Keywords

1 Introduction

In the field of hydropower, transportation and other industries, construction disturbances (excavation, blasting, etc.) will inevitably cause damage to the surrounding rock, the rock belongs to the non-homogeneous initial damage brittle materials, its deformation and destruction process is accompanied by the emergence of local cracks and the expansion of the overall until the destruction of the damage is a cumulative process. Rock damage is a phenomenon that occurs both inside and on the surface at the same time, and the damage process is very complicated. Correctly describing the rock damage evolution phenomenon is a prerequisite for revealing the deformation and damage mechanism of rock, and at the same time, the weakening of the mechanical parameters of the surrounding rock leads to safety risks. Therefore, it is necessary to carry out research on quantitative assessment of rock damage.

Many scholars at home and abroad have carried out fruitful work in rock damage research. At present, rock damage research methods mainly include elastic modulus method, ultrasonic method, dissipated energy method, acoustic emission method, CT scanning method, resistivity method, and damage method, structural modeling method and others [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. With the continuous development of deep learning technology, digital images have also become a hotspot in current rock damage research [18,19,20,21,22,23,24,25,26]. The acoustic wave testing method can reflect the internal structure information of rocks and is widely used in the field of rock mechanics. It is fast, non-destructive and efficient. Cai Z L, et al. [3] obtained the acoustic characteristics of the rock failure process through a uniaxial compression test of granite, and the results showed that the wave velocity it is more sensitive to changes in compressive stress, but it is still difficult to detect changes in local micro defects; Engelder et al. [27] conducted a study on changes in rock ultrasonic waves and strain relaxation, and the results showed that there is a correlation between the change amplitude of wave speed and the change amplitude of strain relaxation; Zhang et al. [28] conducted a full-process ultrasonic detection test on the damage and fracture evolution of cross-cracked rock mass. The test results showed that wave speed can better reflect the damage and fracture evolution process of fractured rock mass; Wang et al. [29] used acoustic emission CT imaging technology obtained the regional characteristics of wave velocity distribution inside the rock during the uniaxial loading process, and analyzed the high and low wave velocity zones and stress response characteristics; Dou et al. [30] proposed an impact hazard vibration wave CT inversion method for impact mine pressure disaster, which can invert the vibration wave speed distribution characteristics in the study area and realize the judgment of impact hazardous area.

From the current research results, rock damage has been the research hotspot of related technicians, rock damage has been carried out a variety of technical methods of research work, wave velocity, acoustic emission, etc., and the relationship between rock damage research has been continuous, but for different weathering degree of rock damage research is less, and the physical significance of damage indicators is not clear. Therefore, in this paper, by conducting uniaxial and wave velocity tests on granite under different weathering conditions, we obtain the characteristic stress and characteristic wave velocity values of the progressive damage process of granite, and establish the density-wave velocity relationship equation for granite with different weathering degrees. At the same time, this paper tries to adopt the density and integrity indexes that can reflect the damage characteristics of the rock body macroscopically to define the damage variables, and discusses the comparison with the rock damage indexes defined by wave velocity.

2 Experimental Design

2.1 Test Principle

Due to weathering, unloading and alteration, granite has the characteristics of inhomogeneity, discontinuity and anisotropy, its internal contains a large number of pores and microfractures, in the loading process of the rock volume generated by the compression and expansion, while the density change is a macroscopic reflection of the change in the volume of the rock, can be through the density of the characterization of the rock damage in the loading process. Rock integrity coefficient is a geological parameter related to the quality and mechanical strength of the rock body, and it is also a link from the rock specimen to the damage of the rock body, which can be obtained by the number of volume nodules of the rock body or the elastic wave velocity. For granite with different degrees of weathering, the macro-parameters of integrated density and integrity of the rock mass solve the problem of quantitative characterization of the damage parameters of the rock mass in the loading process, and at the same time, the change of wave velocity can reflect the rich information of the internal structure of the rock, so the wave velocity parameter of the rock sample in the loading process is obtained by using sonic testing technology.

The wave speed value can be calculated by the length of the rock sample and the time difference between the excitation probe and the receiving probe. The calculation formula is:

$$ V_{\text{p}} = \frac{l}{t - t_0 } $$
(1)

where Vp is compressional wave velocity, m/s; l is the distance between the corresponding acoustic transducers at both ends of the rock sample, m; t is the acoustic signal receiving time, s; t0 is the acoustic signal excitation time, s.

