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Cement grout is widely used in civil engineering and mining engineering. The shear behaviour of the cement grout plays an important role in determining the stability of the systems. To better understand the shear behaviour of the cement grout, numerical direct shear tests were conducted. Cylindrical cement grout samples with two different strengths were created and simulated. The numerical results were compared and validated with experimental results. It was found that, in the direct shear process, although the applied normal stress was constant, the normal stress on the contacted shear failure plane was variable. Before the shear strength point, the normal stress increased slightly. Then, it decreased gradually. Moreover, there was a nonuniform distribution of the normal stress on the contacted shear failure plane. This nonuniform distribution was more apparent when the shear displacement reached the shear strength point. Additionally, there was a shear stress distribution on the contacted shear failure plane. However, at the beginning of the direct shear test, the relative difference of the shear stresses was quite small. In this stage, the shear stress distribution can be assumed uniform on the contacted shear failure plane. However, once the shear displacement increased to around the shear strength point, the relative difference of the shear stresses was obvious. In this stage, there was an apparent nonuniform shear stress distribution on the contacted shear failure plane.

Cement is grey fine powder that is widely used in civil engineering and mining engineering [

The mechanical properties of the cement grout have a significant effect in deciding the performance of the rock reinforcement systems [

To study the axial behaviour of the cement grout, researchers mainly used the Uniaxial Compressive Strength (UCS) tests. Feldman and Beaudoin [

The above research played an important role in revealing the mechanical performance of cement grout. However, experimental tests proved that in the fully grouted rock reinforcing system, failure of the system usually occurred at the bolt/grout interface [

To study the shear behaviour of cement grout, researchers commonly used triaxial tests and direct shear tests. For triaxial tests, Hyett et al. [

Therefore, the direct shear test was a better approach to study the shear behaviour of the cement grout for the rock reinforcement scenario. The direct shear test is a traditional method to evaluate the shear strength of a material. Normally, a shear box is prepared. Then, the tested sample is cut to the desired geometry with the required dimension. After that, the sample was set in the shear box and installed in the apparatus. Operators can apply normal stress on the sample and then apply shear velocity along the shear direction. This test is continued until the shear strength was obtained. In this way, the shear strength of the material can be acquired. Moosavi and Bawden [

Those research provided new insights and knowledge in revealing the shear performance of cement grout. However, most research was conducted with experimental tests. Compared with that, much less work has been performed via numerical simulation. Therefore, this study aims at studying the shear behaviour of the cement grout with numerical simulation.

First, a numerical calculating program was selected to conduct this research. After that, numerical direct shear tests were performed to evaluate the shear behaviour of the cement grout. Then, the numerical calculating results were validated with experimental results. Last, the shear stress distribution on the shear failure plane was investigated.

In this study, the three-dimensional software FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) was used. This program was developed by the Itasca Consulting Group.

The reason to use this program is that the Itasca Company developed the interface element in it. This interface element is composed of triangular elements and corresponding nodes. Moreover, the interface element is defined with the shear coupling constitutive law. In this case, once shear displacement occurs in the interface element, shear stress at the interface accumulates and can be calculated. Relying on this function, the shear behaviour of a material can be studied.

The authors of this study previously used the two-dimensional software FLAC to simulate the shear failure process of the bolt/grout interface [

A vast of direct shear tests were performed by Moosavi and Bawden [

Before the direct shear test was conducted, UCS tests were performed to acquire the basic mechanical properties of the grout, including the UCS, Young’s modulus, and Poisson’s ratio. Detailed information about the UCS test process and results were reported by Moosavi [

In the numerical simulation in FLAC3D, the

Geometry of the UCS test created in numerical simulation.

In the numerical UCS test, a cylindrical mesh was established. At the top and bottom of the cylinder, two square steel plates were established to simulate the loading plates. The whole mesh was composed of 16032 zones and 16531 grid points. For the numerical plate, there were 32 zones and 100 grid points. For the numerical sample, there were 16000 zones and 16441 grid points.

A strain softening model was used for the cylindrical sample. It was developed based on the MC model. Compared with the MC model, the strain softening model had additional input parameters: the cohesion table and the internal friction angle table. With those two parameters, the cohesion and internal friction angle of the materials can decrease with the increasing plastic shear strain. Therefore, this model can simulate the postpeak behaviour of materials.

