# Experimental Investigation of the Liquefaction Properties and Post-Liquefaction Volumetric Strain of Calcareous Sand in Dredger Fill Site

Authors: Shenghua Zhao; Yanlin Zhao; Jiang He; Zhenzhong Cao; Lei Wang
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

In this study, dynamic triaxial cyclic tests were conducted to examine the liquefaction properties and post-liquefaction volumetric strain of calcareous sand from a dredger fill site in the midst of the islands and reefs of the South China Sea. The test results indicated that there were some differences in micromorphology and composition between the calcareous sand obtained via dredging and natural calcareous sand. Axial cyclic stress attenuation can lead to higher cyclic vibration than actual liquefaction vibration, and the modified method can eliminate the effect of axial cyclic stress attenuation. Saturated calcareous sand liquefies under undrained and cyclic loading conditions, and the liquefaction resistance of the calcareous sand decreases with an increase of the effective confining pressure in the dense state. Calcareous sand obtained via dredging exhibited a higher liquefaction resistance compared with other types of calcareous sand. Furthermore, the proposed pore pressure development modified model better describes the pore pressure growth of the calcareous sand from the filling site. The fitting parameters of this model exhibited a high correlation with the relative density. Moreover, the post-liquefaction volumetric strain of the calcareous sand is larger than that of quartz sand, exhibiting a linear relationship with relative density.


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## Body

## 1. Introduction

Coral soil is formed by the physical, biological, and chemical processes corresponding to the remains of marine organisms, such as corals, shells, and algae; because its carbonate content is more than 50%, it is called calcareous soil [1, 2]. When calcareous soil is dominated by sand silt and its particle gradation can be classified as sandy soil, it is called calcareous sand. Calcareous soil is distributed in the coastal area between 30° N and 30° S latitudes and covers approximately 40% of the ocean surface [3]. Many countries have carried out large-scale land reclamation projects, such as the airport expansion project in the Maldives, the Colombo port project in Sri Lanka, and the island and reef filling project in the South China Sea. Most of the materials used in reclamation are obtained by winch or rake suction via large on-board equipment. The calcareous soil obtained through the winch or rake suction process is mainly coral reef debris and coral wreckage. Several structures have been built in these areas; however, these structures are at risk from seismic action. Seismic damage surveys from the 1993 Guam earthquake [4], 2006 Hawaii earthquake [5, 6], and 2010 Haiti earthquake [7, 8] indicated that calcareous soil in dredger fill sites can liquefy and cause critical damage. Therefore, it is of great significance to study the liquefaction characteristics and post-liquefaction volumetric strain of calcareous soil to prevent and reduce the risk of an earthquake disaster at calcareous soil sites.Considerable international research has been performed on calcareous soils in the 1980s as a result of the North Rankin “A” oil platform engineering problems [9]. For instance, Liu and Wang [10], Coop et al. [11], and Zhu et al. [12] studied the mechanical properties, particle breakage, and internal pore characteristics of calcareous sand, and Ma et al. [13, 14] studied the mechanical properties of coral sand particles and the compression properties of coral rocks, respectively. These studies demonstrated that calcareous sand is a special geotechnical material with many pores and an irregular shape, and it can be easily broken in a particle-based manner. The engineering properties of calcareous sand are different from those of general continental cohesionless soil. The consensus of many scholars [15–20] is that the liquefaction resistance of calcareous sand is higher than that of quartz sand, but there are still differences in our understanding of whether calcareous sand is liquefied and the influence of various factors on its liquefaction resistance. Gao and Ye [21] noted that calcareous sand in the South China Sea Island and Reef filling site reached a partial liquefaction state under the condition of unobstructed drainage and no liquefaction occurred under these conditions. Hyodo et al. [22] observed that the confining pressure had only a slight effect on the liquefaction resistance (CRR) of calcareous sand with a relative density of 60%. For calcareous sand with a relative density of 80%, the CRR decreased significantly with an increase in the confining pressure. Salem et al. [23] reported that for the same initial relative density and cyclic stress ratio, the number of liquefaction cycles decreased with an increase in the effective confining pressure. Ma et al. [24] considered that the dynamic strength of coral sand in the South China Sea increased with the increase of relative density and effective confining pressure.However, scholars are more concerned about the liquefaction resistance of calcareous sand and less about the pore pressure growth and volumetric strain after vibration. Sandova and Pando [25] examined the growth characteristics of the excess pore water pressure of calcareous sand and reported that compared with Ottawa quartz sand, Cabo Rojo calcareous sand exhibited a higher CRR as well as a greater fluctuation in the excess pore water pressure curve. Moreover, calcareous sand samples with a higher specific gravity and more uniform grading exhibited a higher CRR. Gao and Ye [21] noted that the normalized cumulative pore pressure to vibration ratio of calcareous sand in the South China Sea islands and reefs conformed with the antisinusoidal pore pressure development model proposed by Seed under the undrained condition. Ma et al. [24] considered that the development mode of the pore water pressure of calcareous sand in the South China Sea was considerably different from that of siliceous sand and proposed a modified Seed model for characterization. In addition, research on the volume deformation of calcareous sand has also been discussed. Shahnazari et al. [26] pointed out that the relative density, effective confining pressure, dynamic stress ratio, pore pressure ratio, and maximum shear strain were related to the postcyclic volumetric strain of calcareous sand, and the maximum shear strain was the most important factor. Rezvani et al. [27] studied how physical properties of soil particles play a key role in the mechanical behavior of deposits and provided an estimation method of volume settlement after sand circulation in Hormuz Island.The above research indicates that conclusions of various studies on the liquefaction characteristics of calcareous sand are different, which may be related to its physical properties. The shape and appearance of calcareous sand in various regions are different, and the particle gradation of calcareous sand obtained using different methods will be different. Therefore, it is necessary to study more liquefaction characteristics of calcareous soil in different regions and sites. The study of post-liquefaction volumetric strain of calcareous sand has an important reference for further study of the antiliquefaction treatment of calcareous sand, i.e., the effective control of drainage conditions of calcareous sand can effectively reduce its potential for liquefaction. To address this, in this study, undrained cyclic triaxial tests of calcareous sand in dredger fill sites of islands and reefs in the South China Sea were conducted. Moreover, the effects of relative density, effective confining pressure, and cyclic stress ratio on the liquefaction resistance of calcareous sand, the pore pressure growth, and post-liquefaction volumetric strain were investigated.


## 2. Test Design

### 2.1. Physical Properties of Calcareous Sand

#### 2.1.1. Shape Characteristics of Calcareous Sand

The calcareous soil used in our tests came from the dredger fill site of the South China Sea Islands and reefs. It is coral debris obtained by the cutter suction or rake suction of large-scale ship-borne equipment. Figure1 shows screened samples of calcareous sand. The particle size range of the calcareous soil was 0–100 mm, the thicker calcareous soil comprising coral branches and coral reef blocks, and the finer calcareous soil being coral clastic and coral reef block fragments. The calcareous soil was sieved, and the calcareous sand (with a particle size of less than 2 mm) accounted for more than 60% of the total mass. There was more silt in the calcareous sand with a particle size of less than 2 mm. A particle size of less than 0.075 mm accounted for 5.88% of the total calcareous sand, which may indicate the occurrence of considerable particle breakage during the cutter suction and dredger filling processes [28]. From its irregular appearance, the thicker calcareous soil shape comprised mainly columnar fragments, including block and limb shapes. The finer calcareous soil comprised columnar, spherical, and block shapes, and the surface of the particles was rough and holey.Figure 1
Calcareous sand samples with different particle sizes (mm).
(a)(b)Electron microscope scanning tests were carried out on the calcareous sand from the dredger fill site and the natural calcareous sand. Figure2 shows the SEM images of the two types of sand. It can be seen from the figure that the fine grains of the calcareous sand in the dredger fill site were irregular in shape (column, block, and angle), with uneven surfaces and undeveloped pores. The natural calcareous sand was mainly spherical in shape but comprised irregular angular and columnar shapes. Compared with the calcareous sand from the dredger fill site, the biggest difference was that the surface was full of holes, the larger holes containing the remains of marine microorganisms.Figure 2
SEM images of calcareous sands. (a) Calcareous sand from dredger fill site. (b) Natural calcareous sand.
(a)(b)The above analysis shows that the particle shape and micromorphology of the calcareous sand from the dredger fill site obtained by cutter suction or trailing suction are quite different from those of the natural calcareous sand, which significantly affects the mechanical properties of the calcareous sand.


#### 2.1.2. Physical Properties of Calcareous Sand

The soil samples had a particle size of 0–2 mm, and Fujian standard sand of China was used as the siliceous sand sample. Table1 lists the physical properties of the calcareous and the Fujian sands, and Figure 3 shows their gradation curves, determined according to the Geotechnical Test Rules SL237-1999 (Nanjing Hydraulic Research Institute) [29]. The Gs of the calcareous sand is larger, the curvature coefficient is 1<Cc=1.53<3, and the nonuniformity coefficient is Cu=4.82. This indicates that the grading curve of calcareous soil is continuous, and the variation range of grain composition is wide, which is close to the index of nonuniform soil. The equivalent carbonate content of the calcareous sand is more than 99%, according to XRF element analysis.Table 1
Physical properties of various calcareous and siliceous sands.
Type of sandCalcareous sandCataño [19]Salem et al. [23]Ma et al. [24]Fujian sandSpecific gravity,Gs2.872.862.792.802.65Diameter corresponding to 50% finer,D50 (mm)0.37——0.310.662Diameter corresponding to 10% finer,D10 (mm)0.0920.20.15—0.101Coefficient of uniformity,Cua4.821.052.44.677.82Coefficient of curvature,Ccb1.53——0.862.733Minimum void ratio,emax1.1161.711.041.720.725Maximum void ratio,emin0.5691.340.750.990.329aCu = D60/D10; bCc = D302/(D60 × D10).Figure 3
Grain-size distribution curves of various calcareous sands and Fujian sand [19, 23, 24].


