# Influence of Chemical Corrosion on Dynamic Fracturing Mechanical Behavior of Marbles

Authors: Chunmei Zheng; Jiayan Zheng; Xiaojuan Peng; Lei Zhou
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

To investigate the influences of the chemical corrosion on the dynamic fracture mechanical properties and failure characteristics of marble, the dynamic fracture test for the notched semicircular bend (NSCB) marble specimens with different degrees of corrosion damage was conducted using a split Hopkinson pressure bar. The results show that both the porosity and corrosion damage variableDc characterized by porosity increase as corrosion time T increases. The dynamic fracture toughness decreases linearly from 5.22 to 2.15 MPa m1/2 as Dc increases from 0 to 4.42%. This is because the corrosion damage done to interior structure leads to a reduction of cohesion and internal friction angle inside the specimen. In the Dc range of 0–4.42%, the fractal dimension of the main crack propagation path increases from 1.47 to 1.59, by an increase rate of 8.16%. Both the joint roughness coefficient and the actual area of the fracture surface increase as Dc increases. Due to the degradation of the connected force between the rock particles inside the specimen, there is an obvious decrease in the fracture energy per unit fracture surface from 0.94 to 0.38 J cm−2, with a decrease rate of 59.39%. With T increases, the contents of CaO, MgO, and Al2O3 in specimen increase, indicating that the degree of corrosion damage increases.


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## Body

## 1. Introduction

Most engineering rock masses exist in a complicated environment and are frequently subjected to varying influences [1–3]. The chemical corrosion damage done to surrounding rock is one of the most important problems that need to be considered and solved, which would result in the degradation of the internal structure of rock mass [4–6]. As a result, a series of disasters can more easily occur, such as collapse, roof failure, and bedrock slippage [7, 8]. Therefore, it is of great significance to investigate the influence of the corrosion damage on the mechanical properties of rock to ensure engineering safety.In recent years, the effects of water and various chemical solutions on the physic-mechanical parameter and mechanical properties of rock have received great attention in the international community. Feucht and Logan [9] evaluated the effect of chemical solutions on the frictional properties of a quartz-rich sandstone, finding that the presence of water alone reduced the ultimate strength by 33%. The NaCl solution of low ionic strength produced similar reductions in strength. Seto et al. [10] performed the splitting tensile tests and compression tests on Gosford sandstone saturated with three different kinds of chemical solutions. They concluded that the tensile strength of the sandstone could be markedly influenced by the zeta potential at the rock-liquid surface. Potyondy [11] described a numerical model for rock that extended the formulation of the bonded-particle model (BPM), which could mimic the stress-dependent corrosion reaction that occurred in silicate rocks in the presence of water. Miao et al. [12] conducted the uniaxial, triaxial compression and splitting tests on granite specimens after acidic solution erosion at a variety of different pH values and flowrates. The interactions between the granite and chemical solutions were analyzed based on the mass and elastic wave velocity data of the specimens and pH values of the solutions at different soaking times. Qiao et al. [13] found that the physical and chemical water-rock reactions led to the generation of secondary porosity of the rock, and this change was time-dependent. After the water-rock reactions continued for 3 months, this increase in porosity began to slow down, and the water-rock reactions tended toward equilibrium after 6 months.However, the above studies focus on investigating the corrosion damage done to rock under static loading, which were limited to mechanical responses at low strain rates. In fact, the rock mass in a deep underground environment is frequently subjected to dynamic disturbance such as explosions, impacts, or seismic activities [14, 15]. Due to the strain rate effect, mechanical properties of rock under dynamic conditions are different from that under static loading [16–18]. Therefore, it is necessary to determine the dynamic mechanical behaviors of rocks with corrosion damage. Among various dynamic mechanical properties, dynamic fracture toughness plays a key role in geophysical processes and project applications, which is closely related to the cracking failure for landslides and plates in engineering [19–21]. To study the fracture behavior of rock, more and more specimen types are developed. Compared with the herringbone bends specimen, short bends specimen [22], and cracked chevron notched Brazilian disc specimen [23, 24], the notched semicircular bend (NSCB) specimen has some advantages as follows [25–29]: (1) The specimen machining process is simple; (2) the artificial crack in the middle of the NSCB specimen is helpful to the observation of crack propagation; (3) the length of NSCB specimen in the loading direction is small, which is convenient for achieving the dynamic force balance in SHPB test; (4) the experimental result on fracture toughness is more reliable than those of other specimens. Substantial efforts have been made to investigate the fracture behaviors of rock under dynamic condition using the NSCB specimens [30–33]. Chen et al. [34] used a laser gap gauge to monitor the crack surface opening displacement of the NSCB specimen, from which the fracture velocity and the fracture energy can be calculated. Dai et al. [35] observed the stable-unstable transition of the crack propagation crack. Based on experimental result and the first law of thermodynamics, several parameters could be calculated, such as the initiation fracture toughness, the average dynamic fracture energy, and the fracture propagation toughness. Yin et al. [36] investigated the effect of thermal treatment on the dynamic fracture toughness of Laurentian granite and the experimental results showed that fracture toughness increased with the loading rate but decreased with the treatment temperature.Given the existing studies discussed above, none of the above dynamic fracture studies took the corrosion effect into account. Therefore, in this paper, the influence of the corrosion damage on the dynamic fracture behaviors and failure characteristics of rock was investigated. Most previous investigation considering the chemical effects on dynamic behavior of rocks used the sandstone/limestone. As one of the main components of marble, calcite can react with H+. Therefore, marble was chosen as the tested rock material for this experiment. First, a batch of natural marble NSCB specimens was corroded in KHSO4 and NaCl mixed solutions. The variation in the porosity of damaged specimens was measured using the nuclear magnetic resonance (NMR) technique and the corrosion damage variable characterized by porosity was quantified. Then, based on the results of the dynamic fracture test, the relationship between the corrosion damage variable and the dynamic fracture properties was established. Moreover, the failure characteristics of the damaged specimens were investigated through the quantitative analyses of the fractal dimension of the main crack and the roughness of the fracture surface. By analyzing the variations of the mineral content of the rock after corrosion treatment, the chemical effect is discussed.


## 2. Experimental Methodology

### 2.1. Specimen Preparation

The rock material tested in this paper is marble, which is taken from DAli, Yunnan province, China. The color of this variety of marble is white. The static uniaxial compressive strength, tensile strength, elastic modulus, density, and Poisson’s ratio are 127.51 MPa, 8.65 MPa, 23.84 GPa, 2.84 g/cm3, and 0.28, respectively. According to the testing results of X-ray diffraction (XRD), the main components of the tested marble are as follows: calcite (92.1%), dolomite (3.1%), mica (2.5%), quartz (0.3%), montmorillonite (1.3%), and other components (0.7%).According to the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested method for measuring dynamic fracture toughness of rock-like material [37], the NSCB specimen was adopted in this study. First, a batch of disc specimens with diameter D = 50 mm and thickness B = 25 mm was prepared. Then, each disc specimen was cut into two equal semicircular specimens along the diameter. An artificial crack was made in the middle of the semicircular specimen. The schematic of the NSCB specimen is presented in Figure 1, in which a, e, R, and s represent the length of the artificial notch (5 mm), the width of the artificial notch (1 mm), the height of the specimen (25 mm), and the distance between the two supporting bars (25 mm), respectively. The two ends of each specimen were ground to ensure the parallel accuracy of the two planes within ±0.05 mm and the accuracy perpendicular to the longitudinal axis was within ±0.25°.Figure 1
Schematic of the notched semicircular bend (NSCB) specimen.Note. a and e represent the length and width of the artificial notch, respectively; D, B, and H represent the diameter, thickness, and height of the specimen, respectively; s represent distance between the two supporting bars.


