Journal of Marine Science and Engineering
Article Experimental Study on the Impact of Water Content on the Strength Parameters of Coral Gravelly Sand
Yang Wu 1, Xing Wang 1,* , Jian-Hua Shen 2, Jie Cui 1, Chang-Qi Zhu 2 and Xin-Zhi Wang 2 1 School of Civil Engineering, Guangzhou University, Guangzhou 510006, China; [email protected] (Y.W.); [email protected] (J.C.) 2 State Key Laboratory of Geotechnical Mechanics and Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [email protected] (J.-H.S.); [email protected] (C.-Q.Z.); [email protected] (X.-Z.W.) * Correspondence: [email protected]
Received: 12 July 2020; Accepted: 18 August 2020; Published: 20 August 2020
Abstract: The effect of capillary water caused by heavy rainfall and groundwater level fluctuations can induce the erosion and collapse of island reef coral sand foundations. Here, the effects of water content (ω) on the shear strength parameters of coral gravelly sand are analyzed at the macro and micro scales by laboratory consolidated-drained triaxial compression and nuclear magnetic resonance tests. Furthermore, particle breakage characteristics of coral gravelly sand under the static load are discussed. With increasing ω, (1) the internal friction angle increases slightly (<1◦) then decreases; (2) the apparent cohesion is more sensitive to the change in the ω; (3) with an increase from 5.4% to 21.3%, the bound water content remains almost unchanged; (4) the capillary water content is the main factor impacting the apparent cohesion; (5) the increase in free water content is the internal cause of the decreasing internal friction angle of coral gravelly sand with ω > 11.1%; and (6) the particle breakage increases, and there is an approximately linear relationship between the median particle diameter (d50) and relative breakage index (Br). The established physical model can reflect the influence of water content and plastic work and describe the evolution law of particle breakage.
Keywords: coral gravelly sand; water content; strength parameters; microstructure; particle breakage; plastic work
Highlights Triaxial shear tests and NMR tests on coral gravelly sand with different water content • were performed. Effects of water content on strength parameters of coral gravelly sand were assessed quantitatively. • Underlying mechanisms of water content on strength parameters of coral gravelly sand • were demonstrated. The relationship among the relative breakage index, plastic work and water content was established. • 1. Introduction Coral sand, also known as calcareous sand, shell sand, or carbonate sand, is a special geotechnical medium with calcium carbonate, magnesium carbonate, and other carbonates as the main mineral components, which are usually formed by biological debris after the death of marine organisms such as coral reefs, shells, seaweeds, etc., through physical, chemical, and biochemical actions. Coral sand mainly appears on the continental shelf and coastline between 30◦ N–30◦ S, and they are also found in the South China Sea [1]. Coral gravelly sand is defined as coral sand having 25%–50% of its total mass comprising particles greater than 2 mm in size. Large-scale hydraulic reclamation construction
J. Mar. Sci. Eng. 2020, 8, 634; doi:10.3390/jmse8090634 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 634 2 of 25 started in the South China Sea at the end of 2013, for which the only available material is the coral sand deposited in the island reef tray and lagoon. Because of the characteristics of the hydraulic reclamation and the intermittent foundation treatment [2], the coral gravelly sand is distributed in the middle of the stratum and is the main supporting layer in the foundation. Therefore, it is crucial to determine the strength parameters of the coral gravelly sand (c, ϕ) for island reef infrastructure design and construction. Terzaghi’s soil mechanics theory and the Mohr–Coulomb strength theory solved the problem of saturated soil strength in the early twentieth century [3]. However, the coral sand in the island reef is mostly unsaturated. Owing to the lack of scientific understanding of the strength characteristics of unsaturated coral gravelly sand, to ensure engineering safety, engineers often use the saturated shear strength for checking calculations in the design of island reef buildings. The related research results [4–6] show that the mechanical properties of coral sand in unsaturated and saturated states are quite different, and buildings designed based on the saturated shear strength will inevitably cause huge economic losses. Therefore, studying the mechanical properties of unsaturated coral gravelly sand is of great significance to the development of soil mechanics and resource conservation. There have been many previous studies on the variation in the strength parameters of unsaturated soils with ω. Most scholars [7,8] believe that the strength parameters of unsaturated soils decrease with increasing ω. However, no consensus has yet been reached on the decreasing trend. For example, Miao et al. [9] believed that the logarithm of the strength parameter of unsaturated expansive soil (lgc, lgϕ) decreased linearly with increasing ω, and the decrease of cohesion (c) was more obvious. Ling and Yin [10] and Shen et al. [11] reported that within a certain range of ω, the strength parameter of unsaturated soil decreased linearly with the increasing ω. Bian and Wang [12] studied the relationship between the strength parameters and ω of silty clay, and found that both cohesion and internal friction angle decreased with increasing ω, there was a linear relationship between the internal friction angle and ω, and the relationship between the cohesion and ω could be approximated by a quadric equation. Some scholars believed that strength parameters of unsaturated soil did not change monotonically with increasing ω. For example, Kong and Tan [13] studied the relationship between the strength parameters of compacted expansive soil and ω and believed that the cohesion of compacted expansive soil also decreased with increasing ω, but when the ω was greater than the plastic limit, the cohesion reached a stable value. Xiong et al. [14] conducted multiple sets of unconsolidated and undrained triaxial shear tests on unsaturated silty clay and found that the relationship between the internal friction angle and ω could be approximated by a W-shaped curve, while the cohesion showed a “mountain peak effect” with increasing ω, which peaked when the ω was 18.16%. Cokca et al. [15] conducted a series of direct shear tests on unsaturated compacted clay, and concluded that the internal friction angle decreased with increasing ω and the cohesion peaked near the optimal ω. Lin et al. [16] studied the influence of ω on the strength parameters of silty sand, sandy silt, and silty clay, respectively, and pointed out that the cohesion of the three kinds of soils reached the maximum when the saturation was 40%–60%, and the internal friction angle continued to decrease with increasing saturation. Huang et al. [17] studied the change in the strength parameters of remolded silty sand with ω through laboratory direct shear tests. The results showed that the cohesion of silty sand first increased and then decreased with increasing ω, and the internal friction angle first decreased and then increased with increasing ω. Chen et al. [18] and Wang et al. [19] studied the relationship between the strength parameters and ω of unsaturated sand, and believed that the cohesion of unsaturated silt first increased then decreased with the increasing ω, and the internal friction angle continued to decrease with increasing ω. This shows that different unsaturated soils have significant differences in their strength parameters depending on the ω. Additionally, most of these research results are based on terrigenous soil. Owing to the special marine organisms in coral sand, it is significantly different from terrigenous soils; it has extremely irregular particle shapes and high porosity and fragility, and is often accompanied by cementation [20], which are significantly different from terrigenous soils. Therefore, whether the above research results are applicable to coral sand remains to be discussed. J. Mar. Sci. Eng. 2020, 8, 634 3 of 25
Since the first discovery of coral sand and reef limestone layers by geotechnical engineers in the Persian Gulf in the early 1960s [21], studies on the mechanical properties of coral sand have been conducted for almost 60 years. In 1988, the first international calcareous soil mechanics conference held in Perth, Australia, triggered a great upsurge in research on the mechanical properties of coral sand. At present, researchers have mainly studied coral fine-grained soil [2,20,22–24], medium-coarse sand [25–31], and coarse-grained soil [32,33]. There are relatively few studies on the mechanical properties of coral gravelly sand [34,35], and these research results are mostly limited to the effects of density, gradation, stress state, etc. on the mechanical properties of coral gravelly sand. There are few studies on the effects of ω on the mechanic characteristics of coral gravelly sand and its microscopic mechanisms. According to the particle size analysis of a core sample of the borehole in the upper fill of the hydraulic island reef in the South China Sea, it was found that coral gravelly sand was widely distributed in the hydraulic foundation of the island reef. Under the influence of factors such as rainfall, seawater tides, drainage, evaporation and other factors, the ω of coral gravelly sand often changes, and there is no conclusive research data to prove whether the related engineering mechanical properties will change. Considering this, a series of laboratory consolidated-drained triaxial compression tests were conducted on the coral gravelly sand, to comparatively study its mechanical properties under different water contents and reveal the variation in the strength parameters of coral gravelly sand with different water contents from a macro perspective. Besides, nuclear magnetic resonance (NMR) tests were carried out on coral gravelly sand with different water contents to study the changes in the pore water content in different occurrence forms with the ω of the sample, revealing the influence mechanism of ω on the macroscopic mechanical properties of coral gravelly sand from a microscopic perspective. Moreover, based on the particle breakage characteristics of coral sand under low stress, the particle breakage degree of coral gravelly sand with different water contents during the triaxial shearing process was quantitatively analyzed. The results of this study could lay the theoretical foundation for subsequent research on the effect of the drying–wetting cycle on the strength characteristics and particle breakage of coral gravelly sand.
