#### Abstract

Coral mud, a kind of special material used for constructing islets in reclamation projects, is widely spread in the South China Sea. Combined with microstructure research, a series of triaxial tests were performed in this paper to study the static shear strength characteristics and potential factors that can influence them. The effective stress path was similar to the total stress path because of the unique microstructure resulting in a high strength and a high dissipation rate of the pore pressure in the coral mud. The initial void ratio and the initial confining pressure affected the strength and deformation characteristics of the coral mud. When the soil came to failure, the pore pressure coefficient *A*_{f} varied linearly with the initial void ratio. The critical friction angle was greatly influenced by the confining pressure, and its magnitude first developed to a peak value and then decreased as the void ratio increased. This change showed that there was a linear relationship between the initial elastic modulus *E*_{0i} and lg*p*_{0} as well as between the secant modulus *E*_{50} and *p*_{0}. The estimation ability of Cam-Clay was verified in this research. The value of parameter *λ* was determined incrementally by a larger initial void ratio, while the value of parameter *M* decreased smoothly first and then rose slightly; the selection of parameter *κ* was approximately 0.0035. The results supported that the Cam-Clay model is able to simulate the stress-strain relationship of coral mud, and a referenced estimation can be reliably and efficiently obtained for the reclamation projects of constructing islets.

#### 1. Introduction

The South China Sea covers a vast area and enjoys a superior geographical location and strategic position [1]. In recent years, China has accelerated the development and utilization of coral reefs in the South China Sea. During the filling process, calcareous soil with large particles is first deposited at the bottom under gravity, while small particles, referred to as coral mud, are suspended in the water to form silty sand after drifting [2]. According to the national panel survey, coral mud is one of the most important submarine sediments in the eastern part of the South China Sea, accounting for 6.12% of the total sediments [3]. In addition, because of the intermittent construction of the filling operation, the coral soil layer presents a discontinuous distribution in the foundation. As a weak interlayer whose settlement and bearing capacity will inevitably affect the whole foundation, it is necessary to conduct in-depth and systematic research on the shear characteristics of coral mud to provide scientific and reasonable design parameters for the engineering construction of coral reefs.

The mineral composition of coral mud is similar to that of calcareous sand, with up to 96% calcium carbonate. A large number of research studies have been devoted to investigating the factors influencing the shear properties of calcareous sand, including the confining pressure, density, particle breakage [4], and shear rate [5]. Studies have found that the shear characteristics of calcareous sand are greatly dependent on the confining pressure [6]. If the confining pressure increases, then the strain under peak stress increases [7], and the initial response under a low confining pressure is rigid, with an obvious yield point and strain hardening stage [8]. The impact of dilatancy on shear strength is far greater than that caused by particle breakage [9, 10].

According to particle size classification, coral mud is silty or silty clay. Geotechnical tests have shown that the water content is an important factor influencing the shear properties of clay and silt. Zhang et al. [11, 12] proposed the influence of the water content on red clay; specifically, with an increase in the water content, the peak cohesion and residual cohesion decrease, and the strain changes from softening to hardening. Xu et al. [13, 14] found that the pore pressure and cohesion increase when Shanghai soft soil is damaged. Feng et al. conducted a series of tests on silty clay and found that the failure shear strain value of silty soil decreases with increasing water content [15], and strain softening shows a weakening trend [16]. Wang et al. [17] found that the relationship between the cohesion and water content of calcareous silt can be represented by an M-shaped curve. The water contents corresponding to the two peaks of the M-type curve increase with increasing dry density.

At present, research on coral mud is scarce and has mostly been focused on the permeability sedimentary aspects. Shen et al. [18] considered the initial concentration to have a significant impact on the isovelocity deposition time of the coral mud. Wang [2] found that the coefficient of permeability of coral mud decreases with increasing density when the initial moisture content remains the same and reaches a maximum at saturation. Based on the existing research of calcareous sand and silty clay, the effects of the confining pressure and water content on coral mud were studied. Considering that, in the saturated triaxial test, the water content can be controlled by the initial void ratio [19] and the initial void ratio is a parameter of the Cam-Clay model, in this paper, the initial confining pressure and the initial void ratio were taken as variables. Taizhou soil was used as the control group. The applicability of the Cam-Clay model was discussed by comparing the simulation results with the experimental results.