The reason to use this strain softening model was that this model could simulate the postpeak behaviour of materials. Therefore, it is better in reflecting the mechanical behaviour of materials.

An elastic model was used for the square plates. The reason to use the elastic model to simulate the square plate was that in the experimental compressive test, the cement-based sample was compressed by the steel plate. Since the strength of the steel plate was much higher than the cement-based sample, failure only occurred in the cement-based sample. The steel plate consistently kept the elastic state. The input parameters for the cylindrical sample and the square plates are tabulated in Table

Input parameters for the sample and the plate.

Group | Input parameter | Value |
---|---|---|

Sample | Bulk modulus (GPa) | 8.44 |

Shear modulus (GPa) | 5.06 | |

Cohesion (MPa) | 19.3 | |

Internal friction angle (degree) | 21 | |

Tension (MPa) | 2 | |

Plate | Bulk modulus (GPa) | 133.33 |

Shear modulus (GPa) | 80 |

The velocity of the plates was fixed. Moreover, the initial velocity of the top plate along the ^{−7} meters per step (minus represented that the velocity was along the negative direction of the

In the simulation process, the displacement along the

Grid points monitored in the simulation process.

Those four displacements were averaged as the uniaxial displacement of the sample, as shown in the following equation:_{a} is the axial displacement, m, and _{ai} is the axial displacement of the grid point

In the UCS test, to calculate Poisson’s ratio, the circumferential strain gauge was usually attached at the middle of the sample to record the circumferential displacement of the sample. Then, in this simulation, the circumferential displacement of four grid points at the middle of the outside surface of the sample was monitored. Those four displacements were also averaged as the circumferential displacement of the sample, as shown in the following equation:_{c} is the circumferential displacement of the sample, m, and _{ci} is the circumferential displacement of the grid point

Since the bottom plate was stabilised in the whole simulation process, the reaction force along the

Then, the numerical UCS test was conducted. The stress to strain relationship of the sample is shown in Figure

Stress to strain relationship of the cement grout sample.

In the experimental test, the UCS of the cement grout sample was 50.6 MPa, which was consistent with the numerical simulation results.

It also shows that in numerical simulation, after the stress of the sample reached the peak, the circumferential strain decreased. To check the reason, the circumferential displacement of a grid point was taken as an example and plotted. The grid point at the right middle of the sample (with an ID of 1430) was selected. The circumferential displacement of the grid point with the calculating time step is shown in Figure

Circumferential displacement of the grid point at the right middle of the sample.

Based on the numerical simulation, Young’s modulus and Poisson’s ratio can also be acquired. The results showed that Young’s modulus in the numerical simulation was 13.47 GPa. Poisson’s ratio can be calculated as follows [_{c} is the circumferential strain of the sample; and _{a} is the axial strain of the sample.

Then, Poisson’s ratio can be calculated as 0.26. Comparing Young’s modulus and Poisson’s ratio acquired from numerical simulation with those acquired from experimental tests, there was a close match between them, as shown in Table

Comparison between the mechanical properties of the cement grout acquired from laboratory tests conducted by Moosavi [

Properties | Laboratory test | Numerical simulation |
---|---|---|

UCS | 50.6 | 55.87 |

Young’s modulus (GPa) | 12.66 | 13.47 |

Poisson’s ratio | 0.25 | 0.26 |

The input mechanical parameters used in the UCS simulation were then used in this section to simulate the direct shear process. Moosavi and Bawden [

In FLAC3D, a numerical cylindrical sample whose dimension was the same as the experimental sample was established. The sample was composed of two sections, namely, the top section and the bottom section. In the whole numerical model, there were 18000 zones and 19232 grid points. It should be mentioned that in the direct shear test, a shear failure plane is a predefined plane. Consequently, in numerical simulation, an interface was created at the middle of the sample, namely between the top section and the bottom section, to simulate the shear failure plane. The interface was composed of 49128 elements and 24725 nodes.

The constitutive law of the created interface was MC model and the input parameters of the interface are tabulated in Table

Input parameters for the interface.

Group | Input parameter | Value |
---|---|---|

Interface | Normal stiffness (GPa/m) | 40 |

Shear stiffness (GPa/m) | 8.28 | |

Cohesion (MPa) | 5.3 | |

Friction angle (degree) | 30 |

The top section was fixed along the ^{−5}. With this method, the initial normal stress equilibrium condition was acquired. The normal stress distribution in the sample is shown in Figure

Normal stress distribution in the sample.

