In this paper, the mechanism of the interface dilatancy of cement mortar rockbolts is studied based on the phenomenon of splitting failure of samples with a high sand content in the grouting material in laboratory tests. A conceptual model of the interface layer is used to explain the dilatancy mechanism of the interface. Based on the thick-walled cylinder theory, the causes of splitting failure of the samples are analyzed. By using the numerical simulation method, the influences of different dilatancy angles of the interface layer on the interface shear stress and the radial stress are analyzed. The results show that the sand content of the grouting material has a substantial effect on the bearing capacity of the rockbolt. The higher the sand content in the grouting material is, the more obvious the interface dilatancy will be, and the greater the radial stress generated by dilatancy will be, which will produce a higher bearing capacity of the anchorage system. Under the same load, the maximum shear stress of the interface layer increases with increasing dilatancy angle. Similarly, the larger the dilatancy angle of the interface layer is, the greater the radial stress caused by dilatancy will be. Away from the interface layer, the radial stress decays rapidly. The influence range of the radial stress caused by dilatancy is mainly in the interface layer and the rock nearby.
Fully grouted bolts have been widely used in underground engineering applications. Such bolts mainly provide the support force through the shear stress between the bolt and the grout and between the grout and the surrounding rock. According to the different grouting materials, full grouted rockbolts can be divided into two categories: cement mortar grouted rockbolts and resin grouted rockbolts. This research focuses on cement mortar grouted rockbolts.
A large number of studies have shown that interface failure is a common failure mode in anchorage systems [
Since the application of anchorage structures in engineering practice, many scholars have noticed the importance of the interface stress distribution for the design of anchorage structures. Benmokrane et al. [
It is generally believed that the shear strength of the interface, except for the bond stress, comes from the friction stress at the interface. Yazici and Kaiser [
After analyzing the literature, it is evident that most scholars focused on the interface between the bolt and the grout. In these studies, the mechanism of dilatancy caused by the roughness of the bolt surface was mainly studied. Surprisingly, scholars paid little attention to the influence of the material composition of the grout, especially the sand content in the cement mortar on the interface dilatancy. Therefore, it is necessary to study the influence of the sand content in the cement mortar on the anchorage mechanism of the anchorage structure. In this paper, the mechanism of the interface dilatancy of cement mortar rockbolts is studied by laboratory tests. The reason for the splitting failure of samples and the mechanism of interface dilatancy are analyzed. Based on the numerical simulation, the influence of different dilatancy degrees of the interface layer on the interface shear stress and the radial stress is analyzed. The research results can provide a reference for the design of cement mortar rockbolts, which can optimize the design and promote the development of anchorage theory.
The purpose of this experiment is to analyze the influence of the sand content in the cement mortar on the anchorage mechanism of the anchorage structure. The influence of the rockbolt length and sand content in the cement mortar on the anchorage mechanism is considered.
A new set of molds is developed to make the samples, as shown in Figure
Diagram of the mold.
C40 concrete is poured to simulate rock, and the heights of the samples are 150 mm, 200 mm, 250 mm, and 300 mm. Cement mortar is used as the grouting material, and the cement-sand ratios (volume ratio) of the grouting material are 1 : 0, 1 : 1, and 3 : 1. The cement is ordinary Portland cement, and the sand is quartz sand. Table
Sample ID, cement-sand ratio, and anchorage length.
Sample ID | 1-0 | 2-0 | 3-0 | 4-0 | 1-1 | 2-1 | 3-1 | 4-1 | 1-3 | 2-3 | 3-3 | 4-3 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Cement-sand ratio | 1 : 0 | 1 : 0 | 1 : 0 | 1 : 0 | 1 : 1 | 1 : 1 | 1 : 1 | 1 : 1 | 1 : 3 | 1 : 3 | 1 : 3 | 1 : 3 |
Anchorage length (mm) | 300 | 250 | 200 | 150 | 300 | 250 | 200 | 150 | 300 | 250 | 200 | 150 |
The rockbolt is simulated with a 16 mm diameter HRB335 steel bar. The steel bar is inserted into the center of the bore hole, and the cement mortar is injected into the hole. To make the cement-sand denser, the pouring process is carried out on a shaking table. The sample after pouring is shown in Figure
Sample after pouring.