### 2.2. Sample Preparation and Testing Procedures

The diameter and height of the sand samples were 50 mm and 100 mm, respectively. When the ratio of height to diameter is 2.0, the phenomenon of stress concentration can be effectively eliminated [30]. Dry packed samples were used. The dried sand was weighed according to the relative density of each sample. Specifically, the sand was poured into the open die in three to five layers and hammered to the design height using a compactor. Scraping was performed between layers to ensure the uniformity of the sample. The finished sample was uniform in size and smooth without obvious rubber film compression, as shown in Figure 4. The rubber film embedding effect of the sample was small and could be neglected [31].Figure 4
Calcareous sand sample.The saturation process of the calcareous sands was as follows: first, after making the sample and connecting the pipeline, air in the CO2 displacement sample, which had a purity of more than 99.9%, was injected from the base intake for 10–20 min. Subsequently, distilled water was added for 30–60 min. Finally, sequential backpressure saturation was performed. When the pore pressure coefficient, B, of the sample rose to more than 0.97, the sand was considered to be saturated.For isobaric consolidation, the relative density,Dr, of the calcareous and the Fujian sands was 30–75% at effective confining pressures, σ3c, of 100–400 kPa, respectively. After consolidation, undrained cyclic triaxial tests were conducted with applied cyclic stress ratios (CSR) ranging from 0.1 to 0.4, in increments of 0.05. Here, CSR =  σd/2σ3c, with σd being the axial dynamic stress. The standard dynamic triaxial test system manufactured by UK-based GDS Instruments was employed for the testing. Loading was applied using stress control mode. The input waveform was sinusoidal, and the frequency was 1 Hz. The standard pore pressure ratio Ru = 1.0, and Ru = Δu/σ3c, where Δu is the excess pore water pressure [32].The test procedure was as follows. First, after the sample was saturated, the loading was stopped manually when the sample reached the liquefaction failure standard. Subsequently, the water in the sample was discharged through the volume change controller of the dynamic triaxial apparatus until the excess pore water pressure dropped to zero, and the discharged water was the volume change of the sample after liquefaction [33]. The relative density Dr in the chart was the relative density after consolidation.


## 2.1. Physical Properties of Calcareous Sand

### 2.1.1. Shape Characteristics of Calcareous Sand

The calcareous soil used in our tests came from the dredger fill site of the South China Sea Islands and reefs. It is coral debris obtained by the cutter suction or rake suction of large-scale ship-borne equipment. Figure1 shows screened samples of calcareous sand. The particle size range of the calcareous soil was 0–100 mm, the thicker calcareous soil comprising coral branches and coral reef blocks, and the finer calcareous soil being coral clastic and coral reef block fragments. The calcareous soil was sieved, and the calcareous sand (with a particle size of less than 2 mm) accounted for more than 60% of the total mass. There was more silt in the calcareous sand with a particle size of less than 2 mm. A particle size of less than 0.075 mm accounted for 5.88% of the total calcareous sand, which may indicate the occurrence of considerable particle breakage during the cutter suction and dredger filling processes [28]. From its irregular appearance, the thicker calcareous soil shape comprised mainly columnar fragments, including block and limb shapes. The finer calcareous soil comprised columnar, spherical, and block shapes, and the surface of the particles was rough and holey.Figure 1
Calcareous sand samples with different particle sizes (mm).
(a)(b)Electron microscope scanning tests were carried out on the calcareous sand from the dredger fill site and the natural calcareous sand. Figure2 shows the SEM images of the two types of sand. It can be seen from the figure that the fine grains of the calcareous sand in the dredger fill site were irregular in shape (column, block, and angle), with uneven surfaces and undeveloped pores. The natural calcareous sand was mainly spherical in shape but comprised irregular angular and columnar shapes. Compared with the calcareous sand from the dredger fill site, the biggest difference was that the surface was full of holes, the larger holes containing the remains of marine microorganisms.Figure 2
SEM images of calcareous sands. (a) Calcareous sand from dredger fill site. (b) Natural calcareous sand.
(a)(b)The above analysis shows that the particle shape and micromorphology of the calcareous sand from the dredger fill site obtained by cutter suction or trailing suction are quite different from those of the natural calcareous sand, which significantly affects the mechanical properties of the calcareous sand.


### 2.1.2. Physical Properties of Calcareous Sand

The soil samples had a particle size of 0–2 mm, and Fujian standard sand of China was used as the siliceous sand sample. Table1 lists the physical properties of the calcareous and the Fujian sands, and Figure 3 shows their gradation curves, determined according to the Geotechnical Test Rules SL237-1999 (Nanjing Hydraulic Research Institute) [29]. The Gs of the calcareous sand is larger, the curvature coefficient is 1<Cc=1.53<3, and the nonuniformity coefficient is Cu=4.82. This indicates that the grading curve of calcareous soil is continuous, and the variation range of grain composition is wide, which is close to the index of nonuniform soil. The equivalent carbonate content of the calcareous sand is more than 99%, according to XRF element analysis.Table 1
Physical properties of various calcareous and siliceous sands.
Type of sandCalcareous sandCataño [19]Salem et al. [23]Ma et al. [24]Fujian sandSpecific gravity,Gs2.872.862.792.802.65Diameter corresponding to 50% finer,D50 (mm)0.37——0.310.662Diameter corresponding to 10% finer,D10 (mm)0.0920.20.15—0.101Coefficient of uniformity,Cua4.821.052.44.677.82Coefficient of curvature,Ccb1.53——0.862.733Minimum void ratio,emax1.1161.711.041.720.725Maximum void ratio,emin0.5691.340.750.990.329aCu = D60/D10; bCc = D302/(D60 × D10).Figure 3
Grain-size distribution curves of various calcareous sands and Fujian sand [19, 23, 24].


## 2.1.1. Shape Characteristics of Calcareous Sand

The calcareous soil used in our tests came from the dredger fill site of the South China Sea Islands and reefs. It is coral debris obtained by the cutter suction or rake suction of large-scale ship-borne equipment. Figure1 shows screened samples of calcareous sand. The particle size range of the calcareous soil was 0–100 mm, the thicker calcareous soil comprising coral branches and coral reef blocks, and the finer calcareous soil being coral clastic and coral reef block fragments. The calcareous soil was sieved, and the calcareous sand (with a particle size of less than 2 mm) accounted for more than 60% of the total mass. There was more silt in the calcareous sand with a particle size of less than 2 mm. A particle size of less than 0.075 mm accounted for 5.88% of the total calcareous sand, which may indicate the occurrence of considerable particle breakage during the cutter suction and dredger filling processes [28]. From its irregular appearance, the thicker calcareous soil shape comprised mainly columnar fragments, including block and limb shapes. The finer calcareous soil comprised columnar, spherical, and block shapes, and the surface of the particles was rough and holey.Figure 1
Calcareous sand samples with different particle sizes (mm).
(a)(b)Electron microscope scanning tests were carried out on the calcareous sand from the dredger fill site and the natural calcareous sand. Figure2 shows the SEM images of the two types of sand. It can be seen from the figure that the fine grains of the calcareous sand in the dredger fill site were irregular in shape (column, block, and angle), with uneven surfaces and undeveloped pores. The natural calcareous sand was mainly spherical in shape but comprised irregular angular and columnar shapes. Compared with the calcareous sand from the dredger fill site, the biggest difference was that the surface was full of holes, the larger holes containing the remains of marine microorganisms.Figure 2
SEM images of calcareous sands. (a) Calcareous sand from dredger fill site. (b) Natural calcareous sand.
(a)(b)The above analysis shows that the particle shape and micromorphology of the calcareous sand from the dredger fill site obtained by cutter suction or trailing suction are quite different from those of the natural calcareous sand, which significantly affects the mechanical properties of the calcareous sand.


## 2.1.2. Physical Properties of Calcareous Sand

The soil samples had a particle size of 0–2 mm, and Fujian standard sand of China was used as the siliceous sand sample. Table1 lists the physical properties of the calcareous and the Fujian sands, and Figure 3 shows their gradation curves, determined according to the Geotechnical Test Rules SL237-1999 (Nanjing Hydraulic Research Institute) [29]. The Gs of the calcareous sand is larger, the curvature coefficient is 1<Cc=1.53<3, and the nonuniformity coefficient is Cu=4.82. This indicates that the grading curve of calcareous soil is continuous, and the variation range of grain composition is wide, which is close to the index of nonuniform soil. The equivalent carbonate content of the calcareous sand is more than 99%, according to XRF element analysis.Table 1
Physical properties of various calcareous and siliceous sands.
Type of sandCalcareous sandCataño [19]Salem et al. [23]Ma et al. [24]Fujian sandSpecific gravity,Gs2.872.862.792.802.65Diameter corresponding to 50% finer,D50 (mm)0.37——0.310.662Diameter corresponding to 10% finer,D10 (mm)0.0920.20.15—0.101Coefficient of uniformity,Cua4.821.052.44.677.82Coefficient of curvature,Ccb1.53——0.862.733Minimum void ratio,emax1.1161.711.041.720.725Maximum void ratio,emin0.5691.340.750.990.329aCu = D60/D10; bCc = D302/(D60 × D10).Figure 3
Grain-size distribution curves of various calcareous sands and Fujian sand [19, 23, 24].