2. Materials and Methods
2.1. Experiment Material The samples were uncemented loose coral sand taken from a hydraulic fill island reef in the South China Sea. The particles were light white with edges and corners. The parent rock was relatively brittle, and the single-particle strength was low. According to the relevant provisions of the Chinese National Standard of Soil Test Method (SL237-2019) [36], the physical properties of the coral sand, such as the particle size distribution, specific gravity, and maximum and minimum dry densities, were tested before the triaxial shear experiment. The test results are shown in Figure1 and Table1. J. Mar. Sci. Eng. 2020, 8, 634 4 of 25 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 4 of 28
100
90
80
70
60
50
40
Finer percent (%) 30
20
10
0 10 1 0.1 0.01 0.001 Grain size (mm) Figure 1. Gradation curve of the coral sand.
As shown in Figure1 and Table1, (1) the mass of the particles greater than 2 mm in size is about 40% of the total mass of the sample, which proves that the coral sand tested is coral gravelly sand. (2) The gradation curve in Figure1 has a gentle slope, and the coral sand have a continuous particle size distribution and a relatively wide particle size distribution range, indicating that the coral gravelly sand tested has a good gradation. As shown in Table1, the non-uniformity coe fficient (Cu) of the sand is greater than 5.0 and the curvature coefficient (Cc) is between 1 to 3, which also confirm the conclusion of good gradation of coral gravelly sand. (3) The specific gravity of coral gravelly sand is 2.73, greater than that of terrigenous quartz sand (2.65); this is due to the difference in the mineral composition of the two sands. The main mineral component of coral gravelly sand is CaCO3, while that of terrigenous quartz sand is SiO2; the density of CaCO3 is larger than that of SiO2, which makes the specific gravity of coral gravelly sand greater than that of terrigenous quartz sand. (4) The maximum and minimum void ratios of the coral gravelly sand tested are greater than those of terrigenous quartz sand with the same particle gradation (emax = 0.85; emin = 0.61). In terms of dry density, the maximum and minimum dry densities of the coral gravelly sand are generally smaller than those of terrigenous 3 3 quartz sand (ρdmax = 1.65 g/cm ; ρdmin = 1.43 g/cm ). The special marine biogenesis of coral gravelly sand results in a large amount of internal pores and irregular particle shape; the irregular particle shape causes relatively large intergranular pores during the accumulation process, which further increases the porosity of coral gravelly sand. This is also the main reason why the specific gravity of coral gravelly sand is larger while the maximum and minimum dry densities are smaller than those of terrigenous quartz sand with the same particle gradation.
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Table 1. Physical parameters of the coral sand tested.
Minimum Dry Maximum Dry Maximum Minimum d10 d50 d60 Specific Gravity Sample Cu Cc Density Density Void Ratio Void Ratio (mm) (mm) (mm) Gs 3 3 ρdmin (g/cm ) ρdmax (g/cm ) emax emin Coral gravelly sand 0.09 1.49 2.00 20 2.08 2.73 1.19 1.52 1.29 0.80
d10 Diameter corresponding to 10% finer in the gradation curve
d50 Diameter corresponding to 50% finer in the gradation curve
d60 Diameter corresponding to 60% finer in the gradation curve Cu Non-uniformity coefficient Cc Curvature coefficient J. Mar. Sci. Eng. 2020, 8, 634 6 of 25
2.2. Experiment Scheme To study the impact of ω on the shear characteristics of coral gravelly sand, and to discuss the evolution of the particle breakage of coral gravelly sand with different water contents during the shearing process, a simple variable method was used to design the experimental scheme and the triaxial shear tests were carried out on the coral gravelly sand under different water contents. On the basis of strictly controlling the particle gradation of the sample, a screening test was carried out on the coral gravelly sand to reveal the variation in its particle breakage characteristics under different water contents and stress conditions. Owing to the coarse particles of coral gravelly sand and fast drainage speed, the stress state during the consolidation drainage shear process is most similar to the actual stress environment [1]. Therefore, a series of consolidated-drained triaxial compression tests on the coral gravelly sand with different water contents were carried out to analyze the variation in the shear characteristics with ω. An in-situ survey of the hydraulic fill island reef in the South China Sea found that the compactness of coral gravelly sand after foundation treatment generally has a relative density of about 70%. Therefore, the relative density of the coral gravelly sand samples in the triaxial shear tests was set at 70%. The coral sand reclamation layer in the island reef is relatively thin, and the buildings on the island reef have a relatively low height, which results in a small base additional stress on the coral sand, generally within 200 kPa. Additionally, for the highest construction on the island reef (such as the maritime lighthouse, airport signal tower, etc.), the base additional stress does not exceed 400 kPa [37]. Thus, 50, 100, 200, and 400 kPa were taken as the confining pressures of coral gravelly sand in the triaxial shear tests, with a view to fit the actual stress state of coral sand. As the proportion of fine particles with a particle size of <0.075 mm ( 8.9%) in the coral gravelly sand is small, the sample has a ≤ poor water-holding capacity. In addition, it was also found in the test that the sample bleeds seriously when the ω exceeded 24%. Therefore, a ω of 24% was taken as the upper limit, and triaxial shear tests were carried out on coral gravelly sand with water contents of 6%, 12%, 18%, and 24%. The sample size was 61.8 120 mm (diameter height). The triaxial shear rate was set to 0.6 mm/min, and the ∅ × × test was terminated when the axial strain reached 20%. A detailed test scheme is shown in Table2.
Table 2. Triaxial shear test scheme.
Relative Water Sample Size Confining Shearing Terminating Sample Density Dr Content ω Test Type Pressure σ Rate ν Diameter Height 3 Strain (%) (%) D (mm) H (mm) (kPa) (mm/min) Coral gravelly 70 6, 12, 18, 24 61.8 120 CD 50, 100, 200, 400 0.6 εa = 20% sand
To reveal the impact of ω on the shear strength parameters of coral gravelly sand from a microscopic perspective, a series of NMR (nuclear magnetic resonance) tests were carried out on coral gravelly sand samples to reveal the variation in the pore water content in different occurrence forms with the ω. The physical parameters of the coral gravelly sand samples used in the NMR test are the same as those of the coral gravelly sand in the triaxial shear test, that is, at a relative density of 70%, coral gravelly sand with water contents of 6%, 12%, 18%, 24% were selected for NMR tests. The sample size is 45 20 mm (diameter height). The specific experiment scheme is shown in Table3. ∅ × × Table 3. Nuclear magnetic resonance experiment scheme.
Sample Size Relative Density Water Content Sample Dr (%) ω (%) Diameter Height D (mm) H (mm) Coral gravelly sand 70 6, 12, 18, 24 45 20 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 8 of 28
To reveal the impact of ω on the shear strength parameters of coral gravelly sand from a microscopic perspective, a series of NMR (nuclear magnetic resonance) tests were carried out on coral gravelly sand samples to reveal the variation in the pore water content in different occurrence forms with the ω. The physical parameters of the coral gravelly sand samples used in the NMR test are the same as those of the coral gravelly sand in the triaxial shear test, that is, at a relative density of 70%, coral gravelly sand with water contents of 6%, 12%, 18%, 24% were selected for NMR tests. The sample size is ∅45 × 20 mm (diameter × height). The specific experiment scheme is shown in Table 3.
Table 3. Nuclear magnetic resonance experiment scheme.
Sample Size Relative Density Water Content Sample Diameter Height Dr (%) ω (%) D (mm) H (mm) J. Mar. Sci.Coral Eng. gravelly2020, 8, sand 634 70 6, 12, 18, 24 45 20 7 of 25
2.3. Experiment Apparatus and Operations 2.3. Experiment Apparatus and Operations In this study, the TKA-Advanced full-automatic stress path triaxial testing apparatus developed by NanjingIn this Tektronix study, the Co., TKA-Advanced Ltd., Nanjing, full-automatic China was employed. stress path The triaxial whole testing test device apparatus is composed developed of fiveby Nanjing parts: The Tektronix data acquisition Co., Ltd., Nanjing, system, Chinapressure was chamber, employed. strain The control whole testsystem, device back is composed pressure controlof five parts:system, The and data confining acquisition pressure system, control pressure system chamber, (see Figure strain 2). control The shear system, rate backof the pressure triaxial shearcontrol apparatus system, and ranges confining from 0.0001 pressure to control1.2 mm/min, system and (see variable Figure2 ).speed The shearloading rate can of be the achieved. triaxial shear The axialapparatus load rangessensor fromhas a 0.0001 measuring to 1.2 mmrange/min, of 15 and kN variable and an speed accuracy loading of can+0.15% be achieved. FS. The confining The axial pressureload sensor and has back a measuring pressure control range of system 15 kN andhas a an stress accuracy control of + range0.15% of FS. 0–3 The MPa confining and an pressure accuracy and of 1.0back kPa. pressure The size control of the system sample has that a stressthat can control fit into range the ofpressure 0–3 MPa chamber and an is accuracy ∅61.8 ×of 120 1.0 mm kPa. (diameter The size ×of the sample that that can fit into the pressure chamber is 61.8 120 mm (diameter height). height). ∅ × ×
①
② ⑥
⑤
③
④
Figure 2. TKA-Advanced full-automatic stress path triaxialtriaxial testingtesting apparatus.apparatus. O①1 —Back pressure control system;system;O 2②—confining—confining pressure pressure control control system; system;O3 —data ③—data acquisition acquisition system; system;O4 —strain ④—strain control controlsystem; system;O5 —pressure ⑤—pressure chamber; chamber;O6 —axial ⑥—axial load sensor. load sensor.