#### 2. Materials and Methods

Based on laboratory experiments, the static shear characteristics of coral mud samples were measured and compared with those of Taizhou soil in Zhejiang Province. The testing results are presented and discussed with respect to the following: (1) stress-strain relationship, (2) pore pressure development, (3) stress path, (4) friction angle (e.g., mobilized friction angle, critical state friction angle, and peak state friction angle), (5) modulus (e.g., initial elastic modulus and secant modulus), and (6) estimation ability of the Cam-Clay model.

##### 2.1. Physical Characteristics of Materials

The coral mud for testing was obtained from the seabed of a reef in the South China Sea. Coral mud is a loose, unconsolidated, powdery deposit, light yellow to white in colour. To highlight the unique physical and mechanical characteristics of coral mud, Taizhou soil with similar liquid limits, plastic limits, and particle gradations was selected for comparison in consolidated undrained triaxial tests. The images of coral mud and Taizhou soil are provided in Figure 1.

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An X-ray diffractometer was used to analyse the mineral composition and tabulate the results in Table 1. Figure 2 presents the distributions of each soil particle size. According to the standard [20], coral mud is silty clay, with a uniformity coefficient of *C*u = 37.5 and coefficient of curvature *C*c = 0.4; it is classified as poorly graded soil. Table 2 provides the basic characteristics.

##### 2.2. Microstructure of the Materials

The microstructures of coral mud and Taizhou soil were magnified by 50 *k* with scanning electron microscopy (SEM). As shown in Figure 3(a), the granule morphology consisted of mainly strips and needles, with a small amount of irregular particles and obvious pore development. Figure 3(b) shows that most particles of Taizhou soil were clustered together in the form of aggregates, where small particles were attached on the surface of the large particles, mainly in face-to-face contact.

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Forty representative particles were randomly selected to obtain the shape parameter circular degree *R* and ring diameter ratio *T* [21–23]. *R* measures the edges and corners. When *R* = 1, the particle is round. *T* represents the ratio of the longest axis to the shortest axis of the particle. The larger the value is, the closer the particle is to the dendritic shape [24]. As shown in Figure 4, *R*_{(coral mud)} is mainly distributed between 0.58 and 0.74, while *T* is between 3.12 and 4.87, consistent with the statistical average values of *R* and *T* (0.687 and 4.178). Compared with the mean values of *R* (0.915) and *T* (1.512) in Taizhou soil, the particle morphology of coral mud is extremely irregular due to its special sedimentary environment and chemical composition.

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##### 2.3. Testing Program

In this study, we first used X-ray diffraction and SEM to understand the chemical composition and microscopic fabric of the testing materials. After that, the effects of the initial confining pressure and initial void ratio on the shear properties were investigated by CU shear tests.

The apparatus used in the triaxial tests was an LSY30-1 stress-strain controlled triaxial instrument. The samples were evenly mixed and stored in a humidor for 24 h before being divided into five layers with the same mass and height. After 24 h of vacuum saturation, the samples were loaded into a pressure chamber, and then the reverse pressure saturation method was adopted until Δ*u/*Δ*σ*_{3}>0.98. The specimen has a diameter of 39.1 mm, a height of 80 mm, and an axial shear rate of 0.04 mm/min. The testing program is provided in Table 3.

#### 3. Results and Discussion

##### 3.1. Stress-Strain Relationship

###### 3.1.1. Effects of the Initial Confining Pressure

The initial void ratio was 0.83, and CU shear tests were performed on the coral mud and Taizhou soil under four confining pressures of 100 kPa, 200 kPa, 300 kPa, and 400 kPa (backpressure 50 kPa). The stress-strain behaviours are given in Figure 5. The strengths of the two soil samples both significantly increase with increasing confining pressure, especially the strength of the coral mud of adjacent confining pressure, which increases by nearly 500 kPa. The strength of coral mud was much higher than that of Taizhou soil under the same confining pressure. For a quantitative comparison, we calculated the *c* and *φ* of the two soil samples and calculated the mean values (Table 4). The mean internal friction angle of Taizhou soil is 15°, in line with the values of engineering experience, which is generally 15° to 25° but far smaller than those of coral mud. This result could be attributed to the slip-like structure and unique physicochemical properties of coral mud, making the bite force generated by interparticle embedding large and strong.