After the samples are cured and meet the test requirements, the bottom of the sample is connected to the steel plate. The pull rod at the bottom of the steel plate is placed in the lower grip of the testing machine. The upper grip of the testing machine is connected to the rockbolt anchored in the sample. It should be noted that the lower pull rod and the upper rockbolt must be on the same axis, as shown in Figure
Sample mounted on the testing machine.
According to the standards for test method of performance on building mortar (JGJ/T70-2009) [
Material properties of the cement mortar.
Cement-sand ratio | Cubic compressive strength (MPa) | Elastic modulus (GPa) |
---|---|---|
1 : 0 | 24.2 | 20.5 |
1 : 1 | 21.4 | 18.9 |
1 : 3 | 10.3 | 16.1 |
The failure modes of all the samples in the test are shown in Table
Failure modes of the samples.
Failure mode | Debonding failure | Splitting failure |
---|---|---|
Sample ID | 1-0, 2-0, 3-0, 4-0, | 1-1, 1-3, 2-3, 3-3 |
2-1, 3-1, 4-1, 4-3 |
Debonding failure of the sample.
Splitting failure of the sample.
In this test, although there is no restraint around the sample, the failure load of the sample is not consistent with the real bearing capacity of the anchorage system. However, it is precisely because of this that there is an opportunity to find a very regular phenomenon in the test; that is, most samples with splitting failure are those with more sand content in the cement mortar, and the failure loads of the samples with a high sand content are much larger than those of the other samples. Table
Failure loads of the samples (kN).
Cement-sand ratio | Anchorage length (mm) | |||
---|---|---|---|---|
300 | 250 | 200 | 150 | |
1 : 0 | 14.0 | 3.5 | 8.1 | 4.7 |
1 : 1 | 20.4 | 16.7 | 9.8 | 12.0 |
1 : 3 | 48.9 | 59.1 | 41.9 | 21.9 |
Failure loads of the samples with splitting failure are in italics in the table.
The dilatancy at the interface of the anchorage structure is generally believed to be caused by relative slip between the steel bar with a rough surface and the grouting material [
Under the same conditions, it is unexpected that the sand content in the grouting material has a substantial effect on the bearing capacity of the anchorage system. This shows that the radial stress produced by dilatancy is very large in the sample with a high sand content. This problem can also be explained by the surface status between the grout and the concrete after the splitting failure of the sample. Figure
Surface statuses of the grouting body.
Figure
Surface statuses of the borehole of the splitting failure sample.
Conceptual model of the interface layer.
The load-displacement curves of samples 2-0 and 2-3 are shown in Figure
Load-displacement curves of samples 2-0 and 2-3.
Figure
Load-displacement curves of samples with a cement-sand ratio of 1 : 3.
Linear stage (OA): in this stage, the deformation of the anchorage structure is very small, and the interface has not yet produced relative slip. The deformation mainly comes from the elastic deformation of the steel rockbolt. Therefore, the load-displacement curve in this stage is approximated as a straight line. As shown in Figure
Dilatancy-hardening stage (AP): in this stage, the interface begins to experience relative slip, and interface dilatancy appears. With the increase in the pull-out load, the interface near the load end begins to debond, and the interface dilatancy effect is more obvious. In this stage, the pull-out load of the anchorage structure does not decrease but increases with increasing displacement. The dilatancy has a substantial effect on the bearing capacity. With the increase in the load, the interface debonding moves from the load end to the depth, the relative length of the interface slip increases gradually, the dilatancy effect becomes increasingly substantial, and the radial stress generated by dilatancy becomes increasingly larger. As a result, radial splitting failure of the concrete occurs, and the whole anchorage structure suddenly collapses and fails. Because the anchorage length of sample 4-3 is only 150 mm, the interface slip distance is short, the radial stress generated by dilatancy is relatively small, and the concrete has not split.
