 in cyclic shearing. (

**a**) Before test; (

**b**) First shearing; (

**c**) Second shearing; (

**d**) Third shearing.

Type | UCS/Mpa | Cohesion/Mpa | Friction Angle/° |
---|---|---|---|

Malmstone (A) | 72.00 | 9.00 | 61.00 |

Red sandstone (B) | 29.50 | 3.93 | 52.00 |

Blue sandstone (C) | 33.00 | 2.60 | 51.70 |

Sample Number | Normal Stress/MPa | Shear Rate/mm × s^{−1} | Shear Times |
---|---|---|---|

AD-1 | 4 | 0.01 | 3 |

AD-2 | |||

AD-3 | |||

BD-1 | |||

BD-2 | 2 | 0.01 | 3 |

CD-1 | |||

CD-2 | |||

CD-3 |

Number | First Shearing Stress/MPa | Second Shearing Stress/MPa | Third Shearing Stress/MPa |
---|---|---|---|

AD-1 | 6.08 | 4.42 | 4.16 |

AD-2 | 6.20 | 4.35 | 4.11 |

AD-3 | 6.29 | 4.43 | 4.32 |

BD-1 | 4.88 | 2.73 | 2.39 |

BD-2 | 3.25 | 2.15 | 1.74 |

CD-1 | 3.91 | 1.82 | 1.61 |

CD-2 | 3.08 | 1.76 | 1.51 |

CD-3 | 2.97 | 1.73 | 1.44 |

Interface Number | Topography Parameters | Before Tests | First Shearing | Second Shearing | Third Shearing |
---|---|---|---|---|---|