### 2.2. Chemical Solutions

Groundwater is a complex chemical solution, in which the dissolved components in various forms and various ion concentrations exist. In general, the primary cations in groundwater are Na+, Ca2+, and Mg2+, and the primary anions are SO42−, Cl−, and HCO3- [8, 13]. In this study, a mixed solution of KHSO4 and NaCl was prepared to simulate the groundwater environment. Both the concentrations of KHSO4 and NaCl solutions are 0.01 mol L−1. There pH values (2, 4, and 6) of chemical solutions were configured, and five corrosion times T (30 d, 60 d, 90 d, 120 d, and 150 d) were designed, as listed in Table 1. For comparison, three natural specimens without corrosion treatment were prepared for the dynamic fracture test, i.e., T = 0 d. A total of 48 NSCB specimens were prepared. The main components of the tested marble, such as calcite and dolomite, are not easy to dissolve in the alkaline environment, so no alkaline solution was configured in this test. During the whole corrosion process, the pH values of the three chemical solutions were detected using the high precision pH acidity meter.Table 1
Corrosion treatment scheme and specimen number.
pHTime30 d60 d90 d120 d150 d66-30-16-60-16-90-16-120-16-150-16-30-26-60-26-90-26-120-26-150-26-30-36-60-36-90-36-120-36-150-344-30-14-60-14-90-14-120-14-150-14-30-24-60-24-90-24-120-24-150-24-30-34-60-34-90-34-120-34-150-322-30-12-60-12-90-12-120-12-150-12-30-22-60-22-90-22-120-22-150-22-30-32-60-32-90-32-120-32-150-3Note. Three natural specimens (T = 0 d) were prepared for comparison.


### 2.3. Split Hopkinson Pressure Bar

As a rock dynamic testing equipment recommended by ISRM, the SHPB system is widely used to perform the impact test [37–41]. In this study, the dynamic fracture test was conducted for the damaged specimens using the SHPB system. As shown in Figure 2(a), this system consists of a gas gun, a striker bar, an incident bar, a transmitted bar, an absorbing bar, and a data acquisition device. All elastic bars are made of maraging steel with a P-wave velocity of 5450 m/s, density of 7800 kg/m3, elastic modulus of 250 GPa, and diameter of 50 mm. The lengths of the incident bar, transmitted bar, and absorption bar are 4000, 2000, and 500 mm, respectively. Two strain gauges are attached to the incident and transmitted bars to collect the stress signals in the impact process. Based on the one-dimensional stress wave theory, the stress σ, strain ε, and strain rate ε˙ of the specimen can be calculated using the following formulae [42]:(1)σ=EbAb2Asεit+εrt+εtt,ε=Cpbls∫0tεit−εrt−εttdt,ε˙=Cpblsεit−εrt−εtt,where εi(t), εr(t), and εt(t) represent the incident wave, reflected wave, and transmitted wave, respectively; Eb, Cb, and Ab represent the elastic modulus, longitudinal wave velocity, and cross-sectional area for the bars, respectively; As and ls represent the original cross-sectional area and length of the specimen, respectively.Figure 2
(a) Schematic of split Hopkinson pressure bar (SHPB) system, (b) dynamic force balance check.
(a)(b)The loading forces on both ends of the specimen are calculated as follows [43]:(2)P1=EbAbεit+εrt,P2=EbAbεtt,where P1 represents the force that is applied on the incident end of the specimen, and P2 represents the force that is exerted on the transmitted end.In this study, the gas pressure of the dynamic fracture test was fixed at 0.1 MPa. Due to the axial inertia effect, the distinct unbalance of the loading stress would reduce the accuracy of the result of the SHPB test. Therefore, the dynamic force balance between the ends of the specimen must be achieved during the impact process [41]. In this paper, a flat rubber disc with a diameter and thickness of 8.0 and 1.5 mm was attached on the front end of the incident bar to serve as a pulse shaper [18]. Figure 2(b) shows the time-varying forces acting on both ends of the specimen during the loading process. A half-sine stress wave with an approximate platform on the reflection wave can be observed, which suggests that the measured waveform essentially eliminated the wave oscillation caused by stress-dispersion, i.e., the constant strain rate loading has been achieved. Moreover, the sum of the incident and reflected stress waves at the front end of the specimen is approximately equal to the transmitted stress at the rear end of the specimen under the strain rate of approximately 28.54 s−1, i.e., P1 = P2, which implies the dynamic forces on both sides of the specimen are in a state of balance. In the present study, the dynamic force balance was checked for all impact tests.


### 2.4. Testing Method

The nuclear magnetic resonance (NMR) technique has been widely used to explore the microstructure of rocks [44–47]. In this study, the MesoMR23-060H–I system was used to measure the porosity of the damaged specimens. The resonance frequency and the temperature of the magnet were set at 23.423 MHz and 32.00 ± 0.02°C, respectively. After corrosion treatment, all tested specimens were saturated in the vacuum saturation device for 24 hours, then wrapped with preservative film to prevent the evaporation of water, and subsequently placed in the NMR machine. After obtaining the testing data of porosity, the preservative ﬁlms were removed, and the subsequent dynamic fracture test was performed.To observe the crack initiation and propagation of rock specimen, a high-speed (HS) camera was used in the dynamic fracture test [48–50]. The HS camera captured images at a constant interframe time of 100 μs (i.e., 10,000 frames per second) with a resolution of 480 × 480 pixels.After specimen failure, the fracture surfaces of the specimen pieces were digitalized by using a high-resolution noncontact 3D laser scanning system, which has the advantage of high precision (±20μm in x- and y-directions and ±10 μm in the height direction) [51]. The interval of the scanning points was 0.1 mm.


## 2.1. Specimen Preparation

The rock material tested in this paper is marble, which is taken from DAli, Yunnan province, China. The color of this variety of marble is white. The static uniaxial compressive strength, tensile strength, elastic modulus, density, and Poisson’s ratio are 127.51 MPa, 8.65 MPa, 23.84 GPa, 2.84 g/cm3, and 0.28, respectively. According to the testing results of X-ray diffraction (XRD), the main components of the tested marble are as follows: calcite (92.1%), dolomite (3.1%), mica (2.5%), quartz (0.3%), montmorillonite (1.3%), and other components (0.7%).According to the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested method for measuring dynamic fracture toughness of rock-like material [37], the NSCB specimen was adopted in this study. First, a batch of disc specimens with diameter D = 50 mm and thickness B = 25 mm was prepared. Then, each disc specimen was cut into two equal semicircular specimens along the diameter. An artificial crack was made in the middle of the semicircular specimen. The schematic of the NSCB specimen is presented in Figure 1, in which a, e, R, and s represent the length of the artificial notch (5 mm), the width of the artificial notch (1 mm), the height of the specimen (25 mm), and the distance between the two supporting bars (25 mm), respectively. The two ends of each specimen were ground to ensure the parallel accuracy of the two planes within ±0.05 mm and the accuracy perpendicular to the longitudinal axis was within ±0.25°.Figure 1
Schematic of the notched semicircular bend (NSCB) specimen.Note. a and e represent the length and width of the artificial notch, respectively; D, B, and H represent the diameter, thickness, and height of the specimen, respectively; s represent distance between the two supporting bars.


## 2.2. Chemical Solutions

Groundwater is a complex chemical solution, in which the dissolved components in various forms and various ion concentrations exist. In general, the primary cations in groundwater are Na+, Ca2+, and Mg2+, and the primary anions are SO42−, Cl−, and HCO3- [8, 13]. In this study, a mixed solution of KHSO4 and NaCl was prepared to simulate the groundwater environment. Both the concentrations of KHSO4 and NaCl solutions are 0.01 mol L−1. There pH values (2, 4, and 6) of chemical solutions were configured, and five corrosion times T (30 d, 60 d, 90 d, 120 d, and 150 d) were designed, as listed in Table 1. For comparison, three natural specimens without corrosion treatment were prepared for the dynamic fracture test, i.e., T = 0 d. A total of 48 NSCB specimens were prepared. The main components of the tested marble, such as calcite and dolomite, are not easy to dissolve in the alkaline environment, so no alkaline solution was configured in this test. During the whole corrosion process, the pH values of the three chemical solutions were detected using the high precision pH acidity meter.Table 1
Corrosion treatment scheme and specimen number.
pHTime30 d60 d90 d120 d150 d66-30-16-60-16-90-16-120-16-150-16-30-26-60-26-90-26-120-26-150-26-30-36-60-36-90-36-120-36-150-344-30-14-60-14-90-14-120-14-150-14-30-24-60-24-90-24-120-24-150-24-30-34-60-34-90-34-120-34-150-322-30-12-60-12-90-12-120-12-150-12-30-22-60-22-90-22-120-22-150-22-30-32-60-32-90-32-120-32-150-3Note. Three natural specimens (T = 0 d) were prepared for comparison.