The entire triaxial shear test can be divided into fo fourur steps: sample sample preparation, preparation, loading, loading, testing, testing, and particle breakage measurement. (1) In the sample preparation process, the coral gravelly sand sample was dried to a constant weight underunder environmentenvironment conditions conditions at at a constant a consta temperaturent temperature of 105 of◦ 105C. After °C. After the sample the sample was cooled was cooledto normal to normal temperature temperature (about (about 25 ◦C), 25 a screening°C), a screen testing was test conducted was conducted on the on sample the sample to separate to separate coral coralgravelly gravelly sand samplessand samples of diff erentof different particle particle sizes (see sizes Figure (see3 )Figure into sealed 3) into bags. sealed During bags. the During screening the test, to avoid errors in screening the particle size due to clogging of the sieve pores with fine particles, it is suggested to not use too many soil samples for each screening test; the screening time should be maintained at longer than 15 min [38]; and a brush can be used to clean the sieve holes before starting the next set of screening tests. After obtaining coral sand grains of different particle sizes, the total mass of the tested sample was calculated according to the relative density and the size of the sample tested in the pressure chamber, and then the sample to be tested was configured according to the coral sand mass ratio of each particle size in the gradation curve and stored in sealed bags. The quantity of the fresh water to be added into the sample was calculated according to the design value of the ω in Table2. The water was mixed with the coral gravelly sand before being sealed and stored for 24 h to ensure that the water was evenly distributed in the sample. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 28
screening test, to avoid errors in screening the particle size due to clogging of the sieve pores with fine particles, it is suggested to not use too many soil samples for each screening test; the screening time should be maintained at longer than 15 min [38]; and a brush can be used to clean the sieve holes before starting the next set of screening tests. After obtaining coral sand grains of different particle sizes, the total mass of the tested sample was calculated according to the relative density and the size of the sample tested in the pressure chamber, and then the sample to be tested was configured according to the coral sand mass ratio of each particle size in the gradation curve and stored in sealed bags. The quantity of the fresh water to be added into the sample was calculated according to the J.design Mar. Sci. value Eng. 2020 of ,the8, 634 ω in Table 2. The water was mixed with the coral gravelly sand before being8 of 25 sealed and stored for 24 h to ensure that the water was evenly distributed in the sample.
Figure 3.3. Fractions of coral sand.
(2) During the loading process, thethe raindrop methodmethod waswas usedused toto load the sample into the rubber membrane in three layers.layers. In the specific specific operatio operation,n, a metal spoon was used to evenly spread the sample into the rubber membrane; and a steel rulerruler waswas usedused toto checkcheck whetherwhether thethe compactnesscompactness ofof the samplesample metmet thethe designdesign requirementsrequirements afterafter eacheach layerlayer waswas installed.installed. If the design value of thethe compactness ofof the tested sample was large, a compactingcompacting hammer would be adopted to gently press the surface of of the the sample sample until until it it reached reached the the compactness compactness set set in inTable Table 2. 2After. After filling filling each each layer, layer, the thesurface surface of the of sample the sample tested tested was wasshaved shaved before before filling filling the next the next layer layer of sample, of sample, and andthe operation the operation was wasrepeated repeated until until the sample the sample height height reached reached the design the design value. value. (3) DuringDuring the the test, test, the the triaxial triaxial consolidation consolidation test wastest carriedwas carried out on out the sampleon the undersample the under designed the confiningdesigned confining pressure. pressure. Due to the Due large to intergranularthe large intergra voidnular of coral void gravel of coral sand, gravel the sand, fast loading the fast methodloading wasmethod used was and used the consolidationand the consolidation time was time set atwas 1.0 set h. at Then, 1.0 h. the Then, triaxial the sheartriaxial test shear was test carried was outcarried at a shearout at ratea shear of 0.6 rate mm of/min 0.6 whilemm/min maintaining while maintaining the same confiningthe same pressure,confining and pressure, the test and was the terminated test was whenterminated the axial when strain the reachedaxial strain 20%. reached 20%. (4) After After the the test, test, the the coral coral gravelly gravelly sand sand sample sample was was washed washed into intoa tray a with tray clean with cleanwater. water. After Afterdrying drying the sample the sample and cooling and cooling it to a normal it to a normal temper temperature,ature, a screening a screening test was test carried was out carried to identify out to identifythe amount the amountof particle of breakage. particle breakage. It is worth It isnoting worth that noting coral that sand coral is a sandspecial is ageotechnical special geotechnical medium mediumwhere particle where breakage particle breakage occurs under occurs low under stress. low To stress. obtain To the obtain amount the amountof particle of particlebreakage breakage of coral ofgravelly coral gravellysand in triaxial sand in shearing triaxial shearingunder different under diwafftererent contents water and contents stress and conditions, stress conditions, it is necessary it is necessaryto avoid particle to avoid breakage particle caused breakage by causedimproper by improperoperation operationduring the during test. the test. The principle of the NMR test is that, when the samplesample is placed in a fixedfixed magnetic fieldfield of a certain strength, it it takes takes a a certain certain time time (i.e., (i.e., the the lateral lateral relaxation relaxation time) time) for for the the hydrogen hydrogen nuclei nuclei in the in thesample sample to return to return to an to equilibrium an equilibrium state state due dueto the to interference the interference of the of radio the radio frequency frequency (RF) (RF)field, field, and andthat thatthe relaxation the relaxation times times for hydrogen for hydrogen nuclei nuclei in diffe in direntfferent physical physical or chemical or chemical states states are different. are different. For Fora given a given sample, sample, the thestrength strength and and location location of the of thesign signalal are arerelated related to the to the content content and and distribution distribution of ofpore pore water water in the in the sample. sample. Therefore, Therefore, the thecontent content of pore of pore water water with with different different occurrence occurrence forms forms in the in thesample sample can can be bequantitatively quantitatively measured measured by by NMR NMR technology. technology. The The nuclear nuclear magnetic magnetic resonance resonance test device deployed was the PQ001 Mini NMR Analyzer,Analyzer, jointly developed by the Wuhan Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, and Suzhou Newman Analytical Instrument Co., Ltd., Suzhou, China, (see Figure4 4).). ThisThis analyzeranalyzer comprisescomprises fivefive parts:parts: TheThe permanentpermanent magnet,magnet, sample tube, RF system, temperature control system,system, and data acquisition and analysis system [39]. [39]. The magnetic fieldfield strength of the permanent magnet is 0.52 T. To ensure the uniformity and stability of the magnetic field, the temperature of the magnet is maintained at 32 0.01 C. The sample tube is a ± ◦ container for the sample to be tested, and its effective test range is 60 60 mm (diameter height). ∅ × × J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 10 of 28
J.of Mar. the Sci.magnetic Eng. 2020 field,, 8, 634 the temperature of the magnet is maintained at 32 ± 0.01 °C. The sample tube9 of 25is a container for the sample to be tested, and its effective test range is ∅60 × 60 mm (diameter × height).