## 2.2. Sample Preparation and Testing Procedures

The diameter and height of the sand samples were 50 mm and 100 mm, respectively. When the ratio of height to diameter is 2.0, the phenomenon of stress concentration can be effectively eliminated [30]. Dry packed samples were used. The dried sand was weighed according to the relative density of each sample. Specifically, the sand was poured into the open die in three to five layers and hammered to the design height using a compactor. Scraping was performed between layers to ensure the uniformity of the sample. The finished sample was uniform in size and smooth without obvious rubber film compression, as shown in Figure 4. The rubber film embedding effect of the sample was small and could be neglected [31].Figure 4
Calcareous sand sample.The saturation process of the calcareous sands was as follows: first, after making the sample and connecting the pipeline, air in the CO2 displacement sample, which had a purity of more than 99.9%, was injected from the base intake for 10–20 min. Subsequently, distilled water was added for 30–60 min. Finally, sequential backpressure saturation was performed. When the pore pressure coefficient, B, of the sample rose to more than 0.97, the sand was considered to be saturated.For isobaric consolidation, the relative density,Dr, of the calcareous and the Fujian sands was 30–75% at effective confining pressures, σ3c, of 100–400 kPa, respectively. After consolidation, undrained cyclic triaxial tests were conducted with applied cyclic stress ratios (CSR) ranging from 0.1 to 0.4, in increments of 0.05. Here, CSR =  σd/2σ3c, with σd being the axial dynamic stress. The standard dynamic triaxial test system manufactured by UK-based GDS Instruments was employed for the testing. Loading was applied using stress control mode. The input waveform was sinusoidal, and the frequency was 1 Hz. The standard pore pressure ratio Ru = 1.0, and Ru = Δu/σ3c, where Δu is the excess pore water pressure [32].The test procedure was as follows. First, after the sample was saturated, the loading was stopped manually when the sample reached the liquefaction failure standard. Subsequently, the water in the sample was discharged through the volume change controller of the dynamic triaxial apparatus until the excess pore water pressure dropped to zero, and the discharged water was the volume change of the sample after liquefaction [33]. The relative density Dr in the chart was the relative density after consolidation.


## 3. Results and Discussion

### 3.1. Cyclic Triaxial Test Results of Representative Samples

Figure5 shows the measured time history curve of the volume of discharged water (V), pore water pressure ratio (Ru), axial strain (εDA), and cyclic stress (σd) of the calcareous and the Fujian sands. It can be observed that with the increase of cyclic vibration times, the cyclic stress (σd) gradually decreased, as shown by the arrow in the figure. The reason is that with the development of excess pore water pressure, the stiffness of the sample becomes smaller, resulting in softening. The axial strain of the calcareous sand increases gradually, and the axial strain curve begins to warp up until the specimen is destroyed. The axial strain curve of the Fujian sand grows slowly during the initial stage of loading and then rapidly increases after the dynamic stress decays and warps up as a whole due to the instability of the sample. The difference in the axial strain growth modes between the two types of sand also indicates the particularity of the physical properties of the calcareous sand particles. The excess pore water pressure (Δu) of the two samples increases continuously with an increase in the cyclic vibration time until ru=1.0. After the liquefaction failure of the samples, the drainage volume increases gradually and stays stable after the excess pore water pressure drops to zero, indicating that the drainage process has been completed. The test results of other samples are similar, which shows that the feasibility of the test scheme.Figure 5
Cyclic triaxial test results of two types of samples: (a) calcareous sand; (b) Fujian sand.
(a)(b)


### 3.2. Modification of the Number of Cycles to Failure (N)

The dynamic strength of soil reflects the dynamic stress of soil under the condition of failure, which can be expressed as the vibration number required to cause soil failure under certain dynamic stress amplitude. It is expressed by drawing a relationship curve between the cyclic stress ratio (CSR) and the number of cycles (N) during the liquefaction failure of sand samples.Figure5 shows that σd remains unchanged in the early stage of loading for both the sands. In the later stage of loading, σd decreases as the specimen stiffness decreases and attenuation occurs before sample liquefaction, as indicated by the arrow in the figure. This phenomenon has been reported in other literature, but there is no relevant treatment. The attenuation of σd leads to an increase in N, the liquefaction resistance of the sample is overestimated, and thus Nf must be corrected.Martin and Seed [34] calculated the stress equivalent of seismic waves with irregular stress magnitudes and reported the corresponding calculation approach. According to this, the number of cycles to failure was modified. The correction method is as follows: firstly, the braking strength curve, CSR∼N, is drawn according to the test results, as shown by the dotted line in Figure 6, and the following formula is obtained:(1)CSR=0.561×N−0.169.Figure 6
Cyclic strength curves of calcareous sand.According to equation (1), the CSR and N of any point on the fitting curve can be obtained.Next, the dynamic stress time history curve of the specimen is drawn. The cyclic vibration times with the same cyclic stress (σ¯i) are divided into one segment, and the corresponding action times Nii=1,2,...,n are obtained, as shown in Figure 7. According to equation (2), the number of actions, Ni, is converted into an equivalent action number xi, as follows:(2)xi=NiNi,L⋅Ne,L,where Ne,L is the number of cycles determined by the test and Ni,L is the cyclic vibration number calculated from equation (1).Figure 7
Measured time histories of test results.Finally, based on equation (3), the equivalent cyclic vibration number (Neq) of the sample is obtained, where Neq is the corrected cyclic vibration number.(3)Neq=Ne,L⋅∑iNiNi,L.The above three steps are repeated to obtain the equivalent cyclic vibration times (N) of all of the samples on the dotted line in Figure 6. The solid line shown in Figure 6 can be obtained, which is the dynamic strength curve corrected by the cyclic vibration number.It can be seen from equation (3) that Neq will be equal to Ne,L for the case of equal radial stress. According to the above steps for iterative calculation, Neq will be infinitely close to Ne,L for a dynamic stress of variable amplitude. It can be seen from Figure 6 that the fitting effect of the dynamic strength curve after cyclic vibration number N is better. In the case of the same CSR, the corrected cyclic vibration number N is smaller, which indicates that the above correction method of cyclic vibration number N is effective and necessary.


### 3.3. Cyclic Strength Characteristics of Calcareous Sand

The dynamic strength curve,CSR∼N, of the calcareous sand under different working conditions is drawn after the cyclic vibration times of each sample are corrected using the above method. It should be noted that the larger N is, the more difficult it is to liquefy the calcareous sand at the same.


#### 3.3.1. Effect of Relative Density on the Cyclic Strength of Calcareous Sand

Figure8 shows the cyclic strength curve of the calcareous sand under different σ3c values. The cyclic strength curve of the calcareous sands pertains to a negative-ghost exponential function, which is the same as that of siliceous sands. The cyclic strength increases with increasing Dr; because the porosity of the sand sample decreases, the distance between the sand particles reduces, and the biting force and friction force between the sand particles increases.Figure 8
Effect ofDr on the cyclic strength curves of calcareous sand. (a) σ3c = 100 kPa. (b) σ3c  = 200 kPa. (c) σ3c = 400 kPa.
(a)(b)(c)


#### 3.3.2. Effect of the Effective Confining Pressure on the Cyclic Strength of Calcareous Sand

Figure9 shows the cyclic strength curve of the calcareous sand for different Dr values. It can be observed from the figure that the effect of effective confining pressure on the dynamic strength of the calcareous sand varies with the degree of soil compaction, which is similar to that in reference [22]. In the loose state (Dr<45%), the dynamic strength of the calcareous sand is close. The reason may be that the loose calcareous sand particles do not make close contact, the structural strength is insufficient, and the increase of effective confining pressure has a limited effect on improving the compactness of the calcareous sand particles. When 50%<Dr<75% and σ3c<400kPa, the cyclic strength of the calcareous sand increases with increasing σ3c, which is consistent with the results for siliceous sand. This phenomenon occurs because the contact force between the particles increases with increasing σ3c. The cyclic strength of the calcareous sand decreases with increasing σ3c when Dr=75%. Weng et al. [35] noted that the crushing degree of the calcareous sand particles increased with the increase of effective confining pressure and the increase of compactness led to the aggravation of particle breakage so that particle breakage reduced the structural strength of sand, thus reducing the dynamic strength of the calcareous sand.Figure 9
Effect ofσ3c on the cyclic strength curves of calcareous sand. (a) Dr = 34.6–40.6%. (b) Dr = 53.4–57.6%. (c) Dr = 67.1–70.6%. (d) Dr = 76.7–79.1%.
(a)(b)(c)(d)


#### 3.3.3. Comparison of the Cyclic Strengths of Calcareous and Siliceous Sands

Figure10 shows the cyclic strength curves of the calcareous and siliceous sands for different Dr values. Both the sands indicate isotropic consolidation. The cyclic strength of the calcareous sand was higher than that of the siliceous sand under the same testing conditions. This is likely due to the calcareous sand involving many edges and irregularly shaped particles, which leads to a higher bite friction between the sand grains than that between the grains of the siliceous sand; this is the same as the literature [13–20, 26]. This effect is more prominent in a loose state. Martin et al. [36] suggested that under M7.5 earthquakes; the CSR corresponding to 20 times the liquefaction under cyclic loading should be used to characterize the CRR of soils.Figure 10
Comparison of cyclic strength of calcareous and Fujian sands.Table2 presents the CRR values of the calcareous and the Fujian sands when liquefaction occurs 20 times under cyclic loading for σ3c = 100 kPa. It can be observed that under the same working conditions, the dynamic strength of the calcareous sand is close to that of the Fujian sand in the medium-dense state, but it is much higher than that of the Fujian sand in the loose and dense states. A possible reason is that the dynamic strength is determined by the contact force rather than the shape of the particles in the medium-dense state.Table 2
Comparison ofCRR values of calcareous and Fujian sands.
Dr (%)34.653.467.176.7Calcareous sand0.2800.2910.4200.693Fujian sand0.1690.2680.4120.538Percentage difference39.688.022.0622.37