## 2.3. Split Hopkinson Pressure Bar

As a rock dynamic testing equipment recommended by ISRM, the SHPB system is widely used to perform the impact test [37–41]. In this study, the dynamic fracture test was conducted for the damaged specimens using the SHPB system. As shown in Figure 2(a), this system consists of a gas gun, a striker bar, an incident bar, a transmitted bar, an absorbing bar, and a data acquisition device. All elastic bars are made of maraging steel with a P-wave velocity of 5450 m/s, density of 7800 kg/m3, elastic modulus of 250 GPa, and diameter of 50 mm. The lengths of the incident bar, transmitted bar, and absorption bar are 4000, 2000, and 500 mm, respectively. Two strain gauges are attached to the incident and transmitted bars to collect the stress signals in the impact process. Based on the one-dimensional stress wave theory, the stress σ, strain ε, and strain rate ε˙ of the specimen can be calculated using the following formulae [42]:(1)σ=EbAb2Asεit+εrt+εtt,ε=Cpbls∫0tεit−εrt−εttdt,ε˙=Cpblsεit−εrt−εtt,where εi(t), εr(t), and εt(t) represent the incident wave, reflected wave, and transmitted wave, respectively; Eb, Cb, and Ab represent the elastic modulus, longitudinal wave velocity, and cross-sectional area for the bars, respectively; As and ls represent the original cross-sectional area and length of the specimen, respectively.Figure 2
(a) Schematic of split Hopkinson pressure bar (SHPB) system, (b) dynamic force balance check.
(a)(b)The loading forces on both ends of the specimen are calculated as follows [43]:(2)P1=EbAbεit+εrt,P2=EbAbεtt,where P1 represents the force that is applied on the incident end of the specimen, and P2 represents the force that is exerted on the transmitted end.In this study, the gas pressure of the dynamic fracture test was fixed at 0.1 MPa. Due to the axial inertia effect, the distinct unbalance of the loading stress would reduce the accuracy of the result of the SHPB test. Therefore, the dynamic force balance between the ends of the specimen must be achieved during the impact process [41]. In this paper, a flat rubber disc with a diameter and thickness of 8.0 and 1.5 mm was attached on the front end of the incident bar to serve as a pulse shaper [18]. Figure 2(b) shows the time-varying forces acting on both ends of the specimen during the loading process. A half-sine stress wave with an approximate platform on the reflection wave can be observed, which suggests that the measured waveform essentially eliminated the wave oscillation caused by stress-dispersion, i.e., the constant strain rate loading has been achieved. Moreover, the sum of the incident and reflected stress waves at the front end of the specimen is approximately equal to the transmitted stress at the rear end of the specimen under the strain rate of approximately 28.54 s−1, i.e., P1 = P2, which implies the dynamic forces on both sides of the specimen are in a state of balance. In the present study, the dynamic force balance was checked for all impact tests.


## 2.4. Testing Method

The nuclear magnetic resonance (NMR) technique has been widely used to explore the microstructure of rocks [44–47]. In this study, the MesoMR23-060H–I system was used to measure the porosity of the damaged specimens. The resonance frequency and the temperature of the magnet were set at 23.423 MHz and 32.00 ± 0.02°C, respectively. After corrosion treatment, all tested specimens were saturated in the vacuum saturation device for 24 hours, then wrapped with preservative film to prevent the evaporation of water, and subsequently placed in the NMR machine. After obtaining the testing data of porosity, the preservative ﬁlms were removed, and the subsequent dynamic fracture test was performed.To observe the crack initiation and propagation of rock specimen, a high-speed (HS) camera was used in the dynamic fracture test [48–50]. The HS camera captured images at a constant interframe time of 100 μs (i.e., 10,000 frames per second) with a resolution of 480 × 480 pixels.After specimen failure, the fracture surfaces of the specimen pieces were digitalized by using a high-resolution noncontact 3D laser scanning system, which has the advantage of high precision (±20μm in x- and y-directions and ±10 μm in the height direction) [51]. The interval of the scanning points was 0.1 mm.


## 3. The Effect of Water-Rock Interaction

### 3.1. Change inpH Value of Chemical Solutions

The variation in thepH value of the chemical solutions is plotted in Figure 3. As T increases, the pH value shows an increasing trend, while the increasing rate steadily diminishes. The pH value shows an increase rate of 9.50%, 23.75%, and 75.50% after 60 days of immersion in the chemical solution with pH values = 6, 4, and 2, respectively. However, as T increases from 60 to 150 d, the corresponding pH value just shows an increase of 3.50%, 5.05%, and 17.38%, respectively. The pH value is closely related to the intensity of water-rock interaction. In the early period of corrosion treatment (0–60 d), many mineral components of the marble, such as calcite and dolomite, react violently with the chemical solution. Many ions in the chemical solution are consumed. Gradually, the number of H+ ions in solution reduces. More and more resultants are produced and attached to the specimen surface in this process, which prevents the solution from further entering the internal structure of the specimen. The extent of the chemical reaction decreases over time.Figure 3
Time-varying curve ofpH value of chemical solution.


### 3.2. Change in Porosity

In the interior of natural marble, there are some primary cracks with varying diameters. The water-rock interaction causes the initiation and propagation of the defects, doubtlessly changing the porosity of specimen. In this study, the variation in the porosity of the damaged specimen was measured using the NMR technique. First, the validity of the porosity obtained by the NMR technique should be verified by comparing the testing result of other measurement methods. The conventional measurement method most commonly used is the weighing method, which has been recommended by ISRM [52] and widely used to calculate the porosity of rocks as follows [44, 53]:(3)ϕ=ms−mdρV,where φ represents the porosity of the specimen; ms and md represent the saturated mass and the dry mass of the specimen, respectively; ρ represents the density of water; V represents the bulk volume of the specimen.Using the NMR technique and the weighing method, the porosities of several damaged specimens are obtained and listed in Table2. It can be seen that the porosity obtained by the NMR test is slightly smaller than that of the weighing method due to the limitation of the NMR technique. Because the relaxation rate of water in these pores is too fast to be completely recorded, pores smaller than 3 nm cannot be measured [44–46]. However, the porosity of rock material is determined by the number of pores with larger sizes [47] and the error between the porosity obtained by two methods is very small (no more than 4%), which would not significantly influence the testing results [44]. Thus, the testing data of the porosity obtained by the NMR technique is reliable.Table 2
The porosity from the NMR test and the weighing method.
Specimen no.Porosity (%)Error (%)NMR testWeighing method0-10.1580.1622.530–20.1970.2012.030–30.1760.1823.41The variation in the porosity of specimens is plotted in Figure4. It can be observed that the effect of water-rock interaction on the porosity of marble is time-dependent. With the continuous increase of T, φ increases, whereas the growth rate gradually diminishes. The amplitude of variation is affected by the pH value of the chemical solution. For the natural specimen, the value of the original porosity is 0.17%, and then the porosity increases to 1.98%, 2.67%, and 3.29% after 150 days of immersion in solutions with pH values = 6, 4, and 2, respectively.Figure 4
Variation in porosity versus corrosion time.