FigureFigure 4. Schematic 4. Schematic diagram diagram of theof the PQ001 PQ001 mini mini nuclear nuclear magnetic magnetic resonance resonance analyzer analyzer and and the samplethe sample tested. tested. Cutting ring was used to prepare soil samples for the NMR test. To avoid the interference of the metalCutting cutting ring was ring used on the to NMRprepare signal, soil samples the cutting for the ring NMR used test. was To made avoid of the PTFE interference material with of the a diametermetal cutting of 45 ring mm on and the a height NMR ofsignal, 20 mm. the It cutting is worth ring noting used that, was owing made toof the PTFE poor material water-holding with a capacitydiameter ofof the45 mm coral and gravelly a height sand, of 20 part mm. of theIt is pore worth water noting will that, overflow owing from to the the poor sample water-holding under the pressurecapacity duringof the coral the process gravelly of sand, making part sample of the by pore the water sample will pressing overflow method; from thisthe sample phenomenon under willthe bepressure particularly during obvious the process when of the ma sampleking sample has a by high theω sample. Therefore, pressing the actualmethod;ω ofthis the phenomenon sample needs will to be particularly tested before obvious the NMR when test. the The sample actual has water a high contents ω. Therefore, of the coral thegravelly actual ωsand of the samples sampleprepared needs to forbe tested the NMR before test the were NMR 5.4%, test. 11.1%, The actual 16.7%, water and 21.3%contents (see of Figure the coral4). Thegravelly four sand kinds samples of coral prepared gravelly sandfor the samples NMR test with were different 5.4%, water 11.1%, contents 16.7%, wereand 21.3 placed% (see in the Figure test area4). The of the four sample kinds tubeof coral to obtain gravelly the RFsand signals samples in the with magnetic different field. water Through contents the were processing placed andin the analysis test area of theof the nuclear sample magnetic tube tosignals, obtain the contentRF signals of pore in the water magnetic in diff erentfield. occurrenceThrough the forms processing can be obtained.and analysis of the nuclear magnetic signals, the content of pore water in different occurrence forms can be obtained. 3. Analysis of Strength Parameters 3. AnalysisConsolidated-drained of Strength Parameters triaxial compression tests were carried out on coral gravelly sand with a relativeConsolidated-drained density of 70% andtriaxial diff erentcompression water contents tests were under carried confining out on coral pressures gravelly of 50,sand 100, with 200, a andrelative 400 kPadensity to obtain of 70% the and peak different and end water shear conten strengthsts under under confining different testpressures conditions. of 50, Then, 100, the200, shear and strength400 kPa to parameters obtain the (c, peakϕ) of and the coralend shear gravelly strengths sand were under determined different accordingtest conditions. to the Mohr–CoulombThen, the shear theory.strength Theparameters results are (c, shownϕ) of the in Tablecoral4 .gravelly It is worth sand noting were thatdetermined the values according of the shear to the strength Mohr– parametersCoulomb theory. (c, ϕ) areThe valid results only are for shown the confining in Table pressure 4. It is worth range testednoting (i.e., that 50–400 the values kPa). of the shear strength parameters (c, ϕ) are valid only for the confining pressure range tested (i.e., 50–400 kPa). Table 4. The shear strength parameters of coral gravelly sand under different stress states.
Relative Density Water Content Saturation Peak State End State Sample Dr (%) ω (%) Sr (%) c (kPa) ϕ (◦) c (kPa) ϕ (◦) 6 17.24 45.88 38.58 27.25 39.33 12 34.48 53.75 39.38 32.29 40.35 Coral gravelly sand 70 18 51.73 57.83 37.88 35.70 38.63 24 68.97 70.39 37.31 38.11 38.50
From Table4, the following can be observed and inferred: (1) Under the same test conditions, the internal friction angle of coral gravelly sand in the peak state was smaller than that in the end state, but the cohesion was greater than that in the end state. Under the effective confining pressure of less than 400 kPa, the shear strength envelope of coral gravelly sand with different water contents in the
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 12 of 28
From Table 4, the following can be observed and inferred: (1) Under the same test conditions, the internal friction angle of coral gravelly sand in the peak state was smaller than that in the end J. Mar. Sci. Eng. 2020, 8, 634 10 of 25 state, but the cohesion was greater than that in the end state. Under the effective confining pressure of less than 400 kPa, the shear strength envelope of coral gravelly sand with different water contents peakin the and peak end and states end states are shown are shown in Figure in Figure5; the 5; peak the shearpeak shear strength strength of coral of coral gravelly gravelly sand sand under under low stresslow stress was greaterwas greater than than that inthat the in end the state, end state, and the and peak the shearpeak shear strength strength under under high stress high wasstress lower was thanlower that than in that the endin the shear end strength.shear strength.
1600 Peak state 1600 End state Mohr's circle at 50 kPa Mohr's circle at 50 kPa Mohr's circle at 100 kPa Mohr's circle at 100 kPa 1400 Mohr's circle at 200 kPa 1400 Mohr's circle at 200 kPa Mohr's circle at 400 kPa Mohr's circle at 400 kPa The shear strength envelope curve The shear strength envelope curve 1200 1200
1000 τ = 0.80σ+45.88
) 1000 ) τ = 0.82σ+27.25 kPa 800 kPa 800 τ ( τ (
600 600
400 400
200 200
0 0 500 1000 1500 2000 0 0 500 1000 1500 2000 σ (kPa) σ (kPa)
(a)
1800 Peak state 1800 End state Mohr's circle at 50 kPa Mohr's circle at 50 kPa Mohr's circle at 100 kPa Mohr's circle at 100 kPa 1600 Mohr's circle at 200 kPa 1600 Mohr's circle at 200 kPa Mohr's circle at 400 kPa Mohr's circle at 400 kPa 1400 The shear strength envelope curve 1400 The shear strength envelope curve
1200 1200 ) τ σ ) τ = 0.85σ+32.29 1000 = 0.82 +53.75 1000 kPa kPa
τ ( 800 τ ( 800
600 600
400 400
200 200
0 0 0 500 1000 1500 2000 0 500 1000 1500 2000 σ (kPa) σ (kPa)
(b)
1600 Peak state 1600 End state Mohr's circle at 50 kPa Mohr's circle at 50 kPa Mohr's circle at 100 kPa Mohr's circle at 100 kPa 1400 Mohr's circle at 200 kPa 1400 Mohr's circle at 200 kPa Mohr's circle at 400 kPa Mohr's circle at 400 kPa The shear strength envelope curve The shear strength envelope curve 1200 1200
1000 τ σ 1000 τ σ = 0.78 +57.83 ) = 0.80 +35.70 ) kPa kPa 800 800 τ ( τ (
600 600
400 400
200 200
0 0 0 500 1000 1500 2000 0 500 1000 1500 2000 σ (kPa) σ (kPa)
(c)
Figure 5. Cont.
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1600 Peak state 1600 End state Mohr's circle at 50 kPa Mohr's circle at 50 kPa Mohr's circle at 100 kPa Mohr's circle at 100 kPa 1400 Mohr's circle at 200 kPa 1400 Mohr's circle at 200 kPa Mohr's circle at 400 kPa Mohr's circle at 400 kPa The shear strength envelope curve The shear strength envelope curve 1200 1200
1000 τ = 0.76σ+70.39 1000 τ = 0.80σ+38.11 ) ) kPa kPa 800 800 τ ( τ (
600 600
400 400
200 200
0 0 0 500 1000 1500 2000 0 500 1000 1500 2000 σ (kPa) σ (kPa)
(d)
Figure 5. The shear strength envelope curv curveses of coral gravelly sand under different different stress states and water contents: ( a) ω = 6%,6%, ( (bb)) ωω == 12%,12%, (c (c) )ωω == 18%,18%, (d (d) )ωω = =24%.24%.
This can bebe explainedexplained by by the the method method for for determining determining shear shear strength strength in thein the peak peak state state and and the endthe endstate, state, and theand variation the variation trend trend of the of deviatoric the deviatoric stress–axial stress–axial strain strain curve curve of coral of gravellycoral gravelly sand under sand underdifferent different stress conditionsstress conditions (see Figure (see6 Figure). According 6). According to the relevant to the relevant provisions provisions in the Chinese in the NationalChinese StandardNational Standard of Soil Test of Method Soil Test(SL237-2019) Method (SL237-2019) [36], when [36], the deviatoric when the stress–axialdeviatoric stress–axial strain curve strain obtained curve by obtainedthe triaxial by shear the triaxial test has shear a peak test value, has a the peak deviatoric value, the stress deviatoric at the peak stress is takenat the aspeak the is peak taken strength; as the peakif the strength; deviatoric if stress–axialthe deviatoric strain stress–axial curve has strain no peak curve value, has theno deviatoricpeak value, stress the deviatoric at 15% of thestress axial at 15%strain of is the taken axial as strain its peak is taken strength. as its Regardless peak strength. of whether Regardless the deviatoric of whether stress–axial the deviatoric strain stress–axial curve had a peakstrain value curve or had not, thea peak corresponding value or not, deviatoric the corr stressesponding when the deviatoric test was terminatedstress when was the taken test as was the terminatedshear strength was in taken the end as state.the shear A relevant strength study in the [1 ]end showed state. that A relevant coral sand study has [1] similar showed dilatancy that coral and sandcontraction has similar properties dilatancy to terrigenous and cont quartzraction sand properties during triaxialto terrigenous shearing. quartz In a low-stress sand during environment, triaxial shearing.the sample In underwent a low-stress dilatation environment, during shearing,the sample and underwent the corresponding dilatation deviatoric during shearing, stress–axial and strain the correspondingcurve was a strain-softening deviatoric stress–axial type curve. strain The curve hadwas aa peakstrain-softening stress greater type than curve. the deviatoric The curve stress had aat peak the end stress of the greater test. While than inthe a highdeviatoric stress environment,stress at the theend sample of the underwent test. While contraction in a high duringstress environment,shearing, and thethe correspondingsample underwent deviatoric contraction stress–axial during strain shearing, curve wasand athe strain-hardening corresponding typedeviatoric curve. stress–axialDuring the entirestrain shearing curve was process, a strain-hardening the deviatoric type stress curve. continued During toincrease the entire with shearing the increasing process, axial the deviatoricstrain, and stress there continued was no peak to increase stress in with the curve; the incr theeasing deviatoric axial strain, stress atand 15% there of thewas axial no peak strain stress was intaken the ascurve; the shearthe deviatoric strength stress at its peakat 15% state, of the and axia thereforel strain was taken smaller as thanthe shear the shear strength strength at its at peak the state,end state. and Withtherefore increasing was smaller confining than pressure, the shear the stre coralngth sand at transitionedthe end state. from With dilatancy increasing to contraction confining pressure,during the the shear coral process, sand transitioned and the corresponding from dilatanc deviatoricy to contraction stress–axial during strain the curve shear changed process, fromand the correspondingstrain-softening deviatoric type to the stress–ax strain-hardeningial strain type, curve which changed was thefrom main the reason strain-softening for the internal type frictionto the strain-hardeningangle of coral sand type, in the which end stagewas the being main larger reason than for that the in internal the peak friction state;however, angle of coral the cohesion sand in wasthe endsmaller stage than being that larger in the than peak that state. in the peak state; however, the cohesion was smaller than that in the peak state.