Dilatancy-softening stage (PC): as seen from the load-displacement curve of sample 4-3 in Figure
Residual stress stage (CD): in this stage, with increasing relative sliding distance of the interface, the interface dilatancy disappears completely. Only the residual shear stress on the interface is left. With increasing displacement, the contact area of the interface decreases, and the bearing capacity of the anchorage system gradually decreases until the rockbolt and grout are pulled out.
By comparing Figures
The rock material concrete strength refers to the maximum load that it can bear when it is damaged under an external load. The determination of the mechanical strength of rock materials is still confined to the traditional solid mechanics system that takes homogeneous materials such as metals as research objects. Although some new research methods have been reported recently [
When splitting failure occurs, the inner wall of the borehole must be subjected to radial stress. During the test, there is no restraint or confining pressure around the sample, so the source of the radial stress is caused by the interface dilatancy when the interface between the grouting body and the concrete produces relative slip. Figure
Schematic diagram of the stress on the borehole and the surrounding concrete.
After there is dilatancy of the interface, the shear strength of the interface is generally expressed by the following equation:
According to the elastic theoretical solution for a thick-walled cylinder, the increment of the normal stress when the cylinder wall expands radially is as follows [
Since the normal stiffness
The physical model test can obtain accurate and reliable results when carried out under strictly controlled test conditions. However, it takes considerable time and money to study the parameters through physical model testing. Moreover, some parameters are difficult to change in physical model tests, such as the dilatancy angle. Numerical simulations can effectively solve this problem. It is very convenient to study the parameters by changing only one parameter at a time. At present, it is true that the selection of input data and parameters does not fully match the actual situation in the numerical simulation. However, we can focus on the influence of the parameters on the dilatancy from the overall trend rather than the accurate value and detailed analysis.
Although the three-dimensional problem is closer to the actual situation, to save calculation time and improve analysis convenience, the calculation model is simplified as an axisymmetric problem. The dead weight of the rockbolt, the grouting body, and the rock is not included in the analysis. The bottom boundary of the model is constrained by the vertical displacement, while the vertical boundary is constrained by the horizontal direction. The numerical calculation model is shown in Figure
(a) Overview of the model; (b) mesh for the numerical model.
It can be seen from the results of the laboratory model test that the main position of dilatancy is the contact surface between the grouting body and the concrete. At present, although there are many interface models that are commonly used in numerical calculations to simulate the contact between the rock and the grouting body, none of these models can simulate the dilatancy characteristics of the interface. Therefore, in this numerical calculation, an interface layer is set between the grouting body and the rock. This interface layer is not a surface but a solid with a certain thickness, which can simulate the dilatancy behavior of the interface. The thickness of the interface layer between the grouting body and the rock may depend on many factors, such as the method of forming the interface and the physical and mechanical properties of the grouting material. Unfortunately, the thickness of this interface layer is still unknown in the existing literature. In this study, considering the following factors, the thickness of the interface layer is selected as 2 mm: The sand commonly used in practical engineering applications can be divided into fine, medium, and coarse types according to the particle size. The average particle sizes are 0.125–0.25 mm, 0.25–0.5 mm, and 0.5–1 mm. According to the surface wear of the grouting body after the test, as shown in Figure In [ A numerical analysis model with the same size and boundary conditions as in the laboratory test is established, and the thickness of the interface layer is verified. The calculation results of the numerical simulation are in agreement with the results of the laboratory test, as shown in Figure
The size of the mesh element is selected appropriately to obtain better convergence, so that substantial computing time is not needed. The finite element mesh is shown in Figure
Comparison between the numerical simulation and laboratory test results.
The rockbolt is simulated by an isotropic material and the cement mortar; rock and interface layer are simulated by the Drucker-Prager material model, which can reflect the dilatancy of the material. The material parameters are shown in Table
Mechanical parameters of the materials.
Rockbolt | 200 | 0.3 | ||
Grout | 18 | 0.24 | 1 | 35 |
Rock | 32.5 | 0.21 | 3.8 | 56 |
Interface layer | 2 | 0.35 | 0.5 | 30 |
At present, there are two extreme methods for addressing the dilatancy angle.