### 3.3. Change in Corrosion Damage Variable

To investigate the influence of the corrosion damage on the deterioration of mechanical properties, a suitable corrosion damage variableDc should be defined [54–56]. On the one hand, for the specimen after corrosion treatment, the growth in the porosity is the root cause of the degradation of mechanical properties [57], which can reflect the microstructural damage. On the other hand, the corrosion damage can be quantified based on the porosity [58]. Therefore, the damage variable characterized by porosity has been widely used [59–64], which can be calculated as follows [65]:(4)Dc=φt−φ01−φ0×100%,where φt represents the porosity of specimen after T days of immersion in the chemical solution; φ0 represents the initial porosity of marble specimen without chemical corrosion.The variation inDc is plotted in Figure 5. The variation trend of Dc is very similar to that of porosity, which is affected by both T and pH value of the chemical solution. Furthermore, the variation in Dc can be divided into two stages. At stage I (0–60 d), lots of active minerals on the surface of the marble react with H+ ions. The degree of the water-rock interaction is determined by the contents of H+ ions in solution and the active minerals in the specimen.Figure 5
Variation in damage variable versus corrosion time.In this process, the compact structure begins to be destroyed, resulting in the propagation of primary pores and the initiation of new cracks, and thenDc increases rapidly. As T continues to increase, both the number of active minerals in the specimen surface and H+ ions in the solutions decrease. Besides, the resultants of water-rock interaction adhere to the surface of the specimen, which prevents the solution from further entering the specimen. Therefore, at stage II (60–150 d), the increase rate of Dc gradually diminishes. In the whole corrosion process, the corrosion damage done to the marble specimen increases to 2.42% pH=6, 3.42% pH=4, and 4.42% pH=2, respectively.


## 3.1. Change inpH Value of Chemical Solutions

The variation in thepH value of the chemical solutions is plotted in Figure 3. As T increases, the pH value shows an increasing trend, while the increasing rate steadily diminishes. The pH value shows an increase rate of 9.50%, 23.75%, and 75.50% after 60 days of immersion in the chemical solution with pH values = 6, 4, and 2, respectively. However, as T increases from 60 to 150 d, the corresponding pH value just shows an increase of 3.50%, 5.05%, and 17.38%, respectively. The pH value is closely related to the intensity of water-rock interaction. In the early period of corrosion treatment (0–60 d), many mineral components of the marble, such as calcite and dolomite, react violently with the chemical solution. Many ions in the chemical solution are consumed. Gradually, the number of H+ ions in solution reduces. More and more resultants are produced and attached to the specimen surface in this process, which prevents the solution from further entering the internal structure of the specimen. The extent of the chemical reaction decreases over time.Figure 3
Time-varying curve ofpH value of chemical solution.


## 3.2. Change in Porosity

In the interior of natural marble, there are some primary cracks with varying diameters. The water-rock interaction causes the initiation and propagation of the defects, doubtlessly changing the porosity of specimen. In this study, the variation in the porosity of the damaged specimen was measured using the NMR technique. First, the validity of the porosity obtained by the NMR technique should be verified by comparing the testing result of other measurement methods. The conventional measurement method most commonly used is the weighing method, which has been recommended by ISRM [52] and widely used to calculate the porosity of rocks as follows [44, 53]:(3)ϕ=ms−mdρV,where φ represents the porosity of the specimen; ms and md represent the saturated mass and the dry mass of the specimen, respectively; ρ represents the density of water; V represents the bulk volume of the specimen.Using the NMR technique and the weighing method, the porosities of several damaged specimens are obtained and listed in Table2. It can be seen that the porosity obtained by the NMR test is slightly smaller than that of the weighing method due to the limitation of the NMR technique. Because the relaxation rate of water in these pores is too fast to be completely recorded, pores smaller than 3 nm cannot be measured [44–46]. However, the porosity of rock material is determined by the number of pores with larger sizes [47] and the error between the porosity obtained by two methods is very small (no more than 4%), which would not significantly influence the testing results [44]. Thus, the testing data of the porosity obtained by the NMR technique is reliable.Table 2
The porosity from the NMR test and the weighing method.
Specimen no.Porosity (%)Error (%)NMR testWeighing method0-10.1580.1622.530–20.1970.2012.030–30.1760.1823.41The variation in the porosity of specimens is plotted in Figure4. It can be observed that the effect of water-rock interaction on the porosity of marble is time-dependent. With the continuous increase of T, φ increases, whereas the growth rate gradually diminishes. The amplitude of variation is affected by the pH value of the chemical solution. For the natural specimen, the value of the original porosity is 0.17%, and then the porosity increases to 1.98%, 2.67%, and 3.29% after 150 days of immersion in solutions with pH values = 6, 4, and 2, respectively.Figure 4
Variation in porosity versus corrosion time.


## 3.3. Change in Corrosion Damage Variable

To investigate the influence of the corrosion damage on the deterioration of mechanical properties, a suitable corrosion damage variableDc should be defined [54–56]. On the one hand, for the specimen after corrosion treatment, the growth in the porosity is the root cause of the degradation of mechanical properties [57], which can reflect the microstructural damage. On the other hand, the corrosion damage can be quantified based on the porosity [58]. Therefore, the damage variable characterized by porosity has been widely used [59–64], which can be calculated as follows [65]:(4)Dc=φt−φ01−φ0×100%,where φt represents the porosity of specimen after T days of immersion in the chemical solution; φ0 represents the initial porosity of marble specimen without chemical corrosion.The variation inDc is plotted in Figure 5. The variation trend of Dc is very similar to that of porosity, which is affected by both T and pH value of the chemical solution. Furthermore, the variation in Dc can be divided into two stages. At stage I (0–60 d), lots of active minerals on the surface of the marble react with H+ ions. The degree of the water-rock interaction is determined by the contents of H+ ions in solution and the active minerals in the specimen.Figure 5
Variation in damage variable versus corrosion time.In this process, the compact structure begins to be destroyed, resulting in the propagation of primary pores and the initiation of new cracks, and thenDc increases rapidly. As T continues to increase, both the number of active minerals in the specimen surface and H+ ions in the solutions decrease. Besides, the resultants of water-rock interaction adhere to the surface of the specimen, which prevents the solution from further entering the specimen. Therefore, at stage II (60–150 d), the increase rate of Dc gradually diminishes. In the whole corrosion process, the corrosion damage done to the marble specimen increases to 2.42% pH=6, 3.42% pH=4, and 4.42% pH=2, respectively.


## 4. The Analysis of Dynamic Fracture Test Results

### 4.1. Dynamic Fracture Toughness

For the dynamic fracture test, the force balance has been achieved, and the evolution of the mode-I stress intensity factorKI(t) can be obtained by the following formula [37]:(5)KIt=PtsBR3/2Yαa,where P(t) represents the loading force on the specimen as a function of time; αa represents the kerf depth of dimension one and is equal to a/R (in this study, the value is 0.2); Y(αa) represents a dimensionless function that depends on the geometry of the artificial crack.For 0.15 <αa < 0.5, when the supporting span αs (s/D) = 0.5, Y(αa) can be determined using the following formula [37]:(6)Yαa=0.5037+3.4409αa−8.079αa2+16.489αa3.The typicalKI(t)-time curve of the NSCB specimen is shown in Figure 6(a). It can be observed that there is an almost linear regime in the KI(t)-time curve. Based on the suggested method for determining the dynamic fracture toughness for rock-like materials [37], the peak point of the KI(t)-time curve is defined as the dynamic fracture toughness KIC. Figure 6(b) displays the variation in KIC versus Dc. As Dc increases from 0 to 4.42%, there is an obvious decrease in KIC from 5.22 to 2.15 MPa m1/2, with a decrease rate of 58.81%. Lots of active minerals in the specimen and H+ ions in the chemical solution provide the sufficient condition for the water-rock interaction. The compact structure of the rock gradually becomes relatively loose. The cohesion and internal friction angle inside the specimen are reduced to a great extent. The bonding strength between mineral particles also decreases. It inevitability leads to the degradation of the dynamic fracture toughness of rock. The variation process of KIC can be fitted using a linear function and the corresponding fitting function is expressed. The fitting coefficient of determination R2 is 0.988, indicating a good fitting quality.Figure 6
(a) Typical stress intensity factor-time curve in a dynamic NSCB test, (b) variation in dynamic fracture toughness versus damage variable.
(a)(b)


### 4.2. The Failure Characteristic

#### 4.2.1. Failure Process

A HS camera was used to monitor the dynamic failure process of specimen. The corresponding photos of six representative specimens with differentDc are presented in Figure 7, demonstrating the process of crack propagation. Each picture corresponds to a specific time point, while the time zero indicates that the incident pulse has just been transmitted to the specimen. Figure 7(a) shows the dynamic failure process of the natural specimen. At the start time 0 μs, a complete NSCB specimen is sandwiched between the incident bar and the transmitted bar. After around 120 μs, the main crack initiates at the artificial notch, in which the tensile stress is the maximum. Then at 160 μs, the main crack subsequently develops into an obvious radial crack along the loading direction. Finally, the main crack propagates throughout the whole specimen, and the specimen is separated into two identical parts along the main crack at 200 μs.Figure 7
The failure processes and corresponding extraction of main crack path of binary images of the NSCB specimens: (a)–(f) corresponding to Dc = 0, 1.16, 1.95, 3.02, 3.62, 4.42%.
(a)(b)(c)(d)(e)(f)It can be seen that the failure process is affected byDc. On the one hand, as Dc increases, the time point of the initiation of the main crack is advanced. When Dc = 4.42%, the main crack (see the white dotted circle in Figure 7(f)) is initiated at 80 μs, which is about 40 μs earlier than that of the natural specimen. On the other hand, although the severely damaged specimens are still separated into two parts, the tortuosity of the main crack path increases. Furthermore, some debris could be found by observing the failure surface of the damaged specimens.