#### 3.3.4. Comparison of Cyclic Strengths of Different Types of Calcareous Sands

Figure11 shows a comparison of the cyclic strength of different types of calcareous sands at σ3c = 100 kPa. It can be seen that the cyclic strength of the calcareous sand used in the study is the highest, primarily due to the following reasons:(1)
Grain grading characteristics: Table1 lists the physical properties of several types of calcareous sands. It can be observed that the calcareous sand employed in this study had a larger GS and better grading.(2)
Influence of particle shape: SEM image analysis shows that the particles of the calcareous sand from the dredger fill site were the fragments and crushed materials of coral reef rocks. Compared with the natural coral sand, the pores were smaller, the surface was rough, and the structural strength of the samples may have been higher.(3)
Effect of average particle sizeD50: Martin et al. [37] reported that under the same conditions, the pore pressure growth of undrained soil was proportional to the residual strain of the drained soil; in other words, a larger volume of the undrained soil corresponded to a more rapid pore pressure growth. Moreover, Shen et al. [38] suggested that the coarser calcareous sand particles exhibited a higher compressibility. This means that a larger D50 corresponded to a larger change in volume of the calcareous sand. According to Martin’s theory, it can be considered that a larger D50 corresponds to a higher compressibility of the soil skeleton, and therefore, a more notable soil drainage trend. When no drainage occurs, the pore pressure of the soil increases more rapidly. Therefore, the D50 values of the other types of calcareous sand are larger, which correspond to a higher compressibility and more rapid increase in the pore pressure under the undrained conditions, thereby leading to a lower cyclic strength.Figure 11
Comparison of the cyclic strength of different types of calcareous sand [19, 23, 24].


### 3.4. Pore Pressure Growth Characteristics of Calcareous Sands

The development of excess pore water pressure is not only the fundamental reason affecting the deformation and strength of saturated sand but also an important factor affecting the seismic stability of geotechnical engineering. The development of excess pore water pressure is usually described by the relationship between pore water pressure ratioRu and vibration number ratio N/Nf of saturated sand, where Nf is the cyclic vibration number of the sand liquefaction failure.


#### 3.4.1. Effect of Cyclic Stress Ratio and Effective Confining Pressure on the Pore Pressure Growth

Figures12(a) and 12(b) show the pore pressure growth curves of the calcareous sand under the following conditions: Dr = 53.2–58.6%, CSR = 0.2, and Dr = 53.2–53.3%, σ3c = 100 kPa, respectively. The data points exhibit a high correlation under similar Dr. This aspect is also true when Dr changes.Figure 12
Pore pressure growth curves of typical samples. (a)CSR = 0.2 of calcareous sands. (b) σ3c = 100 kPa of calcareous sands.
(a)(b)The formation of excess pore water pressure is caused mainly by the compression of the pores between soil particles under the action of a load, the pore water being too late to discharge, resulting in increasing pore pressure. The irregular calcareous soil has a certain structure. When the relative density is similar to each other, its ability to resist deformation is equivalent. Under different working conditions, the variation of pore compression between soil particles is relatively close, resulting in similar pore pressure development curves.


#### 3.4.2. Effect of the Relative Density on the Pore Pressure Growth of Calcareous Sand

Figure13 shows the pore pressure growth curves of the calcareous sands for different Dr values. It can be observed that the relative density has a great influence on the development of the pore water pressure of the calcareous sand. With the increase of relative density, the pore pressure development curve of the calcareous sand tends to bulge upward. The excess pore water pressure of the loose calcareous sand increases gradually in the process of loading and increases rapidly when it is close to liquefaction failure, similar to quartz sand. In the initial stage of loading, the excess pore water pressure of the calcareous sand develops rapidly and then increases slowly until liquefaction failure. The reason may be that the porosity of the calcareous sand is small under the dense state.Figure 13
Effect ofDr on the pore pressure growth curve of calcareous sand.In the initial stage of loading, the pores between the calcareous sand particles are compressed, which leads to the rapid development of pore water pressure. After being compacted, the indirect contact force of the calcareous sand particles increases, and the overall structural strength is high. The elastic deformation is the main deformation of the sample, resulting in the slow development of pore pressure.


#### 3.4.3. Comparison of the Pore Pressure Growth Curves of Different Types of Calcareous Sands

Figure14 shows the pore pressure growth curve of different calcareous sands reported in the literature. It can be observed that the increase in the pore pressure of the calcareous sands exhibits a similar trend. Specifically, in the initial stage of vibration, the pore pressures of the calcareous sands increase rapidly and later decrease. In addition, with increasing Dr, the pore pressure growth curves of the calcareous sands exhibit an upward convex trend.Figure 14
Comparison of pore pressure growth curves of different types of calcareous sand [19, 24].The compressibility of the calcareous sand is higher than that of the siliceous sand. For calcareous sand with a largerDr value, the volume change is larger in the initial stage of vibration, and the pore pressure increases more rapidly. After the initial vibration, the Dr value is considerably higher, and the volume change caused by the cyclic vibration decreases in the later stage, resulting in a slow increase in the pore pressure.Overall,Dr is a key factor affecting the growth curve of the excess pore water pressure. Figure 14 also shows that the relative density influences the pore pressure growth characteristics of the calcareous sand.


#### 3.4.4. Establishment of Pore Pressure Growth Model for Calcareous Sand

The pore pressure development curves measured under all test conditions in this test are plotted in Figure15. The pore pressure curves with similar relative density are represented by the same symbol, and the test conditions are shown above. It can be observed that, under different effective confining pressures and cyclic stress ratios, the development rule of the excess pore water pressure is consistent when the relative densities of the samples are similar.Figure 15
Comparison between the test data and predicted values of excess pore pressure of calcareous sand [24, 39].Considering different experimental conditions, several models of the excess pore water pressure growth of saturated sand under cyclic loading in the undrained condition have been developed, among which, the most popular model is the empirical formula based on the test data proposed by Seed et al. [39]:(4)Ru=12+1πsin−12NNL1/θ−1,where Ru is the residual pore pressure ratio after the Nth vibration, NL is the number of vibrations when the sample reaches initial liquefaction, and θ is the test parameter.At present, there are few studies on pore pressure development models of calcareous sand, especially in the South China Sea. Ma et al. [24] noted that it is not suitable to use the model of Seed directly to describe the pore pressure development of coral sand, so they proposed a modified model of Seed suitable for describing the pore pressure development of coral sands:(5)Ru=a×2πarcsinNNL1/2θ+b×arctanNNL.Equations (4) and (5) were used to fit the pore pressure data of the calcareous sand studied in this paper, and the results are shown in Figure 15. It can be seen that the fitting effect of the two models is better when the relative density is small, and the fitting effect of equation (5) is better when the relative density is large. When equation (5) is used to describe the pore water pressure development of the calcareous sand in a dense state, there is some deviation, especially in the later stage of pore pressure development, which cannot reflect the influence of relative density on the development of pore water pressure. Therefore, in this study, a modified model to describe the pore pressure development of the calcareous sand was established based on equation (5):(6)Ru=3.92∗θ−2.6∗arcsinNNL1/2θ+3.22−3.9∗θ∗arcsinNNL,where θ is the test parameter, and the fitting curve is shown as a solid line in Figure 15. The fitting parameters of equations (4)–(6) are summarized in Table 3, and the average value of the relative density in the table is obtained.Table 3
Fitting coefficients of the model.
ModelDr (%)abθR2Model of Seed [39]37.5——1.6150.98455.4——1.1080.99068.7——0.5220.91677.8——0.3380.855Modified model of Seed [24]37.51.435−0.3910.6650.98955.41.1280.0380.7520.99268.71.0810.3561.4880.95177.81.850−0.2971.3910.955Modified model37.5——0.7320.98955.4——0.8470.99168.7——1.0030.96477.8——1.0910.976Table3 shows that the fitting effect of the data with the modified model was satisfactory, with R2 being greater than 0.96. The relationship between the relative density and the modified model parameters was plotted as shown in Figure 16. It can be seen that the consolidated relative density of the calcareous sand was highly correlated with the parameters of the modified model, indicating that the relative density was the main factor affecting the pore pressure growth of the calcareous sand. When the relative density is known, the parameters θ of the modified model can be obtained by considering Figure 16, making it possible to predict the pore pressure growth curve.Figure 16
Relationship betweenDr and θ.


### 3.5. Volumetric Strain of Calcareous Sand after Liquefaction

When the dynamic load stops, the soil deforms with the dissipation of excess pore water pressure. Scholars have studied the volume deformation characteristics of quartz sand after vibration and achieved many results, but research on the volume deformation characteristics of calcareous sand after liquefaction remains rare. In this test, the effects of relative density, effective confining pressure, and cyclic stress ratio on the volume deformation of saturated calcareous sand after liquefaction are discussed. The volume deformation of the saturated Fujian sand was measured under the same working conditions, for comparison. The volumetric strain after liquefaction is defined as(7)εV=ΔVV0×100%,where ΔV is the volume change of sand before and after liquefaction failure and V0 is the volume of sand after consolidation.