2.2 Test Process

In accordance with the “Standard for Test Methods of Engineering Rock Masses” (GB/T50266-2013), the sample is a standard specimen of a cylinder with a diameter of 5 cm and a height of 10 cm. The end parallelism and axis deflection do not exceed 0.25°. Unqualified samples are removed and dried, and data such as sample size and quality are obtained.

Before the uniaxial test, density and axial wave velocity tests were carried out on the prepared rock samples. The acoustic wave testing system during uniaxial loading uses a compression-resistant acoustic wave transducer. During the test, the acoustic wave transducers are placed at both ends of the rock sample. The acoustic wave testing arrangement is shown in Fig. 1a. To carry out rock uniaxial testing, the testing machine adopts a 3000 kN fully digitally controlled electro-hydraulic servo rock rigid triaxial testing machine, which can obtain physical and mechanical parameters such as rock strain, mechanical strength and compressional wave velocity during uniaxial loading. The test process is shown in Fig. 1b.

Fig. 1.
figure 1

Rock uniaxial test layout and test experiments

Full size image

3 Test Data Statistics

3.1 Basic Physical and Mechanical Parameters of Rock Samples

Obtain the density value of the rock sample based on the geometric parameters and weight of the rock sample. At the same time, a wave velocity test was conducted on the unweathered granite rock sample. The initial compressional wave velocity VP0 = 6000 m/s. Combining the measured wave speed values of each sample, the weathering degree and integrity index can be obtained. The rock sample density, compressional wave velocity, shear wave speed, longitudinal to transverse wave ratio, weathering degree and integrity index (Kv0) are detailed in Table 1. Table 1 VP represents the compressional wave velocity, VS represents the shear wave speed, and VP0 is the initial wave speed of fresh granite.

Table 1. Statistical table of test parameters of rock samples
Full size table

The wave speed ratio of sample H3 is 0.4–0.6, indicating strong weathering, the remaining samples are all greater than 0.85, and are unweathered to slightly weathered.

Judging from the integrity index, the Kv value of the integrity index of the H3 sample is less than 0.35, and the integrity is broken. At the same time, its density value is small, the wave speed is low, and the wave speed ratio data is abnormal than other samples; the H4-2 sample is relatively complete, can be judged by the wave speed value, wave speed ratio and integrity index, but the density value parameter is difficult to evaluate the integrity; the other rock samples are all complete and have a good correspondence with the wave speed parameters.

From the perspective of longitudinal and transverse wave speeds, the higher the degree of weathering, the lower the rock longitudinal and transverse wave speeds. The ratio of H3 transverse waves to the transverse waves of other rock blocks is about 1/3, and the ratio of H3 compressional wave to the compressional waves of other rock blocks is about 1/2. The longitudinal and transverse waves can reflects changes in the physical properties of rocks; from the perspective of longitudinal and transverse wave ratios, H3 samples are all greater than 1.8, while other samples are less than 1.7, reflecting that the weathering degree and integrity of H3 samples are worse than other samples.

It can be seen from the wave speed data that both the shear wave speed and the longitudinal to shear wave ratio can reflect the changes in the physical properties of the rock. Therefore, the comprehensive density, wave speed and wave speed ratio can better evaluate the weathering and integrity of the rock.

3.2 Uniaxial Loading Test Data

Patterns of Change in Intensity

Rock stress and strain data can be obtained through uniaxial loading tests, and H1-2, H2-1, H3-2, and H4-2 stress-strain relationship curves are selected, as shown in Fig. 2 for details.

Fig. 2.
figure 2

Stress-strain curves of uniaxial compression test

Full size image

In a typical stress-strain relationship curve, the rock sample failure process can be divided into a compression section, an elastic deformation section, a stable crack expansion section, an unstable rupture stage (yield stage), and a rupture to residual strength section [31]. While the pressure-dense section in Fig. 2a and b is not significant, the pressure-densified section can be seen in Fig. 2c and d, and the elastic deformation section is very significant overall. Due to the direct destruction of the rock sample in Fig. 2a, c, and d, the yield stage is not visible, Fig. 2b It can be seen that there is a yield section.