Before the direct shear test was performed, the displacement along the shearing direction of four grid points at the top surface of the sample was monitored. In the simulation process, the displacements of those four grid points were averaged as the shear displacement of the sample.

It is more important to monitor the shear stress in the direct shear test process. To acquire this, in each step in the direct shear test process, each node on the interface was checked whether that node was still in contact. If it was, the shear force of that node was recorded and summed. The accumulated shear force was the whole shear force of the interface and was then divided by the area of the interface. The result was regarded as the shear stress of the interface.

Then, the direct shear test was performed. A shearing velocity of 1 × 10^{−6} meters per step was applied on the top section of the sample. This velocity was kept constant in the whole simulation process to simulate the servo control. The direct shear test was conducted until the sample failed.

The comparison between the numerical simulation result and the experimental test result is shown in Figure

Comparison between numerical simulation result and the experimental test conducted by Moosavi and Bawden [

In the shearing process, the averaged normal stress of the interface was also monitored. The variation of the normal stress on the interface is shown in Figure

Variation of the normal stress of the shear failure plane.

After the direct shear test, a plot of the normal stress distribution on the interface is shown in Figure

Normal stress distribution on the shear failure plane.

The results showed that the normal stress at the left side of the interface was zero. This was due to the separation of the top and bottom samples. Consequently, the interface was noncontact around the left side, as shown in Figure

State of the interface in the direct shear test: (a) before the direct shear test; (b) after the direct shear test.

Since it is more important to study the state of the interface that was contacted, the stresses on the contacted interface were further studied. At the left side of the contacted interface, the normal stress was apparently much higher, with a maximum normal stress of 3.56 MPa. Moreover, the normal stress on the interface decreased towards the shearing direction. At the right side, the normal stress was much lower, with minimum normal stress around 0.75 MPa.

As for the shear stresses on the interface, their distribution is shown in Figure

Shear stress distribution on the shear failure plane.

As for the contacted interface, the shear stress distribution was apparently not uniform. At the left side of the contacted interface, the shear stress was much higher, with a maximum of 7.36 MPa. Then, the shear stress decreased towards the shearing direction. On the right side, the shear stress was relatively lower, with a minimum of around 6.0 MPa. This trend was basically consistent with the distribution of the normal stress on the interface.

However, attention should be paid that Figures

After the direct shear test, the plastic state of the sample is shown in Figure

Plastic zone distribution in the sample.

Numerical simulation was also conducted on the same cement grout type while with relatively lower strength. First, the numerical UCS test was performed and compared with the experimental result to confirm the proper input parameters.

The UCS test was simulated in FLAC3D. The simulation process was generally consistent with the procedures described in Section

After the simulation, the stress to strain relationship of the sample was obtained. When the axial strain increased to 0.53%, the axial stress of the sample reached a peak of 46.09 MPa. In the experimental test, the measured UCS was 40.3 MPa. Therefore, there was a close match between them.

The Young’s modulus and Poisson’s ratio were also obtained. In the numerical simulation, Young’s modulus and Poisson’s ratio of the cement grout sample were 8.33 GPa and 0.26. A comparison between experimental and numerical results is shown in Table

Comparison between the experimental result reported by Moosavi [

Properties | Laboratory test | Numerical simulation |
---|---|---|

UCS | 40.3 | 46.09 |

Young’s modulus (GPa) | 8.571 | 8.33 |

Poisson’s ratio | 0.25 | 0.26 |

Then, the numerical direct shear test was performed. And the input parameters of the sample were the same as those used in the UCS simulation. A comparison between the experimental and the numerical results is shown in Figure

Comparison between the experimental result reported by Moosavi and Bawden [

Also, the variation of the normal stress on the shear failure plane was checked. In the simulation process, the normal stress on the shear failure plane was not constant. It had a slightly increasing trend at the beginning and then decreased gradually.

As mentioned in Section

On the numerical shear stress versus shear displacement curve for the cement grout with a

When the shear displacement was 0.6 mm, the shear stress and normal stress distribution on the shear failure plane were shown in Figure

Distribution of the shear stress and normal stress on the shear failure plane when the shear displacement arrived at 0.6 mm: (a) shear stress distribution; (b) normal stress distribution; (c) point selected on shear stress-shear displacement curve.