#### 4.2.2. Fractal Dimension of the Crack Propagation Path

A digital image can be regarded as a matrix of pixel values [30]. If the number of pixels is i, the RGB image is an i×3 matrix and the range of value of each element is 0∼255. For a grey image with i elements, the value range of each element is also 0∼255. For a black and white image with i elements, the value range of each element is {0, 1}, i.e., black and white. Based on the histogram equalization method, the RGB image is enhanced and converted into a grey image. By selecting a suitable grey threshold, the grey image is converted into a black and white picture that is easy to process and analyze. This process is called binarization, as shown in Figure 8. The pictures of the ultimate failure modes of the damaged specimens were processed as the above method (see the rightmost column in Figure 7).Figure 8
Image processing and crack identification of NSCB specimen: (a) Image of NSCB specimen before loading recorded by high-speed camera, (b) image enhancement based on histogram equalization method, (c) binary image of specimen, (d) extraction of crack path in specimen.
(a)(b)(c)(d)To further quantitatively investigate the influence ofDc on the tortuosity of the main crack of the damaged specimen, based on the processed binary images, the box fractal dimension df of the main crack was calculated. The calculation process is to cover the black area of the binary image with square black pixel blocks whose side length r ranges from small to large and to count the number N(r) of pixel blocks that are required for each side length [64, 65]. Changing r could obtain different N(r). Therefore, the df of the crack path can be calculated by the following formula [66]:(7)df=−limr⟶0lgNrlgr.Figure9(a) displays the calculation process of df by the above method. The function of the fitting line is lgN(r) = 3.30 + 1.44 × lgr−1, i.e., df is 1.44. Using this method, the values of df of all specimens are calculated and plotted in Figure 9(b).Figure 9
Fractal dimension calibration and results. (a) Plot of box-counting method applied to curved crack of typical fractured NSCB specimen; (b) variation in fractal dimension versus damage variable.
(a)(b)AsDc increases from 0 to 4.42%, df increases from 1.47 to 1.59, by an increase rate of 8.16%. The linear function expressed in Figure 9(b) fits the df data very well and the fitting coefficient of determination R2 of 0.982. In the corrosion process, lots of active minerals of the specimen participate in water-rock interaction, resulting in the initiation and propagation of defects; these damaged areas are always preferentially through, which result in the continuous change of the direction of the forward propagation of the main crack [67]. As a result, df increases.


#### 4.2.3. Surface Roughness of Fracture

The reconstructed fracture surfaces of the damaged NSCB specimens are shown in Figure10. The digitalized fracture surface can be regarded as an assembly of many elements (0.1 mm × 0.1 mm area) with different asperity heights (the height from the average surface height), slope angles (the angle between normal vectors on each element from the z-direction), and aspect directions (the projection of the element plane orientation with respect to the x-direction) [68]. The variations in the standard deviations of asperity height, slope angle, and aspect direction of the fracture surfaces versus Dc are plotted in Figure 11. The standard deviation of all three spatial distribution parameters shows an increasing trend with increasing Dc. As Dc increases from 0 to 4.42%, the standard deviation of the three parameters shows an increase rate of 41.58% (asperity height), 9.12% (slope angle), and 12.63% (aspect direction), respectively. Therefore, the corrosion damage has a distinct effect on roughness, waviness, and undulation of the fracture surfaces.Figure 10
The digitalized fracture surfaces of damaged specimens: (a)–(f) corresponding toDc = 0, 1.16, 1.95, 3.02, 3.62, 4.42%.Figure 11
Variations in standard deviation of asperity height, slope angle, and aspect direction of fracture surface mesh elements versus damage variable.The joint roughness coefficient (JRC) can quantitatively reflect the roughness of the fracture surface. In previous researches [69, 70], to determine the roughness of a 3D fracture surface, many 2D profiles were extracted from each surface by dividing the fracture surface into several equally spaced lines. Then the JRC of these 2D profiles were calculated, and their average value was regarded as the overall JRC value of the 3D rock fracture surface. It is a dimensionless index generally ranging from 0 to 20, first proposed by Barton and Choubey [71], which could be calculated as follows [72]:(8)JRC=32.20+32.47lgZ2,Z2=1M∑zi−1−zixi−1−xi21/2,where Z2 represents a dimensionless roughness parameter that is defined as the root mean square of the first deviation of a profile; xi and zi represent the coordinates of the fracture surface profile; M represents the number of sampling points along the length of a 2D fracture.The actual area of the fracture surfaceSa can also directly reflect the roughness of the fracture surface. In general, the integral method is adopted to calculate Sa. Assuming the fracture surface is continuum and derivable, the corresponding Sa could be calculated as follows [73]:(9)Sa=∫surface1+∂z∂xx,y2+∂z∂yx,y21/2dxdy≈d2∑i=1Nx−1∑j=1Ny−11+zi+1,j−zi,jd2+zi,j+1−zi,jd2,where Nx and Ny represent the number of points along the x and y axis; d represents the side length of square elementary surfaces; zi, j = z(xi, yj).The variations in JRC andSa versus Dc are plotted in Figures 12(a) and 12(b), respectively. With an increase in Dc from 0 to 4.42%, JRC increases from 12.45 to 16.81, or by 35.05%; Sa increases from 5.3 to 5.82 cm2, or by 9.81%. Furthermore, the results can also be best fitted with a linear function. Both the fitting coefficients of determination R2 are larger than 0.98, implying that the linear function fits the experimental data very well. As Dc increases, the numbers of pores and defects randomly distributed inside the specimen increase. Accordingly, the probability that the main crack encounters the weak interfaces increases in the failure process. The specimen will select the path that is easiest to propagate by continually adjusting the direction of advancement [67]. Therefore, the roughness of the fracture surface increases.Figure 12
Variations in morphology of the fracture surface versus dynamic damage variable: (a) JRC, (b) the actual area.
(a)(b)


### 4.3. Energy Evolution

According to the three-wave method, the energy carried by the various stress wave of the SHPB system could be obtained by the following formulae [74]:(10)Wi=AbCbEb∫0tσit2dt,Wr=AbCbEb∫0tσrt2d,,Wt=AbCbEb∫0tσtt2dt,where Wi, Wr, and Wt represent the incident, reflected, and transmitted energy, respectively.Assuming that the energy loss at ends of specimen and bars is negligible, according to the law of conservation of energy, the fracture energyWF by the specimen in the process of dynamic loading can be calculated by the following formula:(11)WF=Wi−Wr−Wt−K.After specimen fracture, the specimen split into two 1/4 disks, andK is the residual kinetic energy of the two 1/4 disks. As K only accounts for approximately 5% of the dissipated energy of the specimen at low and medium loading rates (10−4 ∼ 102 s−1) [75], neglecting K will not have a substantial influence on the experimental results.Based on equations (11) and (12), the fracture energy WF is obtained and plotted in Figure 13(a). As Dc increases from 0 to 4.42%, there is an obvious decrease in WF from 4.96 to 2.21 J, with a decrease rate of 55.41%. However, it can be observed that, for several specimens, as Dc increases, WF remains unchanged or even increases (see the black dotted circles). To investigate this phenomenon, the fracture energy per unit fracture surface G is calculated by the following formula:(12)G=WFSa.Figure 13
Variations in energy versus damage variable: (a) fracture energy, (b) fracture energy per unit fracture surface.
(a)(b)The variation inG is plotted in Figure 13(b). With an increase in Dc from 0 to 4.42%, G decreases from 0.94 to 0.38 J cm−2, or by 59.39%. The linear function expressed in Figure 13(b) fits the G data very well with the fitting coefficient of determination R2 of 0.983. The reduction in G indicates that the interior structure has been damaged due to corrosion. The particles inside the specimen slide more easily between each other and the links between the molecular bonds are broken. As a result, the fracture energy per unit fracture surface during the crack propagation of the corroded specimens is much less than that of the natural specimen. Moreover, the increase of the number of pores and defects is partly responsible for the reduction in G. It can be said that, in this study, compared with WF, G can more clearly reflect the corrosion damage degree done to the internal structure of the specimen due to taking the dramatic increase in Sa into account.