It can be seen from Fig. 2 that the granite rock sample is significantly brittle under uniaxial action, and the linear elastic stage is obvious. The H3-2 rock sample is strongly weathered and broken. Figure 2c shows that the degree of weathering and completeness do not affect the development of the elastic segment during uniaxial loading; the H4-2 rock sample is slightly weathered and relatively complete, but the peak intensity is low, indicating that the wave speed value It does not completely correspond to the strength of rock, mainly because micro-joints and cracks control the strength of rock blocks.

Wave Speed Change Rules

During the uniaxial loading process, a compression-resistant acoustic wave transducer was used to obtain acoustic wave test data. The wave speed-stress curves of specimens H1-2, H2-1, H3-2, and H4-2 are shown in Fig. 3. In order to better compare and analyze the above sample data, the wave speed is normalized, as shown in Fig. 4.

Fig. 3.
figure 3

Wave speed-stress curves of uniaxial compression test

Full size image
Fig. 4.
figure 4

Relationship curves between wave speed normalization and stress in uniaxial compression test

Full size image

It can be seen from Figs. 3 and 4 that as the uniaxial loading process continues, the wave speed values of samples H3-2 and H4-2 show an increasing trend with the increase of stress. The increase first increases sharply and then develops steadily, and the higher the weathering, the higher the stress. The increase is more obvious in the early stage; the degree of weathering of samples H1-2 and H2-1 is the same, both are unweathered. Among them, sample H1-2 shows a trend of increasing first and then stabilizing, while sample H2-1 increases first and then decreases, but the overall wave speed of the two tends to be stable, indicating that the lower the weathering degree of the rock, the smaller the wave speed value fluctuates during the uniaxial loading process.

It can be seen from Fig. 3 that the higher the wave speed value, the greater the peak stress. There is a positive correlation between wave speed and peak stress. The peak wave speed-stress was fitted. The fitting results are shown in Fig. 5. It can be seen from Fig. 5 that when the wave speed is less than 4000 m/s, the stress level is low and the change amplitude is small. When the wave speed is greater than 4000 m/s, the stress increases sharply, indicating that there is an inflection point effect in the rock strength and wave speed curve. The shape of the stress -wave speed curve in this article is the same as the relationship curve between rock strength and wave speed in the literature of Wang et al. [29] and Zhao et al. [32] indicating that the relationship between stress and compressional wave velocity during rock loading can be established through an exponential function.

Fig. 5.
figure 5

Peak stress- compressional wave velocity curve of uniaxial compression test

Full size image

4 Quantitative Analysis of Rock Damage

Rock damage variables can be selected from micro and macro perspectives [33]. The micro perspective mainly determines the damage benchmark through crack density, such as the GK model [34] and TCK model [35]; the macro perspective is mainly based on rock physical and mechanical properties are used as damage benchmarks, such as elastic modulus method, ultrasonic wave velocity method, energy method, CT number method and acoustic emission cumulative number method, etc.

The internal damage of rock under external force will cause the change of acoustic parameters, which can characterize the change of rock mechanical properties and internal structure, and has the characteristics of non-destructive, therefore, it is more widely used. Jin et al. [36] proposed a method to define the damage variables based on the wave impedance of rocks and gave the expression for defining the damage variables; in order to study the effect of static stress on the propagation of rock stress waves, Jin et al. [37] carried out small disturbance stress wave propagation tests on a long specimen of red sandstone to obtain the propagation and attenuation characteristics of the stress waves under different static stress conditions; Jia et al. [38] used a real-time ultrasonic acoustic parameter prediction method to predict the propagation and attenuation characteristics of stress waves under different static stress conditions. Taking the fine structural characteristics of rocks as the entry point and damage mechanics as the theoretical basis, Li Bo [39] obtained the critical state parameters of rock damage using CT image processing technology, damage theory analysis, fractal theory analysis, and improved crack strain model method. Therefore, this study tries to establish the damage variables by rock physical and mechanical parameters, and based on the wave velocity definition of the damage variables of the previous researchers, it is proposed to use the density and integrity index to define the damage variables.

4.1 Define Damage Variables Based on Wave Speed

The change in rock wave speed can effectively reflect the damage of rock before and after loading. The wave speed expression of the damage variable is:

$$ D = 1 - {(}\frac{V_p }{{V_{p0} }})^2 $$
(2)

where D is the damage variable; Vp is the compressional wave velocity during rock loading, m/s; Vp0 is the initial compressional wave velocity of fresh rock, m/s.