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In addition, the stress-strain growth trends of the two are also significantly different. The stress of coral mud increases rapidly at the initial stage of shear; when *ε* is 1%, the stress reaches approximately 2/3 of the shear strength, and the elastic modulus in the early stage is positively correlated with the confining pressure. In contrast, only when the confining pressure is 100 kPa does the Taizhou soil curve show a platform. The stress under other confining pressures stabilizes or even slightly decreases at approximately 50 kPa before *ε* = 2% and increases sharply between 2% and 3%. After *ε* = 3%, the stress shows an increase with a steady rate whose amplitude accounts for 1/4 to 1/2 of the total stress.

From a microperspective, this increase could be a result of various particle contact responses. Previous studies [25, 26] have shown that the contact between particles includes frictional contact and cemented contact. The contact of Taizhou soil is cemented contact, and its stress-strain behaviour can be divided into the following three stages: (1) the OA stage where the stress increases linearly, (2) the AB stage where cement begins to break or extrude in which the stress develops smoothly or even declines at this stage, and (3) the BC stage where particles come into direct contact. The stress increases rapidly at this stage, and its growth rate is greater than that at the OA stage. Due to the lack of cementing materials, coral mud skips the OA and AB stages. Its irregular particles come into direct contact from the beginning, and the stress levels off after a rapid increase.

###### 3.1.2. Effects of the Initial Void Ratio

Figure 6 shows the stress-strain relationship with different initial void ratios of coral mud and Taizhou soil. For Taizhou soil, the stress-strain behaviours of different *e*_{0} values are roughly the same as the deviatoric stress rising by a small margin with a decrease in *e*_{0}. In addition, the strain when the stress surges declines with decreasing *e*_{0}, which means that the cement is more likely to be extruded and the particles are more likely to come into direct contact with each other under high dry density conditions. In contrast, the coral mud is more significantly affected, manifested as the diverse variation trend as well as the D-value, which can reach 500 kPa. When *e*_{0} = 0.89, the stress-strain plot is obviously different in that it is an enhanced curve whose peak stress is higher than *e*_{0} = 0.83 under different confining pressures. From the perspective of elastoplasticity, when the pressure increases, the coral mud with a large porosity transits from the elastic stage to the ideal plastic stage where part of the structure is broken. Its particles are more prone to particle dislocation and rearrangement, which fills the pores and brings about a growth in the shear strength when *e*_{0} = 0.89 [27]. Taizhou soil has no such feature owing to its shape and cementing substance, which do not facilitate maloperation and occlusion friction compared with needle-like particles [28].

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##### 3.2. Pore Pressure Development

###### 3.2.1. Effects of the Initial Confining Pressure

In this part, we controlled *e*_{0} = 0.69 to study the development law of the pore pressure under different confining pressures. As shown in Figure 7, coral mud has a better permeability with a higher dissipation rate of the pore pressure. Figure 8 presents the pore pressure at the shear stage. For Taizhou soil, the pores are similar to those of common clay that gradually develop to a peak after *ε* = 2% when the cement material is extruded and the particles are in direct contact. During the whole process, the pressures are above zero and are positively correlated with the confining pressure, and the difference value under adjacent confining pressure is up to 80 kPa. In contrast, the pore pressure of the coral mud first rises to a positive peak in a small range and then decreases to a stable negative value. The reason for the difference may be the mineral composition. Calcium carbonate is the main substance that makes up the coral mud, whose coefficient of permeability is higher than that of common clay. Therefore, the pore pressure of coral mud is hard to accumulate.

###### 3.2.2. Effects of the Initial Void Ratio

The pore pressures with different *e*_{0} values are shown in Figure 9. The peak pore pressure of both samples increases with increasing *e*_{0}, but coral mud has a larger difference value with respect to the pore pressure as *e*_{0} changes.