One is to regard the yield function of the material as the plastic potential function of the material, namely, the associated flow rule. In this case, the internal friction angle is equal to the dilatancy angle. The disadvantage of this method is that the influence of the dilatancy angle is given too much consideration.
The other method is the nonassociated flow rule, when the dilatancy angle is equal to zero, and the influence of the dilatancy angle is not considered at all.
In this numerical simulation, the dilatancy angle of the interface layer is set to 5°, 10°, 15°, 20°, 25°, and 30°, respectively, to characterize the dilatancy effect of the interface layer, and the influence of the interface dilatancy on the interface shear stress and the bearing capacity of the anchorage structure is studied.
A pull-out load of 200 kN is applied to the rockbolt, and path 1 is defined on the outside of the interface layer, as shown in Figure
Distributions of the interface shear stress under different dilatancy angles for a rockbolt load of 200 kN.
Maximum shear stress at the interface under different dilatancy angles.
When the dilatancy angle is
The radial stresses around the borehole obtained by the numerical calculation are mapped to path 2 to obtain the curves of the radial stress under different dilatancy angles, as shown in Figure
Curves of the radial stress under different dilatancy angles.
Maximum radial stress at the interface under different dilatancy angles.
As seen from Figure
As shown in Figures
Most scholars focus on the influence of the strength characteristics of the grouting material on the anchorage mechanism of the anchorage structure. A large number of results show that the strength properties of the grouting material play an important role in the shear stress distribution and axial stress distribution along the rockbolt. However, in this study, the research focus is mainly on the influence of the sand content of the grouting material on the interface dilatancy. Through the research of this paper, many valuable conclusions are obtained. Even so, these studies have many other problems that require discussion and deserve further consideration. It is known that there are many factors that affect the dilatancy angle, and, in special cases, the dilatancy angle also changes with the change in the external conditions, so it is very difficult to accurately obtain the dilatancy angle of the interface layer. Therefore, in the numerical calculation, we can only use different dilatancy angle to simulate the influence of the sand content on the bearing capacity. In future research, the influence of the sand content in the grouting material on the dilatancy angle of the interface should be carried out, and the relationship between the sand content and the dilatancy angle should be established to obtain the quantitative expression of the sand content on the improvement of the interface shear strength. In actual engineering design, on the premise of ensuring the strength of the grouting material and other requirements and according to the research conclusions of this paper, the sand content can be appropriately increased to improve the bearing capacity of the anchorage system. However, this needs to be verified by field tests.
In this paper, according to the phenomenon of radial splitting of the samples found in the laboratory model test, the mechanism of the interface dilatancy of cement mortar rockbolt is studied. The primary conclusions are summarized as follows: The sand content of the grouting material has a substantial influence on the ultimate pull-out force of the anchorage system. Under the same conditions, the ultimate pull-out force of the sample increases sharply with increasing sand content in the grouting material. In the grouting material, the higher the sand content is, the more obvious the dilatancy of the interface will be. The larger the radial stress caused by the interface dilatancy is, the higher the interface shear strength is, and the larger the bearing capacity of the anchorage system is. Under the same load conditions, as the dilatancy angle of the interface layer increases, the maximum shear stress of the interface layer also increases. Due to dilatancy, radial stress is generated near the interface layer. With the increase in the dilatancy angle, the radial stress increases. Far away from the interface layer, the radial stress decreases rapidly, and the influence of the radial stress is mainly in the interface layer and the rock nearby. Due to the existence of the radial stress caused by dilatancy, the mechanical properties of the interface layer and the bearing capacity of the anchorage system have been substantially improved. Due to the existence of the interface layer, the interface becomes the weak link of the whole anchorage system. The failure of the anchorage system starts from the position of the interface, and, with increasing stress, relative slip occurs at the interface. If the interface layer can produce dilatancy, the bearing capacity of the anchorage system will be substantially improved.
The data used to support the findings of this study are included within the article.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This study was supported by the National Natural Science Foundation of China (51804182).