#### 3.5.1. Effect of Cyclic Stress Ratio on the Post-Liquefaction Volumetric Strain of Calcareous Sand

Figure17 shows the εV∼CSR curve of the calcareous sand and the Fujian sand after liquefaction. The solid symbol in the figure is the data point of the calcareous sand, and the hollow symbol is the data point of the Fujian sand. The data points with the same relative density and effective confining pressure are plotted on the same curve. It can be seen from the figure that under the same relative density and effective confining pressure, the effect of cyclic stress on the post-liquefaction volumetric strain of the two types of sand is reduced. The reason is that the decrease of porosity is directly proportional to increasing pore pressure. When the porosity of the samples is similar, the change of pore pressure during liquefaction is also similar. Compared to the Fujian sand, the volume of the calcareous sand in the loose state should be higher after liquefaction due to its higher compressibility.Figure 17
εV∼CSR curve of calcareous sand and Fujian sand.


#### 3.5.2. Effect of the Effective Confining Pressure on the Post-Liquefaction Volumetric Strain of Calcareous Sand

Figure18 shows the εV∼σ3c curve of the calcareous sand and the Fujian sand after liquefaction. It can be observed from the figure that when the relative density and cyclic stress ratio are the same, the volume deformation of the calcareous sand after liquefaction increases with increasing effective confining pressure. The volume change of the saturated sand is related to pore pressure. The increase of the effective girth requires more volume deformation in order to achieve the same pore pressure ratio. Therefore, the volume change of sand liquefaction is large.Figure 18
εV∼σ3c curve of calcareous sand and Fujian sand.


#### 3.5.3. Effect of Relative Density on the Post-Liquefaction Volumetric Strain of Calcareous Sand

It can be observed from Figure18 that at the same effective confining pressure and cyclic strain ratio, the post-liquefaction volumetric strain of the calcareous sand increases with decreasing relative density. Lee and Albaisa [33] noted that the average post-liquefaction volumetric strain of quartz sand was related to the relative density. The average value of the post-liquefaction volumetric strain of all the calcareous sand and the Fujian sand samples with similar relative density in this test was taken, εV∼Dr, and a relationship curve was drawn, as shown in Figure 19. The legend in the figure indicates the number of data samples, and the lines in the figure are the data fitting lines of the calcareous sand, the Fujian sand, and the Monterey sand [33]. It can be observed from Figure 19 that there is a good correlation between the average value of post-liquefaction volumetric strain of the three types of sand samples and the relative density, but the fitting line of the calcareous sand is linear. The fitting curves of the Monterey sand and the Fujian sand are different in shape, which may be related to the test conditions. The number of samples and the effective confining pressure at the corresponding points of the Monterey sand and the Fujian sand were insufficient. Generally, under the same relative density, the post-liquefaction volumetric strain of the calcareous sand is larger, which may be related to the special particle shape and gradation of the calcareous sand.Figure 19
εV∼Dr curve of calcareous sand, Fujian sand, and Monterey sand [33].


## 3.1. Cyclic Triaxial Test Results of Representative Samples

Figure5 shows the measured time history curve of the volume of discharged water (V), pore water pressure ratio (Ru), axial strain (εDA), and cyclic stress (σd) of the calcareous and the Fujian sands. It can be observed that with the increase of cyclic vibration times, the cyclic stress (σd) gradually decreased, as shown by the arrow in the figure. The reason is that with the development of excess pore water pressure, the stiffness of the sample becomes smaller, resulting in softening. The axial strain of the calcareous sand increases gradually, and the axial strain curve begins to warp up until the specimen is destroyed. The axial strain curve of the Fujian sand grows slowly during the initial stage of loading and then rapidly increases after the dynamic stress decays and warps up as a whole due to the instability of the sample. The difference in the axial strain growth modes between the two types of sand also indicates the particularity of the physical properties of the calcareous sand particles. The excess pore water pressure (Δu) of the two samples increases continuously with an increase in the cyclic vibration time until ru=1.0. After the liquefaction failure of the samples, the drainage volume increases gradually and stays stable after the excess pore water pressure drops to zero, indicating that the drainage process has been completed. The test results of other samples are similar, which shows that the feasibility of the test scheme.Figure 5
Cyclic triaxial test results of two types of samples: (a) calcareous sand; (b) Fujian sand.
(a)(b)


## 3.2. Modification of the Number of Cycles to Failure (N)

The dynamic strength of soil reflects the dynamic stress of soil under the condition of failure, which can be expressed as the vibration number required to cause soil failure under certain dynamic stress amplitude. It is expressed by drawing a relationship curve between the cyclic stress ratio (CSR) and the number of cycles (N) during the liquefaction failure of sand samples.Figure5 shows that σd remains unchanged in the early stage of loading for both the sands. In the later stage of loading, σd decreases as the specimen stiffness decreases and attenuation occurs before sample liquefaction, as indicated by the arrow in the figure. This phenomenon has been reported in other literature, but there is no relevant treatment. The attenuation of σd leads to an increase in N, the liquefaction resistance of the sample is overestimated, and thus Nf must be corrected.Martin and Seed [34] calculated the stress equivalent of seismic waves with irregular stress magnitudes and reported the corresponding calculation approach. According to this, the number of cycles to failure was modified. The correction method is as follows: firstly, the braking strength curve, CSR∼N, is drawn according to the test results, as shown by the dotted line in Figure 6, and the following formula is obtained:(1)CSR=0.561×N−0.169.Figure 6
Cyclic strength curves of calcareous sand.According to equation (1), the CSR and N of any point on the fitting curve can be obtained.Next, the dynamic stress time history curve of the specimen is drawn. The cyclic vibration times with the same cyclic stress (σ¯i) are divided into one segment, and the corresponding action times Nii=1,2,...,n are obtained, as shown in Figure 7. According to equation (2), the number of actions, Ni, is converted into an equivalent action number xi, as follows:(2)xi=NiNi,L⋅Ne,L,where Ne,L is the number of cycles determined by the test and Ni,L is the cyclic vibration number calculated from equation (1).Figure 7
Measured time histories of test results.Finally, based on equation (3), the equivalent cyclic vibration number (Neq) of the sample is obtained, where Neq is the corrected cyclic vibration number.(3)Neq=Ne,L⋅∑iNiNi,L.The above three steps are repeated to obtain the equivalent cyclic vibration times (N) of all of the samples on the dotted line in Figure 6. The solid line shown in Figure 6 can be obtained, which is the dynamic strength curve corrected by the cyclic vibration number.It can be seen from equation (3) that Neq will be equal to Ne,L for the case of equal radial stress. According to the above steps for iterative calculation, Neq will be infinitely close to Ne,L for a dynamic stress of variable amplitude. It can be seen from Figure 6 that the fitting effect of the dynamic strength curve after cyclic vibration number N is better. In the case of the same CSR, the corrected cyclic vibration number N is smaller, which indicates that the above correction method of cyclic vibration number N is effective and necessary.


## 3.3. Cyclic Strength Characteristics of Calcareous Sand

The dynamic strength curve,CSR∼N, of the calcareous sand under different working conditions is drawn after the cyclic vibration times of each sample are corrected using the above method. It should be noted that the larger N is, the more difficult it is to liquefy the calcareous sand at the same.


### 3.3.1. Effect of Relative Density on the Cyclic Strength of Calcareous Sand

Figure8 shows the cyclic strength curve of the calcareous sand under different σ3c values. The cyclic strength curve of the calcareous sands pertains to a negative-ghost exponential function, which is the same as that of siliceous sands. The cyclic strength increases with increasing Dr; because the porosity of the sand sample decreases, the distance between the sand particles reduces, and the biting force and friction force between the sand particles increases.Figure 8
Effect ofDr on the cyclic strength curves of calcareous sand. (a) σ3c = 100 kPa. (b) σ3c  = 200 kPa. (c) σ3c = 400 kPa.
(a)(b)(c)


### 3.3.2. Effect of the Effective Confining Pressure on the Cyclic Strength of Calcareous Sand

Figure9 shows the cyclic strength curve of the calcareous sand for different Dr values. It can be observed from the figure that the effect of effective confining pressure on the dynamic strength of the calcareous sand varies with the degree of soil compaction, which is similar to that in reference [22]. In the loose state (Dr<45%), the dynamic strength of the calcareous sand is close. The reason may be that the loose calcareous sand particles do not make close contact, the structural strength is insufficient, and the increase of effective confining pressure has a limited effect on improving the compactness of the calcareous sand particles. When 50%<Dr<75% and σ3c<400kPa, the cyclic strength of the calcareous sand increases with increasing σ3c, which is consistent with the results for siliceous sand. This phenomenon occurs because the contact force between the particles increases with increasing σ3c. The cyclic strength of the calcareous sand decreases with increasing σ3c when Dr=75%. Weng et al. [35] noted that the crushing degree of the calcareous sand particles increased with the increase of effective confining pressure and the increase of compactness led to the aggravation of particle breakage so that particle breakage reduced the structural strength of sand, thus reducing the dynamic strength of the calcareous sand.Figure 9
Effect ofσ3c on the cyclic strength curves of calcareous sand. (a) Dr = 34.6–40.6%. (b) Dr = 53.4–57.6%. (c) Dr = 67.1–70.6%. (d) Dr = 76.7–79.1%.
(a)(b)(c)(d)


### 3.3.3. Comparison of the Cyclic Strengths of Calcareous and Siliceous Sands

Figure10 shows the cyclic strength curves of the calcareous and siliceous sands for different Dr values. Both the sands indicate isotropic consolidation. The cyclic strength of the calcareous sand was higher than that of the siliceous sand under the same testing conditions. This is likely due to the calcareous sand involving many edges and irregularly shaped particles, which leads to a higher bite friction between the sand grains than that between the grains of the siliceous sand; this is the same as the literature [13–20, 26]. This effect is more prominent in a loose state. Martin et al. [36] suggested that under M7.5 earthquakes; the CSR corresponding to 20 times the liquefaction under cyclic loading should be used to characterize the CRR of soils.Figure 10
Comparison of cyclic strength of calcareous and Fujian sands.Table2 presents the CRR values of the calcareous and the Fujian sands when liquefaction occurs 20 times under cyclic loading for σ3c = 100 kPa. It can be observed that under the same working conditions, the dynamic strength of the calcareous sand is close to that of the Fujian sand in the medium-dense state, but it is much higher than that of the Fujian sand in the loose and dense states. A possible reason is that the dynamic strength is determined by the contact force rather than the shape of the particles in the medium-dense state.Table 2
Comparison ofCRR values of calcareous and Fujian sands.
Dr (%)34.653.467.176.7Calcareous sand0.2800.2910.4200.693Fujian sand0.1690.2680.4120.538Percentage difference39.688.022.0622.37