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The pore pressure coefficient of sample failure is expressed as *A*_{f} to represent the final failure state. The relationships between *A*_{f} and *e*_{0} are shown in Figure 10. It is clear that *A*_{f} and *e*_{0} are linearly correlated, but the effect of *e*_{0} varies under different *p*_{0} values. When *p*_{0} = 100 kPa, *e*_{0} has the greatest effect, and *A*_{f} tends to be stable with increasing *p*_{0}, demonstrating that the two factors are not independent of each other in terms of their effects on *A*_{f}.

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##### 3.3. Effective Stress Path

In conventional triaxial tests, the effective stress path is usually expressed in the *p’*-*q* plane, where *p’* is mean effective stress and *q* is deviatoric stresses:

As shown in Figure 11, because of the unique pore pressure developments during undrained shearing, the effective stress path of coral mud is unlike the normally consolidated clay curve, which develops to the left [28] or the general silt with an “*S*” curve [29]. Additionally, effective stress path is also not the same as the curve of overconsolidated clay, which obviously develops from right to left [30]. This path is similar to the total stress path curve and develops in a straight line. Although the stress path curves under different confining pressures are always similar, as confining pressure does not change the critical state of the soil mass, compared with Taizhou soil, the stress path of coral mud is less affected. The surge of pore pressure only exists at *e*_{0} = 0.89 and *p*_{0} = 400 kPa in the early shear phase, which causes a significant inflection point, and the inclination of other stress path curves of coral mud is almost equal.

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Drawing the critical state line (CSL) according to the stress path, as shown in Figure 12, there is a good linear relationship between *q*_{cs} and *p*_{cs}´, and it passes through the origin, which is consistent with the studies of other scholars. Figure 12 also shows the effective stress ratio *M*_{cs} at the critical state. It can be concluded that the *M*_{cs} value of Taizhou soil declines with increasing *e*_{0}, while that of coral mud first decreases and then slightly increases with increasing *e*_{0}, corresponding to the testing results that when *e*_{0} = 0.89, the deviatoric stress of coral mud continues to increase and finally is higher than the samples of *e*_{0} = 0.83.

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##### 3.4. Friction Angle

The mobilized friction angle *φ*_{m} under the triaxial compression condition is defined as [31]where *η* is defined as the ratio of the deviatoric stress *q* to the effective mean stress *p’*,

The critical state friction angle *φ*_{cs} under the triaxial compression condition can be defined aswhere *η*_{cs} is critical state stress ratio. The test data show that *η* only changes slightly when the strain is 15%. According to the critical state theory [32], the stress state under this strain could be considered a critical state.

The peak state friction angle *φ*_{ps} is defined aswhere *η*_{ps} is the peak state stress ratio.

Figure 13 presents the mobilized friction angle of coral mud and Taizhou soil at different initial void ratios and pressures. The values of *φ*_{cs} and *φ*_{ps} are shown in Table 5. Similar to the stress-strain relationship, the mobilized friction angle-strain relationship of coral mud presents a platform shape, and when *e*_{0} = 0.89, the curve has the property of overpenetration, while the other curves decrease with an increase in the initial void ratio. Most *φ*_{ps} values overlap with *φ*_{cs,} and the remainder gradually approach the critical state. *φ*_{cs} of coral mud is much greater than that of Taizhou soil, and with increasing confining pressure, *φ*_{cs} of coral mud tends to disperse while the Taizhou soil tends to be dense, indicating that the initial void ratio has a minor effect on *φ*_{cs} of coral mud when the confining pressure is low.