AD-1 | S_{p}/mm | 2.41 | 2.36 | 2.99 | 2.38 |

S_{a}/mm | 1.16 | 1.19 | 1.22 | 1.22 | |

S_{q}/mm | 1.39 | 1.5 | 1.39 | 1.39 | |

S_{sk} | −0.837 | −1.45 | 0.13 | 0.22 | |

S_{ku} | 2.89 | 5.98 | 1.76 | 1.75 | |

AD-2 | S_{p}/mm | 3.96 | 4.2 | 4.07 | 4.81 |

S_{a}/mm | 1.81 | 2.02 | 1.62 | 1.09 | |

S_{q}/mm | 2.21 | 2.71 | 1.85 | 1.82 | |

S_{sk} | −0.386 | −1.37 | 0.31 | 0.12 | |

S_{ku} | 3.09 | 7 | 1.94 | 2.12 | |

AD-3 | S_{p}/mm | 4.76 | 4.57 | 4.23 | 4.13 |

S_{a}/mm | 2.55 | 1.96 | 1.81 | 1.78 | |

S_{q}/mm | 3.51 | 2.32 | 2.12 | 2.07 | |

S_{sk} | −1.25 | −0.13 | −0.03 | 0.01 | |

S_{ku} | 4.11 | 2.06 | 2.06 | 2.01 | |

BD-1 | S_{p}/mm | 4.55 | 4.41 | 3.06 | 6.56 |

S_{a}/mm | 1.84 | 2.18 | 1.61 | 1.28 | |

S_{q}/mm | 2.23 | 2.9 | 1.51 | 1.13 | |

S_{sk} | −0.72 | −1.2 | −0.48 | 0.06 | |

S_{ku} | 3.13 | 3.44 | 2.21 | 1.62 | |

BD-2 | S_{p}/mm | 5.68 | 4.16 | 3.69 | 3.28 |

S_{a}/mm | 1.72 | 1.5 | 1.43 | 1.38 | |

S_{q}/mm | 2.22 | 1.92 | 1.89 | 1.88 | |

S_{sk} | −1.41 | −0.62 | 1.14 | 1.80 | |

S_{ku} | 4.21 | 3.14 | 2.99 | 1.64 | |

CD-1 | S_{p}/mm | 5.27 | 4.79 | 4.62 | 3.7 |

S_{a}/mm | 1.47 | 1.34 | 1.22 | 1.18 | |

S_{q}/mm | 1.82 | 1.6 | 1.52 | 1.4 | |

S_{sk} | −0.29 | −0.004 | 0.31 | 1.38 | |

S_{ku} | 2.81 | 2.18 | 1.97 | 1.18 | |

CD-2 | S_{p}/mm | 5.78 | 3.28 | 3.15 | 2.36 |

S_{a}/mm | 2.04 | 1.11 | 1.19 | 0.88 | |

S_{q}/mm | 2.47 | 1.34 | 1.1 | 0.96 | |

S_{sk} | 0.01 | 0.10 | 0.04 | −0.08 | |

S_{ku} | 2.27 | 2.23 | 1.95 | 1.51 | |

CD-3 | S_{p}/mm | 6.88 | 5.67 | 5.61 | 5.06 |

S_{a}/mm | 1.75 | 1.58 | 1.48 | 1.24 | |

S_{q}/mm | 2.14 | 2.06 | 2.07 | 2.03 | |

S_{sk} | −0.52 | 0.08 | 0.08 | 0.24 | |

S_{ku} | 2.71 | 2.65 | 2.49 | 2.33 |

Interface Number | Topography Parameters | Before Tests | First Shearing | Second Shearing | Third Shearing |
---|---|---|---|---|---|