### 3.3.4. Comparison of Cyclic Strengths of Different Types of Calcareous Sands

Figure11 shows a comparison of the cyclic strength of different types of calcareous sands at σ3c = 100 kPa. It can be seen that the cyclic strength of the calcareous sand used in the study is the highest, primarily due to the following reasons:(1)
Grain grading characteristics: Table1 lists the physical properties of several types of calcareous sands. It can be observed that the calcareous sand employed in this study had a larger GS and better grading.(2)
Influence of particle shape: SEM image analysis shows that the particles of the calcareous sand from the dredger fill site were the fragments and crushed materials of coral reef rocks. Compared with the natural coral sand, the pores were smaller, the surface was rough, and the structural strength of the samples may have been higher.(3)
Effect of average particle sizeD50: Martin et al. [37] reported that under the same conditions, the pore pressure growth of undrained soil was proportional to the residual strain of the drained soil; in other words, a larger volume of the undrained soil corresponded to a more rapid pore pressure growth. Moreover, Shen et al. [38] suggested that the coarser calcareous sand particles exhibited a higher compressibility. This means that a larger D50 corresponded to a larger change in volume of the calcareous sand. According to Martin’s theory, it can be considered that a larger D50 corresponds to a higher compressibility of the soil skeleton, and therefore, a more notable soil drainage trend. When no drainage occurs, the pore pressure of the soil increases more rapidly. Therefore, the D50 values of the other types of calcareous sand are larger, which correspond to a higher compressibility and more rapid increase in the pore pressure under the undrained conditions, thereby leading to a lower cyclic strength.Figure 11
Comparison of the cyclic strength of different types of calcareous sand [19, 23, 24].


## 3.3.1. Effect of Relative Density on the Cyclic Strength of Calcareous Sand

Figure8 shows the cyclic strength curve of the calcareous sand under different σ3c values. The cyclic strength curve of the calcareous sands pertains to a negative-ghost exponential function, which is the same as that of siliceous sands. The cyclic strength increases with increasing Dr; because the porosity of the sand sample decreases, the distance between the sand particles reduces, and the biting force and friction force between the sand particles increases.Figure 8
Effect ofDr on the cyclic strength curves of calcareous sand. (a) σ3c = 100 kPa. (b) σ3c  = 200 kPa. (c) σ3c = 400 kPa.
(a)(b)(c)


## 3.3.2. Effect of the Effective Confining Pressure on the Cyclic Strength of Calcareous Sand

Figure9 shows the cyclic strength curve of the calcareous sand for different Dr values. It can be observed from the figure that the effect of effective confining pressure on the dynamic strength of the calcareous sand varies with the degree of soil compaction, which is similar to that in reference [22]. In the loose state (Dr<45%), the dynamic strength of the calcareous sand is close. The reason may be that the loose calcareous sand particles do not make close contact, the structural strength is insufficient, and the increase of effective confining pressure has a limited effect on improving the compactness of the calcareous sand particles. When 50%<Dr<75% and σ3c<400kPa, the cyclic strength of the calcareous sand increases with increasing σ3c, which is consistent with the results for siliceous sand. This phenomenon occurs because the contact force between the particles increases with increasing σ3c. The cyclic strength of the calcareous sand decreases with increasing σ3c when Dr=75%. Weng et al. [35] noted that the crushing degree of the calcareous sand particles increased with the increase of effective confining pressure and the increase of compactness led to the aggravation of particle breakage so that particle breakage reduced the structural strength of sand, thus reducing the dynamic strength of the calcareous sand.Figure 9
Effect ofσ3c on the cyclic strength curves of calcareous sand. (a) Dr = 34.6–40.6%. (b) Dr = 53.4–57.6%. (c) Dr = 67.1–70.6%. (d) Dr = 76.7–79.1%.
(a)(b)(c)(d)


## 3.3.3. Comparison of the Cyclic Strengths of Calcareous and Siliceous Sands

Figure10 shows the cyclic strength curves of the calcareous and siliceous sands for different Dr values. Both the sands indicate isotropic consolidation. The cyclic strength of the calcareous sand was higher than that of the siliceous sand under the same testing conditions. This is likely due to the calcareous sand involving many edges and irregularly shaped particles, which leads to a higher bite friction between the sand grains than that between the grains of the siliceous sand; this is the same as the literature [13–20, 26]. This effect is more prominent in a loose state. Martin et al. [36] suggested that under M7.5 earthquakes; the CSR corresponding to 20 times the liquefaction under cyclic loading should be used to characterize the CRR of soils.Figure 10
Comparison of cyclic strength of calcareous and Fujian sands.Table2 presents the CRR values of the calcareous and the Fujian sands when liquefaction occurs 20 times under cyclic loading for σ3c = 100 kPa. It can be observed that under the same working conditions, the dynamic strength of the calcareous sand is close to that of the Fujian sand in the medium-dense state, but it is much higher than that of the Fujian sand in the loose and dense states. A possible reason is that the dynamic strength is determined by the contact force rather than the shape of the particles in the medium-dense state.Table 2
Comparison ofCRR values of calcareous and Fujian sands.
Dr (%)34.653.467.176.7Calcareous sand0.2800.2910.4200.693Fujian sand0.1690.2680.4120.538Percentage difference39.688.022.0622.37


## 3.3.4. Comparison of Cyclic Strengths of Different Types of Calcareous Sands

Figure11 shows a comparison of the cyclic strength of different types of calcareous sands at σ3c = 100 kPa. It can be seen that the cyclic strength of the calcareous sand used in the study is the highest, primarily due to the following reasons:(1)
Grain grading characteristics: Table1 lists the physical properties of several types of calcareous sands. It can be observed that the calcareous sand employed in this study had a larger GS and better grading.(2)
Influence of particle shape: SEM image analysis shows that the particles of the calcareous sand from the dredger fill site were the fragments and crushed materials of coral reef rocks. Compared with the natural coral sand, the pores were smaller, the surface was rough, and the structural strength of the samples may have been higher.(3)
Effect of average particle sizeD50: Martin et al. [37] reported that under the same conditions, the pore pressure growth of undrained soil was proportional to the residual strain of the drained soil; in other words, a larger volume of the undrained soil corresponded to a more rapid pore pressure growth. Moreover, Shen et al. [38] suggested that the coarser calcareous sand particles exhibited a higher compressibility. This means that a larger D50 corresponded to a larger change in volume of the calcareous sand. According to Martin’s theory, it can be considered that a larger D50 corresponds to a higher compressibility of the soil skeleton, and therefore, a more notable soil drainage trend. When no drainage occurs, the pore pressure of the soil increases more rapidly. Therefore, the D50 values of the other types of calcareous sand are larger, which correspond to a higher compressibility and more rapid increase in the pore pressure under the undrained conditions, thereby leading to a lower cyclic strength.Figure 11
Comparison of the cyclic strength of different types of calcareous sand [19, 23, 24].


## 3.4. Pore Pressure Growth Characteristics of Calcareous Sands

The development of excess pore water pressure is not only the fundamental reason affecting the deformation and strength of saturated sand but also an important factor affecting the seismic stability of geotechnical engineering. The development of excess pore water pressure is usually described by the relationship between pore water pressure ratioRu and vibration number ratio N/Nf of saturated sand, where Nf is the cyclic vibration number of the sand liquefaction failure.


### 3.4.1. Effect of Cyclic Stress Ratio and Effective Confining Pressure on the Pore Pressure Growth

Figures12(a) and 12(b) show the pore pressure growth curves of the calcareous sand under the following conditions: Dr = 53.2–58.6%, CSR = 0.2, and Dr = 53.2–53.3%, σ3c = 100 kPa, respectively. The data points exhibit a high correlation under similar Dr. This aspect is also true when Dr changes.Figure 12
Pore pressure growth curves of typical samples. (a)CSR = 0.2 of calcareous sands. (b) σ3c = 100 kPa of calcareous sands.
(a)(b)The formation of excess pore water pressure is caused mainly by the compression of the pores between soil particles under the action of a load, the pore water being too late to discharge, resulting in increasing pore pressure. The irregular calcareous soil has a certain structure. When the relative density is similar to each other, its ability to resist deformation is equivalent. Under different working conditions, the variation of pore compression between soil particles is relatively close, resulting in similar pore pressure development curves.


### 3.4.2. Effect of the Relative Density on the Pore Pressure Growth of Calcareous Sand

Figure13 shows the pore pressure growth curves of the calcareous sands for different Dr values. It can be observed that the relative density has a great influence on the development of the pore water pressure of the calcareous sand. With the increase of relative density, the pore pressure development curve of the calcareous sand tends to bulge upward. The excess pore water pressure of the loose calcareous sand increases gradually in the process of loading and increases rapidly when it is close to liquefaction failure, similar to quartz sand. In the initial stage of loading, the excess pore water pressure of the calcareous sand develops rapidly and then increases slowly until liquefaction failure. The reason may be that the porosity of the calcareous sand is small under the dense state.Figure 13
Effect ofDr on the pore pressure growth curve of calcareous sand.In the initial stage of loading, the pores between the calcareous sand particles are compressed, which leads to the rapid development of pore water pressure. After being compacted, the indirect contact force of the calcareous sand particles increases, and the overall structural strength is high. The elastic deformation is the main deformation of the sample, resulting in the slow development of pore pressure.