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1600 1600 σ3=50 kPa σ3=50 kPa σ σ 3=100 kPa 3=100 kPa End point 1400 1400 Peak point σ3=200 kPa σ3=200 kPa Peak point σ3=400 kPa End point σ3=400 kPa 1200 1200 (kPa) (kPa) q q 1000 1000
Peak point End point 800 Peak point End point 800
600 600 Peak point Deviatoric stress Deviatoric stress stress Deviatoric 400 Peak point 400 End point End point 200 Peak point 200 Peak point End point End point 0 0 0 5 10 15 20 0 5 10 15 20 Axial strain ε (%) Axial strain ε (%) a a (a) (b) 1600 1600 σ3=50 kPa σ3=50 kPa σ 3=100 kPa σ3=100 kPa 1400 σ 1400 σ 3=200 kPa 3=200 kPa Peak point σ Peak point End point End point 3=400 kPa σ3=400 kPa 1200 1200 (kPa) (kPa)
q 1000
q 1000
800 Peak point 800 Peak point End point End point 600 600 Peak point Peak point Deviatoric stressDeviatoric
400 Deviatoric stress End point 400 End point Peak point Peak point 200 200 End point End point
0 0 05101520 ε 0 5 10 15 20 Axial strain a (%) Axial strain ε (%) a (c) (d)
Figure 6.6.Deviatoric Deviatoric stress-axial stress-axial strain strain curves curves of coral of gravellycoral gravelly sand under sand diunderfferent different confining confining pressures andpressures water and contents: water (contents:a) ω = 6%, (a ()b ω) ω= 6%,= 12%, (b) (ωc) =ω 12%,= 18%, (c) ω (d =) ω18%,= 24%. (d) ω = 24%.
(2) In the peak state, as the ω increased,increased, thethe valuevalue ofof thethe internalinternal frictionfriction angle of coral gravelly sand ranged from 37.337.3°◦ to 39.439.4°,◦, and the cohesion was between 45.9 and 70.4 kPa; the didifferencefference between the maximum value and the minimum value of the internal frictionfriction angle was only 5.3% of the maximummaximum value,value, andand the the di differencefference between between the the maximum maximum and and minimum minimum cohesion cohesion accounted accounted for 34.8%for 34.8% of the of maximumthe maximum value. value. Similarly, Similarly, in the in end the state, end asstate, the ωasincreased, the ω increased, the values the ofvalues the internal of the frictioninternal anglefriction and angle cohesion and ofcohesion coral gravelly of coral sand gravelly were 38.5–40.4sand were◦ and 38.5–40.4° 27.3–38.1 and kPa, 27.3–38.1 respectively; kPa, therespectively; difference the between difference the maximum between valuethe maximu and them minimum value and value the ofminimum the internal value friction of the angle internal was onlyfriction 4.7% angle of the was maximum only 4.7% value, of the while maximum the di ffvalue,erence while between the di thefference maximum between andminimum the maximum cohesion and valuesminimum accounted cohesion for values 28.3% accounted of the maximum for 28.3% value. of the It can maximum be seen thatvalue. the It impactcan be ofseenω onthat the the cohesion impact of coralω on gravellythe cohesion sand of was coral greater gravelly than sand the internal was greate frictionr than angle. the Classicalinternal friction soil mechanics angle. Classical believes thatsoil sand-likemechanics non-cohesive believes that soilsand-like does not non-cohesive have cohesion, soil does but when not have there cohesion, is water inbut the when sand, there the is internal water poresin the willsand, shrink the internal due to the pores negative will shrink pressure due of capillaryto the negative water, whichpressure creates of capillary cohesion water, for the which sand. Butcreates this cohesion cohesion for gradually the sand. disappears But this cohesion with the gradualgradually increase disappears of ω as with the the capillary gradual water increase gradually of ω turnsas the intocapillary free water, water so gradually it is also calledturns into “fake free cohesion” water, so or it “apparent is also called cohesion”. “fake cohesion” The change or of“apparent the ω in thecohesion”. sand has The a significant change of etheffect ωon in thethe contentsand has and a significant distribution effect of capillary on the content water in and the distribution sand, so the ofω hascapillary a greater water influence in the sand, on the so apparentthe ω has cohesiona greater ofinfluence coral gravelly on the appa sandrent in the cohesion triaxial of shear coral test. gravelly sand(3) in Inthe the triaxial peak shear state andtest. the end state, the internal friction angle of coral gravelly sand increased slightly with increasing ω ( 1 ) and then decreased, reaching its peak at ω = 12%, while the cohesion (3) In the peak state and≤ the◦ end state, the internal friction angle of coral gravelly sand increased continuesslightly with to increaseincreasing with ω (≤ increasing1°) and thenω. decreased, To explain reaching this test its phenomenon, peak at ω = 12%, the authorwhile the carried cohesion out continues to increase with increasing ω. To explain this test phenomenon, the author carried out laboratory compaction tests on coral gravelly sand with different water contents according to the
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 28
(3) In the peak state and the end state, the internal friction angle of coral gravelly sand increased slightly with increasing ω (≤1°) and then decreased, reaching its peak at ω = 12%, while the cohesion continues to increase with increasing ω. To explain this test phenomenon, the author carried out J.laboratory Mar. Sci. Eng. compaction2020, 8, 634 tests on coral gravelly sand with different water contents according 13to ofthe 25 relevant provisions of the Chinese National Standard of Soil Test Method (SL237-2019) [36] and the measured compaction curve is shown in Figure 7. Unlike that of fine-grained soil, the compaction laboratory compaction tests on coral gravelly sand with different water contents according to the curve of coral gravelly sand is a concave parabola, which means, the dry density is the largest in both relevant provisions of the Chinese National Standard of Soil Test Method (SL237-2019) [36] and the the dry state and nearly saturated state; when the ω of coral gravel sand is in the intermediate state, measured compaction curve is shown in Figure7. Unlike that of fine-grained soil, the compaction the dry density under the same compaction is the smallest. The statistical parameter δ is defined as curve of coral gravelly sand is a concave parabola, which means, the dry density is the largest in both the ratio of the dry density of the sample to its maximum dry density at the corresponding ω to the dry state and nearly saturated state; when the ω of coral gravel sand is in the intermediate state, characterize the compactness of the sample under different water contents; its calculation is as the dry density under the same compaction is the smallest. The statistical parameter δ is defined follows: as the ratio of the dry density of the sample to its maximum dry density at the corresponding ω to ρ characterize the compactness of the sampleδ = under d diff ×erent 100% water, contents; its calculation is as follows: ρ (1) dmax,ω ρd δ = 100%, (1) ρdmax,ω × where 𝜌 is the dry density of the sample and ρ is the maximum dry density of the sample dmax,ω wherewhen theρd is water the dry content density is ω of. Although the sample the and relativeρdmax,ω densitythe maximum of coral drygravelly density sand of thewith sample different when water the water content is ω. Although the relative density of coral gravelly sand with3 different water contents contents in this paper was 70% (that is, the dry density 𝜌 was 1.40 g/cm ), the maximum dry density 3 inof thiscoral paper gravelly was sand 70% (thatunder is, different the dry density water contentsρd was 1.40 is different; g/cm ), the therefore, maximum there dry were density differences of coral gravellybetween sandthe δ undervalues di offf coralerent gravelly water contents sand with is di differentfferent; therefore, water contents, there were and dithefferences δ value betweenreached the δmaximumvalues of when coral gravellythe ω was sand 12%. with Therefore, different among water the contents, different and water the δcontentsvalue reached of coral the gravelly maximum sand when(6%, 12%, the ω 18%was and 12%. 24%), Therefore, the highest among compactness the different atwater the same contents relative of coral density gravelly was observed sand (6%, when 12%, 18%the ω and was 24%), 12%, theandhighest the sliding compactness friction and at occlusion the same friction relative between density wasparticles observed were whenmore severe the ω wasand 12%,the internal and the friction sliding frictionangle peaked. and occlusion Overall; friction however, between the ω particles had little were impact more on severe the internal and the internalfriction frictionangle. On angle the peaked.other hand, Overall; it is however,known from the ωthehad ab littleove analysis impact on that the the internal apparent friction cohesion angle. of On coral the othergravelly hand, sand it iswith known different from thewater above contents analysis is thatclosely the related apparent to cohesionthe capillary of coral water gravelly content sand inside. with diThefferent apparent water cohesion contents isof closely the coral related gravelly to the capillarysand with water a relative content density inside. Theof 70% apparent in this cohesion paper ofcontinued the coral to gravelly increase sand as the with ω increased a relative from density 6% of to 70% 24%, in indicating this paper that continued the capillary to increase wateras content the ω increasedin the coral from gravelly 6% to 24%, sand indicating sample thatcontinuously the capillary increased water content with increasing in the coral ω gravelly but did sand not sample reach continuouslysaturation. increased with increasing ω but did not reach saturation.