As for the normal stress, on the contacted interface, there was a nonuniform distribution. Specifically, the maximum normal stress was around 2.96 MPa, while the minimum normal stress was around 1.69 MPa. The relative difference between the maximum and the minimum normal stresses was 1.27 MPa, and the standard deviation was 0.29.

When the shear displacement increased to 0.94 m, the distribution of the shear stress and normal stress is shown in Figure

Distribution of the shear stress and normal stress on the shear failure plane when the shear displacement arrived at 0.94 mm: (a) shear stress distribution; (b) normal stress distribution; (c) point selected on shear stress-shear displacement curve.

The results also revealed that the nonuniform distribution of the normal stress became more apparent. On the contacted interface, the maximum normal stress was 3.63 MPa, occurring on the left side, while the minimum normal stress was 1.55 MPa, occurring on the right side. The relative difference between the maximum normal stress and minimum normal stress was 2.08 MPa, and the standard deviation was 0.5.

When the shear displacement reached 1.2 mm, the nonuniform shear stress distribution was still maintained, as shown in Figure

Distribution of the shear stress and normal stress on the shear failure plane when the shear displacement arrived at 1.2 mm: (a) shear stress distribution; (b) normal stress distribution; (c) point selected on shear stress-shear displacement curve.

As for the normal stress distribution, it was still nonuniform. At the left side of the contacted interface, the normal stress was much higher, with a maximum of 3.61 MPa. On the right side, the normal stress was smaller, with a minimum of 1.52 MPa. The relative difference between the maximum normal stress and minimum normal stress was 2.09 MPa, and the standard deviation was 0.5.

The above three figures showed that at the beginning of the direct shear test, on the contacted area of the shear failure plane, the relative difference between the maximum shear stress and minimum shear stress was quite small. However, with the shear displacement increasing, the relative difference became larger.

To show the variation of the relative difference of the shear stresses, in the calculating process, the relative difference between the maximum shear stress and the minimum shear stress was monitored, as shown in Figure

Variation of the relative difference of shear stresses in the numerical test.

Meanwhile, the relative difference between the maximum normal stress and minimum normal stress was monitored, as shown in Figure

Variation of the relative difference of normal stresses in the numerical test.

Following the current study, the authors plan to continue the numerical study on the shear behaviour of cement grouts. Considering that the shear behaviour of cement grouts can also be studied with triaxial tests, the authors may use the numerical method to evaluate the mechanical response of cement grouts under the triaxial loading condition. Its purpose is to reveal the shear failure mechanism of cement grout during the triaxial loading process.

The shear behaviour of the cement grout plays a significant role in determining the stability of systems and structures in civil and mining engineering. To better understand the shear behaviour of the cement grout, numerical direct shear tests were performed with the FLAC3D software.

Cylindrical cement grout samples with two different strengths were established and numerically simulated. The numerical simulation results were compared with experimental results. There was a good correlation between them, confirming that numerical simulation can be used to evaluate the shear behaviour of the cement grout.

The numerical direct shear test results showed that in the shearing process, along the shear failure plane, the shear stress at each point was not identical. There was a shear stress distribution on the contacted shear failure plane. At the beginning of the direct shear test, the relative difference of the shear stresses was quite small. Then, in this stage, it can be assumed that there was a uniform shear stress distribution on the contacted shear failure plane. However, once the shear displacement increased to around the shear strength point, the relative difference of the shear stresses became much larger. In this stage, the shear stress was nonuniformly distributed on the contacted shear failure plane. After that, the relative difference of the shear stress became stable.

Additionally, although the applied normal stress on the sample was constant, the normal stress on the contacted shear failure plane was variable. Before the shear strength point, the normal stress increased slightly. After that, the normal stress gradually decreased. There was also a distribution of the normal stress on the contacted shear failure plane. This normal stress distribution was not apparent at the beginning of the test. However, when the shear displacement increased to around the shear strength point, it became much obvious. Moreover, after that, this nonuniform normal stress distribution became stable.

The data used to support the findings of this study were included in the article.

The authors declare that they have no conflicts of interest.

This study was supported by the National Natural Science Foundation of China (51904302 and 52034009), the Yue Qi Distinguished Scholar Project (800015Z1179), and the Fundamental Research Funds for the Central Universities (2021YQNY05).

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