### 3.4.3. Comparison of the Pore Pressure Growth Curves of Different Types of Calcareous Sands

Figure14 shows the pore pressure growth curve of different calcareous sands reported in the literature. It can be observed that the increase in the pore pressure of the calcareous sands exhibits a similar trend. Specifically, in the initial stage of vibration, the pore pressures of the calcareous sands increase rapidly and later decrease. In addition, with increasing Dr, the pore pressure growth curves of the calcareous sands exhibit an upward convex trend.Figure 14
Comparison of pore pressure growth curves of different types of calcareous sand [19, 24].The compressibility of the calcareous sand is higher than that of the siliceous sand. For calcareous sand with a largerDr value, the volume change is larger in the initial stage of vibration, and the pore pressure increases more rapidly. After the initial vibration, the Dr value is considerably higher, and the volume change caused by the cyclic vibration decreases in the later stage, resulting in a slow increase in the pore pressure.Overall,Dr is a key factor affecting the growth curve of the excess pore water pressure. Figure 14 also shows that the relative density influences the pore pressure growth characteristics of the calcareous sand.


### 3.4.4. Establishment of Pore Pressure Growth Model for Calcareous Sand

The pore pressure development curves measured under all test conditions in this test are plotted in Figure15. The pore pressure curves with similar relative density are represented by the same symbol, and the test conditions are shown above. It can be observed that, under different effective confining pressures and cyclic stress ratios, the development rule of the excess pore water pressure is consistent when the relative densities of the samples are similar.Figure 15
Comparison between the test data and predicted values of excess pore pressure of calcareous sand [24, 39].Considering different experimental conditions, several models of the excess pore water pressure growth of saturated sand under cyclic loading in the undrained condition have been developed, among which, the most popular model is the empirical formula based on the test data proposed by Seed et al. [39]:(4)Ru=12+1πsin−12NNL1/θ−1,where Ru is the residual pore pressure ratio after the Nth vibration, NL is the number of vibrations when the sample reaches initial liquefaction, and θ is the test parameter.At present, there are few studies on pore pressure development models of calcareous sand, especially in the South China Sea. Ma et al. [24] noted that it is not suitable to use the model of Seed directly to describe the pore pressure development of coral sand, so they proposed a modified model of Seed suitable for describing the pore pressure development of coral sands:(5)Ru=a×2πarcsinNNL1/2θ+b×arctanNNL.Equations (4) and (5) were used to fit the pore pressure data of the calcareous sand studied in this paper, and the results are shown in Figure 15. It can be seen that the fitting effect of the two models is better when the relative density is small, and the fitting effect of equation (5) is better when the relative density is large. When equation (5) is used to describe the pore water pressure development of the calcareous sand in a dense state, there is some deviation, especially in the later stage of pore pressure development, which cannot reflect the influence of relative density on the development of pore water pressure. Therefore, in this study, a modified model to describe the pore pressure development of the calcareous sand was established based on equation (5):(6)Ru=3.92∗θ−2.6∗arcsinNNL1/2θ+3.22−3.9∗θ∗arcsinNNL,where θ is the test parameter, and the fitting curve is shown as a solid line in Figure 15. The fitting parameters of equations (4)–(6) are summarized in Table 3, and the average value of the relative density in the table is obtained.Table 3
Fitting coefficients of the model.
ModelDr (%)abθR2Model of Seed [39]37.5——1.6150.98455.4——1.1080.99068.7——0.5220.91677.8——0.3380.855Modified model of Seed [24]37.51.435−0.3910.6650.98955.41.1280.0380.7520.99268.71.0810.3561.4880.95177.81.850−0.2971.3910.955Modified model37.5——0.7320.98955.4——0.8470.99168.7——1.0030.96477.8——1.0910.976Table3 shows that the fitting effect of the data with the modified model was satisfactory, with R2 being greater than 0.96. The relationship between the relative density and the modified model parameters was plotted as shown in Figure 16. It can be seen that the consolidated relative density of the calcareous sand was highly correlated with the parameters of the modified model, indicating that the relative density was the main factor affecting the pore pressure growth of the calcareous sand. When the relative density is known, the parameters θ of the modified model can be obtained by considering Figure 16, making it possible to predict the pore pressure growth curve.Figure 16
Relationship betweenDr and θ.


## 3.4.1. Effect of Cyclic Stress Ratio and Effective Confining Pressure on the Pore Pressure Growth

Figures12(a) and 12(b) show the pore pressure growth curves of the calcareous sand under the following conditions: Dr = 53.2–58.6%, CSR = 0.2, and Dr = 53.2–53.3%, σ3c = 100 kPa, respectively. The data points exhibit a high correlation under similar Dr. This aspect is also true when Dr changes.Figure 12
Pore pressure growth curves of typical samples. (a)CSR = 0.2 of calcareous sands. (b) σ3c = 100 kPa of calcareous sands.
(a)(b)The formation of excess pore water pressure is caused mainly by the compression of the pores between soil particles under the action of a load, the pore water being too late to discharge, resulting in increasing pore pressure. The irregular calcareous soil has a certain structure. When the relative density is similar to each other, its ability to resist deformation is equivalent. Under different working conditions, the variation of pore compression between soil particles is relatively close, resulting in similar pore pressure development curves.


## 3.4.2. Effect of the Relative Density on the Pore Pressure Growth of Calcareous Sand

Figure13 shows the pore pressure growth curves of the calcareous sands for different Dr values. It can be observed that the relative density has a great influence on the development of the pore water pressure of the calcareous sand. With the increase of relative density, the pore pressure development curve of the calcareous sand tends to bulge upward. The excess pore water pressure of the loose calcareous sand increases gradually in the process of loading and increases rapidly when it is close to liquefaction failure, similar to quartz sand. In the initial stage of loading, the excess pore water pressure of the calcareous sand develops rapidly and then increases slowly until liquefaction failure. The reason may be that the porosity of the calcareous sand is small under the dense state.Figure 13
Effect ofDr on the pore pressure growth curve of calcareous sand.In the initial stage of loading, the pores between the calcareous sand particles are compressed, which leads to the rapid development of pore water pressure. After being compacted, the indirect contact force of the calcareous sand particles increases, and the overall structural strength is high. The elastic deformation is the main deformation of the sample, resulting in the slow development of pore pressure.


## 3.4.3. Comparison of the Pore Pressure Growth Curves of Different Types of Calcareous Sands

Figure14 shows the pore pressure growth curve of different calcareous sands reported in the literature. It can be observed that the increase in the pore pressure of the calcareous sands exhibits a similar trend. Specifically, in the initial stage of vibration, the pore pressures of the calcareous sands increase rapidly and later decrease. In addition, with increasing Dr, the pore pressure growth curves of the calcareous sands exhibit an upward convex trend.Figure 14
Comparison of pore pressure growth curves of different types of calcareous sand [19, 24].The compressibility of the calcareous sand is higher than that of the siliceous sand. For calcareous sand with a largerDr value, the volume change is larger in the initial stage of vibration, and the pore pressure increases more rapidly. After the initial vibration, the Dr value is considerably higher, and the volume change caused by the cyclic vibration decreases in the later stage, resulting in a slow increase in the pore pressure.Overall,Dr is a key factor affecting the growth curve of the excess pore water pressure. Figure 14 also shows that the relative density influences the pore pressure growth characteristics of the calcareous sand.


## 3.4.4. Establishment of Pore Pressure Growth Model for Calcareous Sand

The pore pressure development curves measured under all test conditions in this test are plotted in Figure15. The pore pressure curves with similar relative density are represented by the same symbol, and the test conditions are shown above. It can be observed that, under different effective confining pressures and cyclic stress ratios, the development rule of the excess pore water pressure is consistent when the relative densities of the samples are similar.Figure 15
Comparison between the test data and predicted values of excess pore pressure of calcareous sand [24, 39].Considering different experimental conditions, several models of the excess pore water pressure growth of saturated sand under cyclic loading in the undrained condition have been developed, among which, the most popular model is the empirical formula based on the test data proposed by Seed et al. [39]:(4)Ru=12+1πsin−12NNL1/θ−1,where Ru is the residual pore pressure ratio after the Nth vibration, NL is the number of vibrations when the sample reaches initial liquefaction, and θ is the test parameter.At present, there are few studies on pore pressure development models of calcareous sand, especially in the South China Sea. Ma et al. [24] noted that it is not suitable to use the model of Seed directly to describe the pore pressure development of coral sand, so they proposed a modified model of Seed suitable for describing the pore pressure development of coral sands:(5)Ru=a×2πarcsinNNL1/2θ+b×arctanNNL.Equations (4) and (5) were used to fit the pore pressure data of the calcareous sand studied in this paper, and the results are shown in Figure 15. It can be seen that the fitting effect of the two models is better when the relative density is small, and the fitting effect of equation (5) is better when the relative density is large. When equation (5) is used to describe the pore water pressure development of the calcareous sand in a dense state, there is some deviation, especially in the later stage of pore pressure development, which cannot reflect the influence of relative density on the development of pore water pressure. Therefore, in this study, a modified model to describe the pore pressure development of the calcareous sand was established based on equation (5):(6)Ru=3.92∗θ−2.6∗arcsinNNL1/2θ+3.22−3.9∗θ∗arcsinNNL,where θ is the test parameter, and the fitting curve is shown as a solid line in Figure 15. The fitting parameters of equations (4)–(6) are summarized in Table 3, and the average value of the relative density in the table is obtained.Table 3
Fitting coefficients of the model.
ModelDr (%)abθR2Model of Seed [39]37.5——1.6150.98455.4——1.1080.99068.7——0.5220.91677.8——0.3380.855Modified model of Seed [24]37.51.435−0.3910.6650.98955.41.1280.0380.7520.99268.71.0810.3561.4880.95177.81.850−0.2971.3910.955Modified model37.5——0.7320.98955.4——0.8470.99168.7——1.0030.96477.8——1.0910.976Table3 shows that the fitting effect of the data with the modified model was satisfactory, with R2 being greater than 0.96. The relationship between the relative density and the modified model parameters was plotted as shown in Figure 16. It can be seen that the consolidated relative density of the calcareous sand was highly correlated with the parameters of the modified model, indicating that the relative density was the main factor affecting the pore pressure growth of the calcareous sand. When the relative density is known, the parameters θ of the modified model can be obtained by considering Figure 16, making it possible to predict the pore pressure growth curve.Figure 16
Relationship betweenDr and θ.