The initial compressional wave velocity of fresh granite is 6000 m/s. Taking sample H1-2 as an example to calculate the damage change of the rock sample under uniaxial loading of the granite sample, the damage variable changes with stress curve is shown in Fig. 6.

It can be seen from Fig. 6 that under uniaxial loading conditions, the damage variables of granite do not increase linearly with the increase of stress. Instead, they first decrease, then become dynamically stable and finally increase sharply. This shows that as the stress increases, the damage variables of rock first decrease due to crack closure. Small, the damage variables change dynamically within a small range during the stable crack expansion stage, and the damage variables increase sharply during the unstable expansion of the crack to the failure stage. Generally speaking, the change pattern of damage variables is consistent with the rock loading failure process.

Fig. 6.
figure 6

Relationship curve between damage variable D and stress in uniaxial compression test

Full size image

4.2 Define Damage Variables Based on Density and Integrity

The density of rock will change during the loading process. In order to establish the density-wave speed relationship, combined with previous research results, a relationship curve between rock density and wave speed in Table 1 was established and fitted (the red line is the fitting curve). See Fig. 7 for details. The fitting relationship between density and wave speed is:

$$ \rho { = }0.80303V_{\text{P}}^{0.13745} $$
(3)

Where ρ is rock density, g/cm3; Vp is rock compressional wave velocity, m/s.

Fig. 7.
figure 7

Fitting curve of rock density and wave speed

Full size image

Rock integrity can be characterized by the rock mass integrity row index Kv, which quantitatively reflects the integrity condition. The relationship expressions of comprehensive density and integrity index definition of damage variables and integrity index are respectively:

$$ D^{\prime}{ = }\frac{{\rho K_{\text{V}} }}{{\rho_0 K_{{\text{V0}}} }} $$
(4)
$$ K_{\text{v}} { = (}\frac{V_p }{{V_{p0} }})^2 $$
(5)

where ρ is rock density, g/cm3; \(\rho_0\) is initial density of rock, 2.7 g/cm3; Kv0 is initial rock integrity index, ranging from 0 to 1; Vp0 is initial wave speed of rock, 6000 m/s.

Taking sample H1-2 as an example, the change curve of damage variables with stress under rock uniaxial loading is shown in Fig. 8.

Fig. 8.
figure 8

Relationship curve between damage variable D′ and stress in uniaxial compression test

Full size image

Comparing Figs. 6 and 8, since the relationship between the rock density and rock wave speed parameters in the damage variable D′ has been established, from a morphological point of view, the shape of the damage variable D′ and the damage variable D with the stress change curve are consistent; from the damage perspective From the numerical perspective of the variables, the D′ value is slightly smaller than the D value, and the change is small; from the definition parameter index, the physical meaning of the damage variable D′ based on density and integrity index is more clear, and the damage variable values are equivalent, indicating that the damage variable The definition is feasible.

5 Conclusion

By conducting uniaxial loading and compressional wave velocity tests on granite with different weathering degrees, the conclusions are as follows:

  1. (1)

    Density, wave velocity and wave velocity ratio can better evaluate the degree of rock weathering and integrity, meanwhile, considering the change of density of rock in the loading process, the exponential function relationship between density and wave velocity is established, and the rock damage indexes of density and integrity are constructed, which provides a new idea for the study of rock damage evolution.

  2. (2)

    Granite rock samples in the uniaxial action of the rock brittleness is significant, the line elasticity stage is obvious, but the degree of weathering and integrity does not affect the development of the elastic section of the uniaxial loading; uniaxial loading process, the wave velocity value with the stress of the first increase in the trend of smooth development, and the higher the weathering of the increase in the first period of time is more pronounced, and the strength of the rock and the wave velocity curves there is a point of inflexion effect.

  3. (3)

    Based on the density and integrity of the definition of damage variables, the physical significance of the damage variables is clear, and can better characterize the damage process in the process of uniaxial loading of rocks, but the density and integrity of the indicators did not take into account the characteristics of the nodule production and filler, the author will follow up from the indoor experiments, numerical analyses, theoretical calculations, etc., to carry out systematic research on the effect of nodules on the indicators, and to establish a quantitative relationship between the number of groups of nodules, the production of nodules, the filler, etc., and the indicators, to further expand the damage model. The relationship between the number of nodule groups, yield and filling materials and the damage indexes will be established to further expand the application scope of the damage model.