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As shown in Figure 14, *φ*_{cs} of Taizhou soil decreases first and then tends to be stable with an increase in the confining pressure, which indicates that an increase in the confining pressure gradually has less influence on the critical friction angle of Taizhou soil. Figure 15(b) also proves this conclusion, as the 300 kPa and 400 kPa curves almost coincide. In contrast, the confining pressure is an important parameter on *φ*_{cs} of coral mud. With an increase in the confining pressure, *φ*_{cs} first decreases and then increases when *e*_{0} = 0.78 and *e*_{0} = 0.83; first increases, then decreases, and then increases when *e*_{0} = 0.69; and first decreases, then increases, and then decreases when *e*_{0} = 0.89. Figure 15(a) illustrates that, at 100 kPa, the effect of the initial void ratio is minor as the curve approximates a straight line, which is consistent with the phenomenon of the high coincidence of *φ*_{cs} in Figure 13(a). Under the other confining pressures, *φ*_{cs} of coral mud first decreases and then increases with the increase in *e*_{0}.*p*_{0} is the initial confining pressure, *e*_{0} is the initial void ratio, *φ*_{cs-c} is the critical state friction angle of coral mud, *φ*_{ps-c} is the peak state friction angle of coral mud, *φ*_{cs-T} is the critical state friction angle of Taizhou soil, and *φ*_{ps-T} is the peak state friction angle of Taizhou soil.

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##### 3.5. Modulus

The initial elastic modulus *E*_{0i} is an important parameter, indicating the deformation behaviour of coral mud. It can be expressed as [33]where *ε*_{a} means the axial strain constrained within 0.1% for the initial slope of the stress-strain curve, where the deformation is supposed to be elastic.

*E*_{50} is the ratio of the stress of half of the peak stress of soil to the corresponding strain [34], which is defined aswhere *q*_{ps} is peak stress during shearing and *ε*_{aps} is the corresponding strain. Table 6 presents the values of *E*_{0i} and *E*_{50}, and the relationships between *E*_{0i} and *E*_{50} and *p*_{0} and *e*_{0} are shown in Figures 16 and 17, respectively.

The initial elastic modulus of coral mud is nearly 10 times that of Taizhou soil, and the influences of *p*_{0} and *e*_{0} on coral mud are more obvious and regular. *E*_{0i} of coral mud can be expressed as a linear function of the logarithm of *p*_{0} (*R*^{2}˃0.98), while the slope of the fitted line equation does not change with the change in *e*_{0}; this result means that *E*_{0i} increases 139.55 MPa for every 100 kPa increase in lg*p*_{0}, independent of *e*_{0}. With an increase in *e*_{0}, *E*_{0i} of coral mud first decreases and then increases, but the growth range is small and the whole tends to be stable. The relationship between *E*_{0i} and *e*_{0} under different confining pressures is similar, which also proves that the two factors are independent of each other.

Similar to the initial elastic modulus, the secant modulus of coral mud is also much higher than that of Taizhou soil. *E*_{50} increases linearly with increasing lg*p*_{0}, but the effects of *p*_{0} and *e*_{0} on *E*_{50} of coral mud are not completely independent. As shown in Figure 18, when *e*_{0} = 0.89, the slope of the equation of the fitting line is much smaller than the others due to its special hardening law. Its stress increases continuously with the strain, the strain corresponding to 0.5 *q*_{ps} is larger, and the secant modulus decreases accordingly. This characteristic is also shown in Figure 19; with the increase in *e*_{0} under different confining pressures, *E*_{50} curve tends to be concentrated from parallel.

##### 3.6. Finite Element Simulation of the Stress-Strain Relationship

The Cam-Clay model is suitable for predicting the properties of normally consolidated and weakly overconsolidated clay under critical conditions [35], but whether it is suitable for coral mud remains to be studied. The model parameters *λ*, *κ*, and *M* obtained from one-dimensional compression tests and CU shear tests under confining pressures of 100 kPa–400 kPa were used to simulate the tests under 200 kPa, 400 kPa, and 600 kPa according to the Cam-Clay model.

###### 3.6.1. Calculation of the Cam-Clay Model Parameters

Figure 20 shows the one-dimensional compression trial curve of coral mud. The curve is much gentler than the general compression curve, and the rebounding curve and unloading curve are close to coinciding, indicating that the compressibility and resilience of coral mud are very low.

The relationship among *λ, κ, M*, and *e*_{0} was plotted according to the compression index (Table 7). As shown in Figure 21, *λ* is determined incrementally by a larger initial void ratio and *κ* fluctuates by approximately 0.0035, while *M* first decreases, then stabilizes, and slightly rises. These trends are different from those of Taizhou soil in which *M* linearly decreases with increasing *e*_{0}.