1.52 Compaction curve ) 3 1.48 (g/cm d ρ δ=92.1% δ=93.3% 1.44
δ=94.0% Dry density δ=95.2% δ=96.6%
1.40
0 6 12 18 24 ω Water content (%) Figure 7. Compaction curve of coral gravelly sand. Figure 7. Compaction curve of coral gravelly sand. 4. Microstructure Analysis 4. Microstructure Analysis The macroscopic mechanical properties of a soil are comprehensively determined by its particle composition,The macroscopic pore structure, mechanical and poreproperties water of distribution. a soil are comprehensively Under constant determined compactness, by theits particle change incomposition,ω of coral gravellypore structure, sand will and changepore water the proportiondistribution. of Under pore waterconstant in dicompfferentactness, occurrence the change states, in which will further affect the mechanical properties of the coral gravelly sand. To explain the results of the above triaxial shear tests from a micro perspective, a series of NMR tests were carried out on coral gravelly sand samples with 70% relative density and water contents of 5.4%, 11.1%, 16.7%, and 21.3%, respectively. Through the analysis of the test results, the pore distribution characteristics of the sample J. Mar. Sci. Eng. 2020, 8, 634 14 of 25 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 16 of 28 cansample be quantitatively can be quantitatively described, described, and the variationand the variation in the pore in water the pore content water in dicontentfferent in occurrence different statesoccurrence with thestates sample with waterthe sample content water can content be determined. can be determined. Figure8 shows the T distribution curves of the coral gravel sand (that is, the transverse relaxation Figure 8 shows the2 T2 distribution curves of the coral gravel sand (that is, the transverse time)relaxation with ditime)fferent with water different contents. water Transverse contents. relaxation Transverse time relaxation in abscissa time is the in timeabscissa required is the for time the attenuationrequired for of the the attenuation transverse magnetization of the transverse by 63%, magnetization and the value by is positively63%, and correlatedthe value withis positively the pore T radius;correlated that with is, the the larger pore radius;2 is, the that larger is, thethe correspondinglarger T2 is, the pore larger radius the corresponding will be. The ordinate pore radius represents will thebe. nuclearThe ordinate magnetic represents signal correspondingthe nuclear magnetic to a diff erentsignal pore corresponding radius, whose to a value different is proportional pore radius, to T thewhose pore value water is content. proportional It can to be the seen pore from water Figure co8 ntent.that the It can2 distribution be seen from curves Figure of coral8 that gravelly the T2 sanddistribution samples curves with di offf erentcoral watergravelly contents sand aresamples all 2–3 with peak different structures, water showing contents a certain are all change 2–3 peak law. Forstructures, the convenience showing ofa certain analysis, change the pores law. corresponding For the convenience to the first, of analysis, second, andthe pores third peakscorresponding in the T2 distributionto the first, second, curve are and defined third aspeaks small, in medium,the T2 distribution and large pores,curve respectively.are defined as Each small, peak medium, area reflects and thelarge water pores, content respectively. in pores Each of di ffpeakerent area radius; reflects the totalthe water area of contentT2 distribution in pores curveof different characterizes radius; the total amountarea of T of2 distribution pore water withincurve characterizes samples; and the the total proportion amount of of each pore peak water area within relative samples; to the total and T areathe proportion of 2 distribution of each curvepeak area reflects relative the ratioto the of total the waterarea of content T2 distribution in pores curve of diff reflectserent radius the ratio to the of totalthe water water content content in in pores sample. of different radius to the total water content in sample.
Figure 8. T2 distributiondistribution curves curves of coral gravelly sand with different different water contents.
In thethe classicalclassical soil mechanics,mechanics, according to thethe compactness of pore water and soil particles, pore waterwater cancan be be divided divided into into three three types: types: bound boun water,d water, capillary capillary water, water, and freeand water. free water. Bound Bound water, alsowater, known also asknown adsorbed as adsorbed water or irreduciblewater or irreduci water,ble refers water, to the refers pore to water the thatpore is water mechanically that is adsorbedmechanically between adsorbed the soilbetween particles, the soil exists particles, in the ex formists in of the neutral form waterof neutral molecules, water molecules, and does and not participatedoes not participate in the formation in the formation of the crystal of lattice.the crystal Capillary lattice. water Capillary refers water to the refers pore water to the stored pore inwater the capillarystored in poresthe capillary under the pores action under of capillary the action suction of capillary when suction the water when content the water exceeding content the molecularexceeding waterthe molecular holding capacitywater holding of the soilcapacity particles, of the which soil particles, is not subject which to gravity.is not subject Free water to gravity. refers toFree the water pore waterrefers thatto the is pore free amongwater that soil is particles. free among The soil water particles. content The of the water sample content is the of sumthe sample of the poreis the water sum contentsof the pore of the water three contents different of forms. the three The bounddifferen water,t forms. capillary The bound water water, and free capillary water are water distributed and free in small,water mediumare distributed and large in pores. small, Thus, medium pore waterand large content pores. in di Thus,fferent pore occurrence water formscontent can in be different decided usingoccurrence Equation forms (2). can be decided using Equation (2). Si ωi0 = S ω (2) = Si ω (2) S
where i = 1,2,3, corresponds to the three peak of T2 distribution curve; ω is the water content of sample; Si is the peak area of the ith number; S is the summary of each peak area of T2 distribution curve; refers to the pore water content in different pore radius corresponding to the the ith peak. From J. Mar. Sci. Eng. 2020, 8, 634 15 of 25
where i = 1, 2, 3, corresponds to the three peak of T2 distribution curve; ω is the water content of sample; Si is the peak area of the ith number; S is the summary of each peak area of T2 distribution curve; ωi0 refers to the pore water content in different pore radius corresponding to the the ith peak. From previous analysis, ω10 , ω20 , and ω30 are the amount of bound water, capillary water, and free water, respectively. The pore water content in three different occurrence states of coral gravelly sand with different water contents was obtained, as shown in Figure9. Figures8 and9 show that (1) the pore water contents of the three different occurrence forms in the same sample were different, among which the capillary water content was the highest, followed by bound water and free water. When the sample water content ( 5.4%) was low, pore water mainly occurred in the micropores and mesopores among ≤ the particles in the form of bound water and capillary water, respectively, and the free water content was 0 (see Figure 10a). When the ω of the sample was increased from 5.4% to 11.1%, the free water content increased slightly (see Figure 10b). A small amount of free water intensifies the relative motion between particles, so the internal friction angle increased slightly within 1.2◦. When the ω of the sample was relatively high (>11.1%), the increase in the free water content reduces the sliding friction and occluding friction in the relative motion between particles, so the internal friction angle presents a decreasing trend. When the ω of the sample increased from 11.1% to 21.3%, the free water content in the sample showed a limited increased. Therefore, the internal friction angle of the sample decreased with increasing ω, but the total variation range was less than 3◦. (2) When the ω of the sample increased from 5.4% to 21.3% in turn, the pore water content of three different occurrence forms presented an increasing trend with increasing sample water content. However, there were significant differences in the growth rate: the growth rate of the capillary water content was the highest, followed by those of bound water and free water. (I) When the sample does not reach the saturation state, water prefers to exist in the micropores and mesopores in the form of bound water and capillary water. Only when the bound water and capillary water are almost saturated, the free water content in the macropore increases rapidly with increasing sample water content. On the other hand, the intergranular pores of coral gravel sand are larger than those of other coral sand classifications (see Figure 10). Therefore, it is difficult for free water to be preserved in the sample under the action of gravity; the sample has a poor water-holding capacity, which is one of the main reasons for the lowest free water content and growth rate. (II) Bound water is water adsorbed on the surface of coral sand particles under the action of an electric field (see Figure 10). Because coral sands with different water contents have the same compactness, there is little difference in the skeleton structure for adsorption by the bound water. With the increasing ω, the bound water content increased slightly, but the overall change was not great. It was observed that the bound water has little influence on the shear characteristics of coral gravel sand with different water contents. (III) Part of the pore water existed in the form of capillary water under the action of capillary suction. With the increasing ω in the sample, the capillarity water content increased successively, which also indicates that when the ω of the coral gravel sand increased from 5.4% to 21.3%, the capillarity water content does not reach its saturation, and thus does not begin to change from capillarity water to free water. The apparent cohesion is derived from the capillary suction inside the sample and thus also increases with increasing sample water content. J. Mar. Sci. Eng. 2020, 8, 634 16 of 25 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 18 of 28
Bound water 20 19.07 Capillary water
16 14.96
12 9.40 8 4.21 4 2.13 1.19 1.62 1.65 0 0.00 free water
0.04 Mass ratio of pore water to dry soil (%)
0.08 0.08 0.09 0.10 0.12 5.4 11.1 16.7 21.3 Water content ω (%)
Mass ratio of pore water to dry soil (%) FigureFigure 9. Variation 9. Variation in thein the mass mass ratio ratio of of pore pore waterwater in di differentfferent occurrence occurrence forms forms to dry to drysoil soilmass mass with with the watertheJ. Mar. water content Sci. Eng.content 2020 of the , of8, xthe sample.FOR sample. PEER REVIEW 19 of 28
Figure 10.FigureSchematic 10. Schematic diagram diagram of poreof pore water water inin didifferefferentnt occurrence occurrence forms forms under underdifferentdi waterfferent water
contents: (contents:a) ω = 5.4%, (a) ω = ( 5.4%,b) ω (=b)11.1%, ω = 11.1%, (c )(cω) ω= =16.7%, 16.7%, (d (d) ω) ω= 21.3%.= 21.3%.