## 3.5. Volumetric Strain of Calcareous Sand after Liquefaction

When the dynamic load stops, the soil deforms with the dissipation of excess pore water pressure. Scholars have studied the volume deformation characteristics of quartz sand after vibration and achieved many results, but research on the volume deformation characteristics of calcareous sand after liquefaction remains rare. In this test, the effects of relative density, effective confining pressure, and cyclic stress ratio on the volume deformation of saturated calcareous sand after liquefaction are discussed. The volume deformation of the saturated Fujian sand was measured under the same working conditions, for comparison. The volumetric strain after liquefaction is defined as(7)εV=ΔVV0×100%,where ΔV is the volume change of sand before and after liquefaction failure and V0 is the volume of sand after consolidation.


### 3.5.1. Effect of Cyclic Stress Ratio on the Post-Liquefaction Volumetric Strain of Calcareous Sand

Figure17 shows the εV∼CSR curve of the calcareous sand and the Fujian sand after liquefaction. The solid symbol in the figure is the data point of the calcareous sand, and the hollow symbol is the data point of the Fujian sand. The data points with the same relative density and effective confining pressure are plotted on the same curve. It can be seen from the figure that under the same relative density and effective confining pressure, the effect of cyclic stress on the post-liquefaction volumetric strain of the two types of sand is reduced. The reason is that the decrease of porosity is directly proportional to increasing pore pressure. When the porosity of the samples is similar, the change of pore pressure during liquefaction is also similar. Compared to the Fujian sand, the volume of the calcareous sand in the loose state should be higher after liquefaction due to its higher compressibility.Figure 17
εV∼CSR curve of calcareous sand and Fujian sand.


### 3.5.2. Effect of the Effective Confining Pressure on the Post-Liquefaction Volumetric Strain of Calcareous Sand

Figure18 shows the εV∼σ3c curve of the calcareous sand and the Fujian sand after liquefaction. It can be observed from the figure that when the relative density and cyclic stress ratio are the same, the volume deformation of the calcareous sand after liquefaction increases with increasing effective confining pressure. The volume change of the saturated sand is related to pore pressure. The increase of the effective girth requires more volume deformation in order to achieve the same pore pressure ratio. Therefore, the volume change of sand liquefaction is large.Figure 18
εV∼σ3c curve of calcareous sand and Fujian sand.


### 3.5.3. Effect of Relative Density on the Post-Liquefaction Volumetric Strain of Calcareous Sand

It can be observed from Figure18 that at the same effective confining pressure and cyclic strain ratio, the post-liquefaction volumetric strain of the calcareous sand increases with decreasing relative density. Lee and Albaisa [33] noted that the average post-liquefaction volumetric strain of quartz sand was related to the relative density. The average value of the post-liquefaction volumetric strain of all the calcareous sand and the Fujian sand samples with similar relative density in this test was taken, εV∼Dr, and a relationship curve was drawn, as shown in Figure 19. The legend in the figure indicates the number of data samples, and the lines in the figure are the data fitting lines of the calcareous sand, the Fujian sand, and the Monterey sand [33]. It can be observed from Figure 19 that there is a good correlation between the average value of post-liquefaction volumetric strain of the three types of sand samples and the relative density, but the fitting line of the calcareous sand is linear. The fitting curves of the Monterey sand and the Fujian sand are different in shape, which may be related to the test conditions. The number of samples and the effective confining pressure at the corresponding points of the Monterey sand and the Fujian sand were insufficient. Generally, under the same relative density, the post-liquefaction volumetric strain of the calcareous sand is larger, which may be related to the special particle shape and gradation of the calcareous sand.Figure 19
εV∼Dr curve of calcareous sand, Fujian sand, and Monterey sand [33].


## 3.5.1. Effect of Cyclic Stress Ratio on the Post-Liquefaction Volumetric Strain of Calcareous Sand

Figure17 shows the εV∼CSR curve of the calcareous sand and the Fujian sand after liquefaction. The solid symbol in the figure is the data point of the calcareous sand, and the hollow symbol is the data point of the Fujian sand. The data points with the same relative density and effective confining pressure are plotted on the same curve. It can be seen from the figure that under the same relative density and effective confining pressure, the effect of cyclic stress on the post-liquefaction volumetric strain of the two types of sand is reduced. The reason is that the decrease of porosity is directly proportional to increasing pore pressure. When the porosity of the samples is similar, the change of pore pressure during liquefaction is also similar. Compared to the Fujian sand, the volume of the calcareous sand in the loose state should be higher after liquefaction due to its higher compressibility.Figure 17
εV∼CSR curve of calcareous sand and Fujian sand.


## 3.5.2. Effect of the Effective Confining Pressure on the Post-Liquefaction Volumetric Strain of Calcareous Sand

Figure18 shows the εV∼σ3c curve of the calcareous sand and the Fujian sand after liquefaction. It can be observed from the figure that when the relative density and cyclic stress ratio are the same, the volume deformation of the calcareous sand after liquefaction increases with increasing effective confining pressure. The volume change of the saturated sand is related to pore pressure. The increase of the effective girth requires more volume deformation in order to achieve the same pore pressure ratio. Therefore, the volume change of sand liquefaction is large.Figure 18
εV∼σ3c curve of calcareous sand and Fujian sand.


## 3.5.3. Effect of Relative Density on the Post-Liquefaction Volumetric Strain of Calcareous Sand

It can be observed from Figure18 that at the same effective confining pressure and cyclic strain ratio, the post-liquefaction volumetric strain of the calcareous sand increases with decreasing relative density. Lee and Albaisa [33] noted that the average post-liquefaction volumetric strain of quartz sand was related to the relative density. The average value of the post-liquefaction volumetric strain of all the calcareous sand and the Fujian sand samples with similar relative density in this test was taken, εV∼Dr, and a relationship curve was drawn, as shown in Figure 19. The legend in the figure indicates the number of data samples, and the lines in the figure are the data fitting lines of the calcareous sand, the Fujian sand, and the Monterey sand [33]. It can be observed from Figure 19 that there is a good correlation between the average value of post-liquefaction volumetric strain of the three types of sand samples and the relative density, but the fitting line of the calcareous sand is linear. The fitting curves of the Monterey sand and the Fujian sand are different in shape, which may be related to the test conditions. The number of samples and the effective confining pressure at the corresponding points of the Monterey sand and the Fujian sand were insufficient. Generally, under the same relative density, the post-liquefaction volumetric strain of the calcareous sand is larger, which may be related to the special particle shape and gradation of the calcareous sand.Figure 19
εV∼Dr curve of calcareous sand, Fujian sand, and Monterey sand [33].


## 4. Conclusions

A series of undrained cyclic triaxial tests were conducted on calcareous sand samples obtained from a reef reclamation project site in the South China Sea. The factors influencing the liquefaction resistance, the pore pressure growth, and the post-liquefaction volumetric strain of the saturated calcareous sand were analyzed. The following conclusions were derived:(i)
The particle shape and micromorphology of the calcareous sand from the dredger fill site obtained by cutter suction or trailing suction are quite different from those of natural calcareous sand, which will affect the mechanical properties of the calcareous sand.(ii)
The dynamic stress attenuation leads to cyclic vibration times higher than the actual liquefaction vibration times. A correction method based on the equivalent concept can better eliminate the influence of dynamic stress attenuation.(iii)
Saturated calcareous sand will liquefy under undrained cyclic load. The liquefaction resistance of calcareous sand with high relative density is high, but the liquefaction resistance of calcareous sand decreases with increasing effective confining pressure under the dense condition.(iv)
Due to the porous and irregular shape of the calcareous sand, its liquefaction resistance is higher than that of the Fujian sand, and the difference between them is the largest in the loose and dense states. Compared with the calcareous sand studied in other literature, the particle size distribution of the calcareous sand from the dredger fill site was better and had higher anti-liquefaction ability.(v)
The experimental results show that the model of Seed was not suitable for describing the pore pressure development of calcareous sand, and a modified model was proposed, which better described the pore pressure growth characteristics of calcareous sand. The fitting parameters of this model were well-correlated with the relative density.(vi)
The post-liquefaction volumetric strain of the calcareous sand should be larger under conditions of higher effective confining pressure and smaller relative density. The results show that the post-liquefaction volumetric strain of the calcareous sand was larger than that of the quartz sand, and the post-liquefaction volumetric strain of the calcareous sand had a linear relationship with relative density.(vii)
The above research has some limitations. It is necessary to further study the influence of different types of calcareous sand shape on liquefaction characteristics and volumetric strain of calcareous sand.



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