## 4.1. Dynamic Fracture Toughness

For the dynamic fracture test, the force balance has been achieved, and the evolution of the mode-I stress intensity factorKI(t) can be obtained by the following formula [37]:(5)KIt=PtsBR3/2Yαa,where P(t) represents the loading force on the specimen as a function of time; αa represents the kerf depth of dimension one and is equal to a/R (in this study, the value is 0.2); Y(αa) represents a dimensionless function that depends on the geometry of the artificial crack.For 0.15 <αa < 0.5, when the supporting span αs (s/D) = 0.5, Y(αa) can be determined using the following formula [37]:(6)Yαa=0.5037+3.4409αa−8.079αa2+16.489αa3.The typicalKI(t)-time curve of the NSCB specimen is shown in Figure 6(a). It can be observed that there is an almost linear regime in the KI(t)-time curve. Based on the suggested method for determining the dynamic fracture toughness for rock-like materials [37], the peak point of the KI(t)-time curve is defined as the dynamic fracture toughness KIC. Figure 6(b) displays the variation in KIC versus Dc. As Dc increases from 0 to 4.42%, there is an obvious decrease in KIC from 5.22 to 2.15 MPa m1/2, with a decrease rate of 58.81%. Lots of active minerals in the specimen and H+ ions in the chemical solution provide the sufficient condition for the water-rock interaction. The compact structure of the rock gradually becomes relatively loose. The cohesion and internal friction angle inside the specimen are reduced to a great extent. The bonding strength between mineral particles also decreases. It inevitability leads to the degradation of the dynamic fracture toughness of rock. The variation process of KIC can be fitted using a linear function and the corresponding fitting function is expressed. The fitting coefficient of determination R2 is 0.988, indicating a good fitting quality.Figure 6
(a) Typical stress intensity factor-time curve in a dynamic NSCB test, (b) variation in dynamic fracture toughness versus damage variable.
(a)(b)


## 4.2. The Failure Characteristic

### 4.2.1. Failure Process

A HS camera was used to monitor the dynamic failure process of specimen. The corresponding photos of six representative specimens with differentDc are presented in Figure 7, demonstrating the process of crack propagation. Each picture corresponds to a specific time point, while the time zero indicates that the incident pulse has just been transmitted to the specimen. Figure 7(a) shows the dynamic failure process of the natural specimen. At the start time 0 μs, a complete NSCB specimen is sandwiched between the incident bar and the transmitted bar. After around 120 μs, the main crack initiates at the artificial notch, in which the tensile stress is the maximum. Then at 160 μs, the main crack subsequently develops into an obvious radial crack along the loading direction. Finally, the main crack propagates throughout the whole specimen, and the specimen is separated into two identical parts along the main crack at 200 μs.Figure 7
The failure processes and corresponding extraction of main crack path of binary images of the NSCB specimens: (a)–(f) corresponding to Dc = 0, 1.16, 1.95, 3.02, 3.62, 4.42%.
(a)(b)(c)(d)(e)(f)It can be seen that the failure process is affected byDc. On the one hand, as Dc increases, the time point of the initiation of the main crack is advanced. When Dc = 4.42%, the main crack (see the white dotted circle in Figure 7(f)) is initiated at 80 μs, which is about 40 μs earlier than that of the natural specimen. On the other hand, although the severely damaged specimens are still separated into two parts, the tortuosity of the main crack path increases. Furthermore, some debris could be found by observing the failure surface of the damaged specimens.


### 4.2.2. Fractal Dimension of the Crack Propagation Path

A digital image can be regarded as a matrix of pixel values [30]. If the number of pixels is i, the RGB image is an i×3 matrix and the range of value of each element is 0∼255. For a grey image with i elements, the value range of each element is also 0∼255. For a black and white image with i elements, the value range of each element is {0, 1}, i.e., black and white. Based on the histogram equalization method, the RGB image is enhanced and converted into a grey image. By selecting a suitable grey threshold, the grey image is converted into a black and white picture that is easy to process and analyze. This process is called binarization, as shown in Figure 8. The pictures of the ultimate failure modes of the damaged specimens were processed as the above method (see the rightmost column in Figure 7).Figure 8
Image processing and crack identification of NSCB specimen: (a) Image of NSCB specimen before loading recorded by high-speed camera, (b) image enhancement based on histogram equalization method, (c) binary image of specimen, (d) extraction of crack path in specimen.
(a)(b)(c)(d)To further quantitatively investigate the influence ofDc on the tortuosity of the main crack of the damaged specimen, based on the processed binary images, the box fractal dimension df of the main crack was calculated. The calculation process is to cover the black area of the binary image with square black pixel blocks whose side length r ranges from small to large and to count the number N(r) of pixel blocks that are required for each side length [64, 65]. Changing r could obtain different N(r). Therefore, the df of the crack path can be calculated by the following formula [66]:(7)df=−limr⟶0lgNrlgr.Figure9(a) displays the calculation process of df by the above method. The function of the fitting line is lgN(r) = 3.30 + 1.44 × lgr−1, i.e., df is 1.44. Using this method, the values of df of all specimens are calculated and plotted in Figure 9(b).Figure 9
Fractal dimension calibration and results. (a) Plot of box-counting method applied to curved crack of typical fractured NSCB specimen; (b) variation in fractal dimension versus damage variable.
(a)(b)AsDc increases from 0 to 4.42%, df increases from 1.47 to 1.59, by an increase rate of 8.16%. The linear function expressed in Figure 9(b) fits the df data very well and the fitting coefficient of determination R2 of 0.982. In the corrosion process, lots of active minerals of the specimen participate in water-rock interaction, resulting in the initiation and propagation of defects; these damaged areas are always preferentially through, which result in the continuous change of the direction of the forward propagation of the main crack [67]. As a result, df increases.