5. Analysis of Particle Breakage
5.1. Relation between Particle Breakage and Water Content To reveal the variation in the particle breakage of coral gravelly sand with ω during triaxial shearing, a series of triaxial shear tests was initially carried out on coral gravelly sand with different water contents under different confining pressures, and the particle gradation was measured before and after the test. Then, the median particle diameter (d50) and the relative breakage index (Br) proposed by Hardin [40] were used to evaluate the particle breakage of coral gravelly sand under different test conditions. It is worth noting that although several sets of triaxial shear tests were carried out on coral gravelly sand under the control ω and confining pressure conditions, as this paper aims to study the effect of ω on the particle breakage of coral gravelly sand, based on the statistical analysis of the triaxial shear test data under different water contents and confining pressure, the box plots were used to present the variation in the particle breakage of coral gravelly sand with changing ω (see Figure 11).
J. Mar. Sci. Eng. 2020, 8, 634 17 of 25
5. Analysis of Particle Breakage
5.1. Relation between Particle Breakage and Water Content To reveal the variation in the particle breakage of coral gravelly sand with ω during triaxial shearing, a series of triaxial shear tests was initially carried out on coral gravelly sand with different water contents under different confining pressures, and the particle gradation was measured before and after the test. Then, the median particle diameter (d50) and the relative breakage index (Br) proposed by Hardin [40] were used to evaluate the particle breakage of coral gravelly sand under different test conditions. It is worth noting that although several sets of triaxial shear tests were carried out on coral gravelly sand under the control ω and confining pressure conditions, as this paper aims to study the effect of ω on the particle breakage of coral gravelly sand, based on the statistical analysis of the triaxial shear test data under different water contents and confining pressure, the box plots were used to present the variation in the particle breakage of coral gravelly sand with changing ω (see Figure 11). The box plots in Figure 11a describe the relationship between the median particle diameter (d50) of coral gravelly sand with different water contents (ω). The mean and median lines in the figure are statistical values of the median particle diameter (d50) of the coral gravelly sand samples with the same ω after the triaxial shear test under four different confining pressures. Figure 11a shows that the mean and median particle diameter (d50) of the coral gravelly sand sample decreased with increasing ω, which means that under the same stress condition, the sample with a high ω will produce more fine particles after the triaxial shear test, and the amount of particle breakage will be greater, which is consistent with the test results in Figure 11b. Figure 11b depicts the change in the relative breakage index (Br) of coral gravelly sand with different water contents (ω). It can be seen from Figure 11b that with the increasing ω, the relative breakage index (Br) of coral gravelly sand and the amount of particle breakage gradually increased due to the lubricating role of water during the relative movement of the particles. The larger the ω, the more likely the coral sand particles are to roll and move relative to each other, and the increased breakage and grinding during the relative motion increase the particle breakage. It can also be seen in Figure 11 that the median particle diameter (d50) and relative breakage index (Br) show opposite variation trends with increasing ω. To explore the relationship between the median particle diameter (d50) and the relative breakage index (Br) of coral gravelly sand, the median particle diameter (d50) and relative particle breakage index (Br) of coral gravelly sand under different test conditions were statistically analyzed (as shown in Figure 12). It can be seen from Figure 12 that the median particle diameter (d50) decreased almost linearly with increasing relative breakage index, (Br) except for individual discrete points, and there was a significant negative correlation between the median particle diameter (d50) and relative breakage index (Br). The greater the particle breakage in the sample, the greater the relative breakage index, the higher the fine particle content in the sample, and the smaller the corresponding particle size when the cumulative particle mass content reaches 50%. J. Mar. Sci. Eng. 2020, 8, 634 18 of 25 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 20 of 28
1.5 Median line Average value 1.46
1.42 1.4 1.4 1.38 (mm) 50 d
1.3
1.26 1.24 1.25 1.2
1.1
1.06 1.05 1.05
1.0 1.01 Median particle diameter
0.943 0.9 6121824 ω Water content (%) (a) 10 Median line Average value
9.21
8 (%) Br
6 6.16 6.28
4.68 4.56 4
3.31 3.43
2 2.11 2.19 Relative breakage index
1.33 0.913 0.574 0 6121824 ω Water content (%) (b)
FigureFigure 11. 11. ParticleParticle breakage breakage amount amount versus versus wate waterr content content of of coral coral gravelly gravelly sand: sand: (a ()a )Median Median particle particle diameterdiameter versus versus water water content; content; and and (b (b) )relative relative breakage breakage index index versus versus water water content. content.
The box plots in Figure 11a describe the relationship between the median particle diameter (d50) of coral gravelly sand with different water contents (ω). The mean and median lines in the figure are statistical values of the median particle diameter (d50) of the coral gravelly sand samples with the same ω after the triaxial shear test under four different confining pressures. Figure 11a shows that the mean and median particle diameter (d50) of the coral gravelly sand sample decreased with increasing ω, which means that under the same stress condition, the sample with a high ω will produce more fine particles after the triaxial shear test, and the amount of particle breakage will be
J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 20 of 28 produce more fine particles after the triaxial shear test, and the amount of particle breakage will be greater, which is consistent with the test results in Figure 11b. Figure 11b depicts the change in the relative breakage index (Br) of coral gravelly sand with different water contents (ω). It can be seen from Figure 11b that with the increasing ω, the relative breakage index (Br) of coral gravelly sand and the amount of particle breakage gradually increased due to the lubricating role of water during the relative movement of the particles. The larger the ω, the more likely the coral sand particles are to roll and move relative to each other, and the increased breakage and grinding during the relative motion increase the particle breakage. It can also be seen in Figure 11 that the median particle diameter (d50) and relative breakage index (Br) show opposite variation trends with increasing ω. To explore the relationship between the median particle diameter (d50) and the relative breakage index (Br) of coral gravelly sand, the median particle diameter (d50) and relative particle breakage index (Br) of coral gravelly sand under different test conditions were statistically analyzed (as shown in Figure 12). It can be seen from Figure 12 that the median particle diameter (d50) decreased almost linearly with increasing relative breakage index, (Br) except for individual discrete points, and there was a significant negative correlation between the median particle diameter (d50) and relative breakage index (Br). The greater the particle breakage in the sample, the greater the relative breakage index, the higher the fine particle content in the J.sample, Mar. Sci. and Eng. 2020the ,smaller8, 634 the corresponding particle size when the cumulative particle mass content19 of 25 reaches 50%.