AD-1 | S_{tr} | 0.383 | 0.379 | 0.382 | 0.384 |

S_{td}/° | 48.6 | 49.6 | 48.2 | 48 | |

S_{pd}/mm^{−2} | 0.241 | 0. 207 | 0.187 | 0.176 | |

S_{pc}/mm^{−1} | 0.31 | 0.291 | 0.142 | 0.129 | |

AD-2 | S_{tr} | 0.3 | 0.284 | 0.309 | 0.346 |

S_{td}/° | 44 | 46,2 | 45.7 | 45.6 | |

S_{pd}/mm^{−2} | 0.314 | 0.339 | 0.257 | 0.252 | |

S_{pc}/mm^{−1} | 0.348 | 0.677 | 0.615 | 0.538 | |

AD-3 | S_{tr} | 0.258 | 0.29 | 0.371 | 0.378 |

S_{td}/° | 47 | 46.1 | 45.9 | 45.5 | |

S_{pd}/mm^{−2} | 0.782 | 0.621 | 0.522 | 0.494 | |

S_{pc}/mm^{−1} | 0. 802 | 0.766 | 0.751 | 0.732 | |

BD-1 | S_{tr} | 0.307 | 0.311 | 0.336 | 0.376 |

S_{td}/° | 36.5 | 36.1 | 35.7 | 35.5 | |

S_{pd}/mm^{−2} | 0.491 | 0.392 | 0.321 | 0.301 | |

S_{pc}/mm^{−1} | 0.314 | 0.302 | 0.275 | 0.223 | |

BD-2 | S_{tr} | 0.289 | 0.319 | 0.325 | 0.33 |

S_{td}/° | 51.2 | 51 | 50.7 | 50.6 | |

S_{pd}/mm^{−2} | 0.411 | 0.377 | 0.369 | 0.362 | |

S_{pc}/mm^{−1} | 0.278 | 0.241 | 0.223 | 0.22 | |

CD-1 | S_{tr} | 0.382 | 0.431 | 0.436 | 0.466 |

S_{td}/° | 33.3 | 32 | 31.5 | 31.3 | |

S_{pd}/mm^{−2} | 0.583 | 0.544 | 0.497 | 0.437 | |

S_{pc}/mm^{−1} | 0.254 | 0.196 | 0.127 | 0.126 | |

CD-2 | S_{tr} | 0.192 | 0.197 | 0.263 | 0.291 |

S_{td}/° | 36.1 | 35.7 | 35.5 | 35 | |

S_{pd}/mm^{−2} | 0.732 | 0.724 | 0.688 | 0.685 | |

S_{pc}/mm^{−1} | 0.409 | 0.351 | 0.299 | 0.229 | |

CD-3 | S_{tr} | 0.312 | 0.314 | 0.32 | 0.329 |

S_{td}/° | 40 | 36.2 | 35.6 | 31.1 | |

S_{pd}/mm^{−2} | 0.781 | 0.755 | 0.692 | 0.663 | |

S_{pc}/mm^{−1} | 0.313 | 0.282 | 0.259 | 0.234 |

Interface Number | Topography Parameters | Before Tests | First Shearing | Second Shearing | Third Shearing |
---|---|---|---|---|---|

AD-1 | S_{dq} | 2.13 | 2.07 | 1.64 | 1.3 |

S_{dr}/% | 22 | 30.6 | 24.17 | 22 | |

D_{s} | 2.24 | 2.43 | 2.21 | 2.23 | |

AD-2 | S_{dq} | 3.42 | 3.46 | 2.11 | 0.005 |

S_{dr}/% | 89.9 | 109 | 87.1 | 86.7 | |

D_{s} | 2.28 | 2.29 | 2.22 | 2.19 | |

AD-3 | S_{dq} | 3.15 | 3.05 | 1.72 | 0.782 |

S_{dr}/% | 70.5 | 84.7 | 76.5 | 70.3 | |

D_{s} | 2.21 | 2.26 | 2.29 | 2.26 | |

BD-1 | S_{dq} | 2.48 | 1.68 | 1.64 | 1.62 |

S_{dr}/% | 76.8 | 56.6 | 49 | 48 | |

D_{s} | 2.49 | 2.29 | 2.3 | 2.28 | |

BD-2 | S_{dq} | 3.21 | 2.17 | 1.88 | 1.72 |

S_{dr}/% | 66 | 57.3 | 52.1 | 50 | |

D_{s} | 2.31 | 2.28 | 2.28 | 2.21 | |

CD-1 | S_{dq} | 3.06 | 2.57 | 1.62 | 1.39 |

S_{dr}/% | 51.2 | 47 | 42.7 | 36 | |

D_{s} | 2.59 | 2.32 | 2.23 | 2.21 | |

CD-2 | S_{dq} | 2.749 | 2.12 | 0.98 | 1.297 |

S_{dr}/% | 31.9 | 26.6 | 16 | 15 | |

D_{s} | 2.34 | 2.29 | 2.25 | 2.25 | |

CD-3 | S_{dq} | 2.6 | 2.1 | 1.71 | 0.48 |

S_{dr}/% | 67 | 61 | 54 | 52 | |

D_{s} | 2.36 | 2.3 | 2.28 | 2.22 |

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## Share and Cite

**MDPI and ACS Style**

Xie, L.; Tang, W.; Lin, H.; Lei, F.; Chen, Y.; Wang, Y.; Zhao, Y. Apparent Deterioration Law and Shear Failure Mode of Rock–Mortar Interface Based on Topography-Sensing Technology. *Materials* **2023**, *16*, 763.
https://doi.org/10.3390/ma16020763

**AMA Style**

Xie L, Tang W, Lin H, Lei F, Chen Y, Wang Y, Zhao Y. Apparent Deterioration Law and Shear Failure Mode of Rock–Mortar Interface Based on Topography-Sensing Technology. *Materials*. 2023; 16(2):763.
https://doi.org/10.3390/ma16020763

**Chicago/Turabian Style**

Xie, Linglin, Wenyu Tang, Hang Lin, Fan Lei, Yifan Chen, Yixian Wang, and Yanlin Zhao. 2023. "Apparent Deterioration Law and Shear Failure Mode of Rock–Mortar Interface Based on Topography-Sensing Technology" *Materials* 16, no. 2: 763.
https://doi.org/10.3390/ma16020763