### 4.2.3. Surface Roughness of Fracture

The reconstructed fracture surfaces of the damaged NSCB specimens are shown in Figure10. The digitalized fracture surface can be regarded as an assembly of many elements (0.1 mm × 0.1 mm area) with different asperity heights (the height from the average surface height), slope angles (the angle between normal vectors on each element from the z-direction), and aspect directions (the projection of the element plane orientation with respect to the x-direction) [68]. The variations in the standard deviations of asperity height, slope angle, and aspect direction of the fracture surfaces versus Dc are plotted in Figure 11. The standard deviation of all three spatial distribution parameters shows an increasing trend with increasing Dc. As Dc increases from 0 to 4.42%, the standard deviation of the three parameters shows an increase rate of 41.58% (asperity height), 9.12% (slope angle), and 12.63% (aspect direction), respectively. Therefore, the corrosion damage has a distinct effect on roughness, waviness, and undulation of the fracture surfaces.Figure 10
The digitalized fracture surfaces of damaged specimens: (a)–(f) corresponding toDc = 0, 1.16, 1.95, 3.02, 3.62, 4.42%.Figure 11
Variations in standard deviation of asperity height, slope angle, and aspect direction of fracture surface mesh elements versus damage variable.The joint roughness coefficient (JRC) can quantitatively reflect the roughness of the fracture surface. In previous researches [69, 70], to determine the roughness of a 3D fracture surface, many 2D profiles were extracted from each surface by dividing the fracture surface into several equally spaced lines. Then the JRC of these 2D profiles were calculated, and their average value was regarded as the overall JRC value of the 3D rock fracture surface. It is a dimensionless index generally ranging from 0 to 20, first proposed by Barton and Choubey [71], which could be calculated as follows [72]:(8)JRC=32.20+32.47lgZ2,Z2=1M∑zi−1−zixi−1−xi21/2,where Z2 represents a dimensionless roughness parameter that is defined as the root mean square of the first deviation of a profile; xi and zi represent the coordinates of the fracture surface profile; M represents the number of sampling points along the length of a 2D fracture.The actual area of the fracture surfaceSa can also directly reflect the roughness of the fracture surface. In general, the integral method is adopted to calculate Sa. Assuming the fracture surface is continuum and derivable, the corresponding Sa could be calculated as follows [73]:(9)Sa=∫surface1+∂z∂xx,y2+∂z∂yx,y21/2dxdy≈d2∑i=1Nx−1∑j=1Ny−11+zi+1,j−zi,jd2+zi,j+1−zi,jd2,where Nx and Ny represent the number of points along the x and y axis; d represents the side length of square elementary surfaces; zi, j = z(xi, yj).The variations in JRC andSa versus Dc are plotted in Figures 12(a) and 12(b), respectively. With an increase in Dc from 0 to 4.42%, JRC increases from 12.45 to 16.81, or by 35.05%; Sa increases from 5.3 to 5.82 cm2, or by 9.81%. Furthermore, the results can also be best fitted with a linear function. Both the fitting coefficients of determination R2 are larger than 0.98, implying that the linear function fits the experimental data very well. As Dc increases, the numbers of pores and defects randomly distributed inside the specimen increase. Accordingly, the probability that the main crack encounters the weak interfaces increases in the failure process. The specimen will select the path that is easiest to propagate by continually adjusting the direction of advancement [67]. Therefore, the roughness of the fracture surface increases.Figure 12
Variations in morphology of the fracture surface versus dynamic damage variable: (a) JRC, (b) the actual area.
(a)(b)


## 4.2.1. Failure Process

A HS camera was used to monitor the dynamic failure process of specimen. The corresponding photos of six representative specimens with differentDc are presented in Figure 7, demonstrating the process of crack propagation. Each picture corresponds to a specific time point, while the time zero indicates that the incident pulse has just been transmitted to the specimen. Figure 7(a) shows the dynamic failure process of the natural specimen. At the start time 0 μs, a complete NSCB specimen is sandwiched between the incident bar and the transmitted bar. After around 120 μs, the main crack initiates at the artificial notch, in which the tensile stress is the maximum. Then at 160 μs, the main crack subsequently develops into an obvious radial crack along the loading direction. Finally, the main crack propagates throughout the whole specimen, and the specimen is separated into two identical parts along the main crack at 200 μs.Figure 7
The failure processes and corresponding extraction of main crack path of binary images of the NSCB specimens: (a)–(f) corresponding to Dc = 0, 1.16, 1.95, 3.02, 3.62, 4.42%.
(a)(b)(c)(d)(e)(f)It can be seen that the failure process is affected byDc. On the one hand, as Dc increases, the time point of the initiation of the main crack is advanced. When Dc = 4.42%, the main crack (see the white dotted circle in Figure 7(f)) is initiated at 80 μs, which is about 40 μs earlier than that of the natural specimen. On the other hand, although the severely damaged specimens are still separated into two parts, the tortuosity of the main crack path increases. Furthermore, some debris could be found by observing the failure surface of the damaged specimens.


## 4.2.2. Fractal Dimension of the Crack Propagation Path

A digital image can be regarded as a matrix of pixel values [30]. If the number of pixels is i, the RGB image is an i×3 matrix and the range of value of each element is 0∼255. For a grey image with i elements, the value range of each element is also 0∼255. For a black and white image with i elements, the value range of each element is {0, 1}, i.e., black and white. Based on the histogram equalization method, the RGB image is enhanced and converted into a grey image. By selecting a suitable grey threshold, the grey image is converted into a black and white picture that is easy to process and analyze. This process is called binarization, as shown in Figure 8. The pictures of the ultimate failure modes of the damaged specimens were processed as the above method (see the rightmost column in Figure 7).Figure 8
Image processing and crack identification of NSCB specimen: (a) Image of NSCB specimen before loading recorded by high-speed camera, (b) image enhancement based on histogram equalization method, (c) binary image of specimen, (d) extraction of crack path in specimen.
(a)(b)(c)(d)To further quantitatively investigate the influence ofDc on the tortuosity of the main crack of the damaged specimen, based on the processed binary images, the box fractal dimension df of the main crack was calculated. The calculation process is to cover the black area of the binary image with square black pixel blocks whose side length r ranges from small to large and to count the number N(r) of pixel blocks that are required for each side length [64, 65]. Changing r could obtain different N(r). Therefore, the df of the crack path can be calculated by the following formula [66]:(7)df=−limr⟶0lgNrlgr.Figure9(a) displays the calculation process of df by the above method. The function of the fitting line is lgN(r) = 3.30 + 1.44 × lgr−1, i.e., df is 1.44. Using this method, the values of df of all specimens are calculated and plotted in Figure 9(b).Figure 9
Fractal dimension calibration and results. (a) Plot of box-counting method applied to curved crack of typical fractured NSCB specimen; (b) variation in fractal dimension versus damage variable.
(a)(b)AsDc increases from 0 to 4.42%, df increases from 1.47 to 1.59, by an increase rate of 8.16%. The linear function expressed in Figure 9(b) fits the df data very well and the fitting coefficient of determination R2 of 0.982. In the corrosion process, lots of active minerals of the specimen participate in water-rock interaction, resulting in the initiation and propagation of defects; these damaged areas are always preferentially through, which result in the continuous change of the direction of the forward propagation of the main crack [67]. As a result, df increases.


## 4.2.3. Surface Roughness of Fracture

The reconstructed fracture surfaces of the damaged NSCB specimens are shown in Figure10. The digitalized fracture surface can be regarded as an assembly of many elements (0.1 mm × 0.1 mm area) with different asperity heights (the height from the average surface height), slope angles (the angle between normal vectors on each element from the z-direction), and aspect directions (the projection of the element plane orientation with respect to the x-direction) [68]. The variations in the standard deviations of asperity height, slope angle, and aspect direction of the fracture surfaces versus Dc are plotted in Figure 11. The standard deviation of all three spatial distribution parameters shows an increasing trend with increasing Dc. As Dc increases from 0 to 4.42%, the standard deviation of the three parameters shows an increase rate of 41.58% (asperity height), 9.12% (slope angle), and 12.63% (aspect direction), respectively. Therefore, the corrosion damage has a distinct effect on roughness, waviness, and undulation of the fracture surfaces.Figure 10
The digitalized fracture surfaces of damaged specimens: (a)–(f) corresponding toDc = 0, 1.16, 1.95, 3.02, 3.62, 4.42%.Figure 11
Variations in standard deviation of asperity height, slope angle, and aspect direction of fracture surface mesh elements versus damage variable.The joint roughness coefficient (JRC) can quantitatively reflect the roughness of the fracture surface. In previous researches [69, 70], to determine the roughness of a 3D fracture surface, many 2D profiles were extracted from each surface by dividing the fracture surface into several equally spaced lines. Then the JRC of these 2D profiles were calculated, and their average value was regarded as the overall JRC value of the 3D rock fracture surface. It is a dimensionless index generally ranging from 0 to 20, first proposed by Barton and Choubey [71], which could be calculated as follows [72]:(8)JRC=32.20+32.47lgZ2,Z2=1M∑zi−1−zixi−1−xi21/2,where Z2 represents a dimensionless roughness parameter that is defined as the root mean square of the first deviation of a profile; xi and zi represent the coordinates of the fracture surface profile; M represents the number of sampling points along the length of a 2D fracture.The actual area of the fracture surfaceSa can also directly reflect the roughness of the fracture surface. In general, the integral method is adopted to calculate Sa. Assuming the fracture surface is continuum and derivable, the corresponding Sa could be calculated as follows [73]:(9)Sa=∫surface1+∂z∂xx,y2+∂z∂yx,y21/2dxdy≈d2∑i=1Nx−1∑j=1Ny−11+zi+1,j−zi,jd2+zi,j+1−zi,jd2,where Nx and Ny represent the number of points along the x and y axis; d represents the side length of square elementary surfaces; zi, j = z(xi, yj).The variations in JRC andSa versus Dc are plotted in Figures 12(a) and 12(b), respectively. With an increase in Dc from 0 to 4.42%, JRC increases from 12.45 to 16.81, or by 35.05%; Sa increases from 5.3 to 5.82 cm2, or by 9.81%. Furthermore, the results can also be best fitted with a linear function. Both the fitting coefficients of determination R2 are larger than 0.98, implying that the linear function fits the experimental data very well. As Dc increases, the numbers of pores and defects randomly distributed inside the specimen increase. Accordingly, the probability that the main crack encounters the weak interfaces increases in the failure process. The specimen will select the path that is easiest to propagate by continually adjusting the direction of advancement [67]. Therefore, the roughness of the fracture surface increases.Figure 12
Variations in morphology of the fracture surface versus dynamic damage variable: (a) JRC, (b) the actual area.
(a)(b)