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###### 3.6.2. Simulation Results Analysis

According to the laboratory test results, the saturated coral mud sample with *e*_{0} = 0.89 was subjected to a CU shear test simulation. The sample parameters were set as follows: diameter = 39.1 mm, height = 80 mm, confining pressures = 200 kPa, 400 kPa, and 600 kPa*, v* = 0.38, *λ* = 0.065, *κ* = 0.003, *M* = 1.655, *e*_{0} = 0.89, and soil permeability coefficient = 1.13 × 10^{−6} cm/s.

Figure 22 presents the relationship between the test results and the simulation. Particularly, the predicted modulus in the early stage is smaller than the measured value, and the model could not well reflect the hardening characteristics in the later stage. The unique microstructure of coral mud may be the reason why simulated results do not match the experimental data at low strain range. The irregular particles of coral mud come into direct contact from the beginning and stress increases rapidly at the initial stage of shear, different from common clay whose stress gradually increases at a slower rate. However, the error between the predicted peak and the measured value is small, indicating that the Cam-Clay model has a certain reference for the stress-strain development of coral mud.

#### 4. Conclusions

In this paper, SEM was implemented to better understand the microstructure of coral mud in the South China Sea. A series of triaxial tests were conducted to study the static shear strength behaviour. Cam-Clay was employed to simulate the stress-strain behaviour of the coral mud to verify the estimation ability. The main conclusions can be summarized as follows:(1)The morphology of coral mud particles was extremely irregular, mainly strip and needle shaped. The strength of coral mud under the same confining pressure was much higher than that of Taizhou soil. The initial void ratio *e*_{0} and the initial confining pressure *p*_{0} affected the strength and deformation characteristics. When *e*_{0} = 0.89, the stress-strain plot exhibited an enhanced curve regardless of the confining pressure.(2)The dissipation rate of the pore pressure in the consolidation and shear stages of coral mud was much higher than that of Taizhou soil, and the dilatancy characteristic was significant. When the failure occurred, the pore pressure coefficient varied linearly with the initial void ratio.(3)The effective stress path of coral mud was similar to the total stress path due to the unique pore pressure development.(4)The peak friction angle of coral mud mostly coincided with the critical friction angle. The initial confining pressure had an important influence on the critical friction angle of coral mud. With the exception of 100 kPa, the critical friction angle of coral mud first declined and then developed with an increase in the initial void ratio.(5)The initial elastic modulus of coral mud was nearly 10 times that of Taizhou soil. This result showed that there was a linear relationship between the initial elastic modulus *E*_{0i} and lg*p*_{0} as well as between the secant modulus *E*_{50} and *p*_{0}. The effects of *p*_{0} and *e*_{0} on the *E*_{0i} of coral mud were independent of each other.(6)The value of parameter *λ* was determined incrementally by a larger initial void ratio, while the value of parameter *M* decreased smoothly first and then rose slightly; the selection of parameter *κ* was approximately 0.0035. The results suggest that the Cam-Clay model has a certain reference for predicting the stress-strain relationship of coral mud.

#### Notations

Cc: | Coefficient of curvature |

Cu: | Coefficient of uniformity |

R: | Roundness |

T: | Aspect ratio |

p_{0}: | Initial confining pressure |

ρd: | Dry density |

e_{0}: | Initial void ratio |

c: | Coulomb-molar parameter |

φ: | Internal friction angle |

A: | Pore pressure coefficient |

p’: | Mean effective stress |

q: | Deviatoric stress |

p’_{cs}: | Mean effective stress at the critical state |

q_{cs}: | Deviatoric stress at the critical state |

M_{cs}: | Effective stress ratio at critical state |

φ_{cs}: | Critical state peak state |

φ_{ps}: | Peak state peak state |

ηps: | Peak state stress ratio |

E0_{i}: | Initial elastic modulus |

E50: | Secant modulus at 50% of the peak strength |

C_{s}: | Swelling index |

λ: | Compression index |

κ: | Recompression index. |

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

The authors would like to acknowledge the financial support of the National Natural Science Foundation of China under Grant 51979087.