## 4.3. Energy Evolution

According to the three-wave method, the energy carried by the various stress wave of the SHPB system could be obtained by the following formulae [74]:(10)Wi=AbCbEb∫0tσit2dt,Wr=AbCbEb∫0tσrt2d,,Wt=AbCbEb∫0tσtt2dt,where Wi, Wr, and Wt represent the incident, reflected, and transmitted energy, respectively.Assuming that the energy loss at ends of specimen and bars is negligible, according to the law of conservation of energy, the fracture energyWF by the specimen in the process of dynamic loading can be calculated by the following formula:(11)WF=Wi−Wr−Wt−K.After specimen fracture, the specimen split into two 1/4 disks, andK is the residual kinetic energy of the two 1/4 disks. As K only accounts for approximately 5% of the dissipated energy of the specimen at low and medium loading rates (10−4 ∼ 102 s−1) [75], neglecting K will not have a substantial influence on the experimental results.Based on equations (11) and (12), the fracture energy WF is obtained and plotted in Figure 13(a). As Dc increases from 0 to 4.42%, there is an obvious decrease in WF from 4.96 to 2.21 J, with a decrease rate of 55.41%. However, it can be observed that, for several specimens, as Dc increases, WF remains unchanged or even increases (see the black dotted circles). To investigate this phenomenon, the fracture energy per unit fracture surface G is calculated by the following formula:(12)G=WFSa.Figure 13
Variations in energy versus damage variable: (a) fracture energy, (b) fracture energy per unit fracture surface.
(a)(b)The variation inG is plotted in Figure 13(b). With an increase in Dc from 0 to 4.42%, G decreases from 0.94 to 0.38 J cm−2, or by 59.39%. The linear function expressed in Figure 13(b) fits the G data very well with the fitting coefficient of determination R2 of 0.983. The reduction in G indicates that the interior structure has been damaged due to corrosion. The particles inside the specimen slide more easily between each other and the links between the molecular bonds are broken. As a result, the fracture energy per unit fracture surface during the crack propagation of the corroded specimens is much less than that of the natural specimen. Moreover, the increase of the number of pores and defects is partly responsible for the reduction in G. It can be said that, in this study, compared with WF, G can more clearly reflect the corrosion damage degree done to the internal structure of the specimen due to taking the dramatic increase in Sa into account.


## 5. Discussion

The dynamic fracture properties of the damaged specimen decrease to various degrees after corrosion treatment, which results in the complex hydrophysical and hydrochemical effects on the marble. In terms of physical effect, water lubricates and softens the interface between the mineral particles, decreasing the friction coefficient and cohesion along the interface. In terms of chemical effect, the reaction between the chemical solution and the active mineral particle in the marble plays a crucial role in the deterioration of the mechanical properties. Under acidic conditions, some active main mineral components, such as CaO, Al2O3, and MgO, react with the H+ ions in solution as follows:(13)CaO+2H+⟶Ca2++H2O,MgO+2H+⟶Mg2+H2O,Al2O3+6H+⟶2Al3++3H2O,and based on the result of XRD test, the main components of the tested marble in this study are as follows: calcite, dolomite, and mica. Under acidic conditions, these main mineral components are susceptible to chemical reactions with the H+ ions in solution as follows:(14)CaCO3Calcite+2H+⟶Ca2++H2O+CO2↑,CaMgCO32Dolomite+4H+⟶Ca2++Mg2++2H2O+2CO2↑,KAl3Si3O10OH2Mica+10H+⟶K++3Al3++3H4SiO4.Compared with XRD test, X-ray fluorescence (XRF) technique can directly determine the mineral content of the rock. So in this study, the XRF test was carried out for the damaged specimens to determine the content of active minerals. Based on the testing results, the variations in the contents of the minerals involved in the above reaction equations (CaO, MgO, Al2O3, and SiO2) are plotted in Figure 14. The contents of CaO, MgO, and Al2O3 for Dc = 0 are 92.45%, 4.34%, and 1.95%, whereas for Dc = 4.42%, the contents of CaO, MgO, and Al2O3 are 85.51%, 3.35%, and 0.61%, showing an decrease of 7.51%, 22.81%, and 68.69%, respectively. Conversely, the content of SiO2 shows an increase factor of 5.89 in the Dc range of 0–4.42%.Figure 14
Variations in mineral contents of marbles versus damage variable.The increase/decrease rates of these minerals can reflect the severity of the chemical reaction. In the corrosion process, certain ions in solution are adsorbed onto the surfaces of these minerals and substitute for ions in the mineral structure. New resultants are generated. In terms of composition, weight, and density, the new resultants and the original minerals are different. As a result, the volumetric space occupied by minerals changes and both the inter- and intraparticle dissolution pores generate. In this process, the bonding strength between minerals particles would reduce, which leads to the degradation of the dynamic fracture toughness and the decrease in fracture energy. Due to the generation of weak interfaces, the propagation path of the main crack is more tortuous, which results in the growth in both the main crack fractal dimension and the roughness of the fracture surface. Therefore, through the analysis of the variations of contents of various active minerals, the response of dynamic fracture mechanical behavior of marble after corrosion treatment could be essentially explained.


## 6. Conclusions

In this paper, a batch of notched semicircular bend (NSCB) marble specimens was prepared and then saturated with chemical solutions with variouspH values (2, 4, and 6) and corrosion times (0, 30, 60, 90, 120, and 150 d). Then, the dynamic fracture test was conducted for the damaged specimens using the split Hopkinson pressure bar. The following main conclusions can be drawn:Using the nuclear magnetic resonance (NMR) technique, the variation in porosity of the damaged specimens is obtained. Furthermore, the corrosion damage variableDc characterized by porosity is quantitatively calculated.The dynamic fracture toughness decreases linearly asDc increases. This is because the growth of the corrosion damage done to the interior structure of the marble specimen reduces the cohesion and internal friction angle inside the specimen to a great extent. The bonding strength between mineral particles decreases.Using a high-speed camera, the failure process of the damage specimens in the dynamic fracture test is monitored. The fractal dimension of the main crack is calculated based on the processed binary images. AsDc increases, the value of factual dimension increases. The fracture surface of the specimen is also digitalized. Both the joint roughness coefficient and the actual area of the fracture surface increase as Dc increases.The fracture energy per unit fracture surface decreases with an increasingDc. The reduction indicates that the links between the molecular bonds are destroyed and the particles inside the specimen slide more easily between each other.The hydrophysical and hydrochemical coupled effect causes the degradation of mechanical properties done to the specimen. For the hydrophysical effect, water lubricates and softens the interfaces between the mineral particles. For the hydrochemical effect, the active minerals react with the H+ in solution. By measuring the contents of several active minerals, combining with reaction equations, the hydrochemical effect on the specimen is analyzed essentially.In this paper, the dynamic fracture test was conducted at a constant air pressure. Many test conditions were not considered, such as specimen size, strain rate effect, and so on. These factors can significantly influence the fracturing behavior, which should be analyzed in the future works.



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*Source: 8182504-2022-04-29.xml*