1.5
1.4 (mm) 50 d 1.3 − d50 = 0.06Br+1.48 2 1.2 R = 0.9630
1.1 Discrete points
1.0 Median particle diameter particle diameter Median
0.9 0246810
Relative breakage index Br (%) Figure 12. The relationship between median particle diameter and relative breakage index. Figure 12. The relationship between median particle diameter and relative breakage index. 5.2. Relationship between Particle Breakage and Plastic Work 5.2. Relationship between Particle Breakage and Plastic Work Several related studies [41–50] have shown that particle breakage is an energy dissipation process. Therefore,Several this related paper analyzesstudies the[41–50] variation have in shown the particle that breakageparticle ofbreakage coral gravelly is an sandenergy under dissipation different waterprocess. contents Therefore, from this the paper perspective analyzes of the energy. variatio Plasticn in workthe particle is defined breakage as the of irrecoverable coral gravelly energy sand absorbedunder different by the specimenwater contents during from the entirethe perspect triaxialive test of [42 energy.]; it can bePlastic expressed work usingis defined Equation as the (3) duringirrecoverable the triaxial energy shear absorbed condition: by the specimen during the entire triaxial test [42]; it can be expressed using Equation (3) during the triaxial shear condition: Z Z Z Z Z e e Wp = dWp = qdεd + p’ 0dεv qde εd ’ pe 0dεv (3) Wp = dWp = qdεd + p dεv -− qdεd - − p dεv (3)
e e where Wp is the plastic work, εd is the elastic shear strain, εv is the elastomer strain, and q and p0 are the deviatoric stress and mean effective stress of the specimen during the triaxial shear test, respectively. Since plastic deformation is the main deformation form of coral sand during the triaxial test [51], the energy associated with its elastic deformation is ignored when calculating the plastic work of coral gravelly sand with Equation (3). The results are shown in Table5. From Table5, (1) it is known that the elastic deformation is ignored in the determination of plastic R work. The plastic work is summary of portion originated from deviatoric stress ( qdε ) and the portion R d originated from mean effective stress ( p0dεv). The plastic work is mainly contributed by the portion induced by deviatoric stress q. (2) The plastic work Wp originated from deviatoric stress q is positive because both of quantities are positive. On the other hand, the coral sand samples maybe display dilation and compression behavior during shearing. When the sample compresses (dε is positive), R v the plastic work by mean effective stress ( p dε ) is positive (see Figure 13a). When the sample 0 v R dilates (dε is negative), the plastic work by mean effective stress ( p dε ) is negative (see Figure 13b). v R 0 v The magnitude of the plastic work by mean effective stress ( p0dεv) ultimately depends on the contribution of dilation and contraction degree of samples. Under low confining pressure, the degree of dilation of coral gravel sand is greater than that of contraction; therefore, the plastic work by mean R effective stress ( p0dεv) is negative. On the contrary, the degree of contraction of coral gravel sand is greater than that of dilation under high confining pressure, and the plastic work by mean effective R stress ( p0dεv) is positive. J. Mar. Sci. Eng. 2020, 8, 634 20 of 25
Table 5. Each component of plastic work in triaxial shear test under different test conditions.
Water Content Confining R R Plastic Work 0 Sample qdεd (kPa) p dεv (kPa) ω (%) Pressure σ3 (kPa) (kPa) 50 58.04 4.73 53.30 − 100 96.07 5.40 90.67 6 − 200 153.01 1.17 154.18 400 235.98 11.17 247.16 50 66.19 2.57 63.62 − 100 118.61 3.14 115.47 12 − 200 181.48 2.16 179.31 − Coral gravelly 400 262.74 25.30 288.04 sand 50 77.05 8.57 68.48 − 100 111.07 8.51 102.55 18 − 200 172.32 0.80 173.12 400 261.91 22.81 284.72 50 76.80 9.82 66.97 − 100 116.33 9.83 106.51 24 − 200 173.91 2.02 171.89 − J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 400 278.16 16.38 294.54 23 of 28
(a) (b)
Figure 13.13. Schematic diagram of the directions of mean eeffectiveffective stressstress andand volumetricvolumetric strainstrain underunder didifferentfferent deformationdeformation patterns:patterns: ((aa)) Contraction,Contraction, ((bb)) dilatancy.dilatancy.
Figure 1414 shows the relationship betweenbetween thethe relative breakagebreakage indexindex ((BrBr)) ofof coralcoral gravellygravelly sandsand particlesparticles withwith didifferentfferent waterwater contentscontents andand thethe plasticplastic workwork ((WWpp). It can be seen from FigureFigure 1414 thatthat thethe relativerelative breakagebreakage indexindex ofof coralcoral gravellygravelly sandsand withwith didifferentfferent waterwater contentscontents graduallygradually increasedincreased withwith thethe increasingincreasing plasticplastic work,work, andand thethe powerpower functionfunction in Equation (4) can be usedused toto expressexpress thethe increasingincreasing trendtrend ofof relativerelative breakagebreakage indexindex withwith thethe increasedincreased plasticplastic work.work. Lee andand CoopCoop [[52]52] andand Chen et al.al. [[53]53] studiedstudied thethe relationshiprelationship betweenbetween thethe relativerelative breakagebreakage indexindex andand plasticplastic workwork ofof terrigenousterrigenous quartzquartz sand and granite soil with diff different water contents, respectively, andand also reached similarsimilar conclusions.conclusions. ααand andβ βin in Equation Equation (4) (4) are are the the coe coefficientsfficients related related to theto the physical physical properties properties of the of samplethe sample (i.e., (i.e., mineral mineral composition, composition, particle particle size, gradation, size, gradation, strength strength and shape, and density,shape, density, water content, water etc.)content, and etc.) stress and condition, stress condition, respectively; respectively;α represents α represents the impact the of impact other factors of other on factors the relative on the breakage relative breakage index of the coral gravelly sand when the plastic work is 1.0 and takes a positive value; β reflects the increasing rate of the relative particle breakage index as the plastic work increases, and also takes a positive value.
J. Mar. Sci. Eng. 2020, 8, 634 21 of 25 index of the coral gravelly sand when the plastic work is 1.0 and takes a positive value; β reflects the increasing rate of the relative particle breakage index as the plastic work increases, and also takes a positive value. β Br = αWp (4) J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 24 of 28
10 ω = 6% 9 ω = 12% ω = 18% ω 8 = 24% (%)
Br 7
6
5
4
3
2 Relative breakage index index breakage Relative
1
0 50 100 150 200 250 300 Plastic work W (kPa) p Figure 14.14.Relationship Relationship between between relative relative breakage breakage index index and plasticand plastic work under work diunderfferent different water contents. water contents. Since the test conditions of the coral gravelly sand samples used in this paper are the same except for the ω, it can be considered that the difference in ω leadsβ to the difference in the relative breakage index–plastic power function curve of the coralB gravellyr = αWp sand with different water contents in Figure(4) 14 . To exploreSince the the test effect conditions of ω on theof the growth coral gravelly trend of sand the relative samples breakage used in this index paper of coralare the gravelly same except sand withfor the increasing ω, it can plasticbe considered work, the that relative the difference breakage inindex–plastic ω leads to the work difference curves in of the coral relative gravelly breakage sand withindex–plastic four different power water function contents curve were of the fitted coral and gravel the equationly sand with and different parameters water are contents shown in in Table Figure6. It14. can To beexplore seen fromthe effect Table of6 ωthat on (1)the αgrowthincreased trend gradually of the relative with breakage increasing indexω as of a verycoralsmall gravelly amount sand ofwith particle increasing breakage plastic occurs work, under the relative the influence breakage of other index–plastic factors (such work as curves hydration) of coral even gravelly when theresand werewith four no external different forces water at contents work on were the coralfitted sand;and the and equation the larger and the parametersω, the larger are shown the amount in Table of particles6. It can be breakage seen from caused Table by 6 factorsthat (1) otherα increased than plastic gradually work. with (2) increasing The β value ω graduallyas a very small decreased amount as theof particleω increased, breakage indicating occurs under that when the influence the plastic of workother isfactors constant, (such the as amount hydration) of particle even when breakage there causedwere no by external the plastic forces work at work decreases on the with coral increasing sand; andω; the and larger the results the ω in, the Figure larger 11 theshow amount that the of amountparticles of breakage particle breakagecaused by increased factors other with than increasing plasticω work., indicating (2) The that β value when gradually the ω of sample decreased is high, as otherthe ω factorsincreased, except indicating for plastic that work when are the the plastic dominant work factors is constant, that cause the theamount particle of particle breakage breakage of coral sand.caused This by isthe in plastic accordance work with decreases the foregoing with increasing conclusions ω; and drawn the from results the in changing Figure law11 show of α withthat the ωamount. (3) The of relationshipparticle breakage between increased the parameters with increasingα and β andω, indicating the ω can bethat expressed when the by ωEquations of sample (5) is andhigh, (6), other and factors there was except a high for correlationplastic work between are the them.dominant factors that cause the particle breakage
of coral sand. This is in accordance with the6 foregoing0.14695ω conclusions2 drawn from the changing law of α = 8 10− e R = 0.9928 (5) α with the ω. (3) The relationship between× the parameters α and β and the ω can be expressed by Equations (5) and (6), and there was a high correlation2 between2 them. β = 2.4087 10− ω + 1.5437 R = 0.9902 (6) − × Table 6. Relative breakage index–plastic work fitting formula and parameters.
Water Content Sample Expressions α β R2 ω (%) –5 1.3898 –5 6 Br = 2 × 10 WP 2 × 10 1.3898 0.9883 Coral gravelly –5 1.2783 –5 12 Br = 5 × 10 WP 5 × 10 1.2783 0.9901 sand –4 1.0910 –4 18 Br = 1 × 10 WP 1 × 10 1.0910 0.9970
J. Mar. Sci. Eng. 2020, 8, 634 22 of 25
Table 6. Relative breakage index–plastic work fitting formula and parameters.
Water Content Sample Expressions α β R2 ω (%) 5 1.3898 5 6 Br= 2 10− W 2 10− 1.3898 0.9883 × P × 5 1.2783 5 12 Br= 5 10− W 5 10− 1.2783 0.9901 × P × Coral gravelly sand 4 1.0910 4 18 Br= 1 10− W 1 10− 1.0910 0.9970 × P × 4 0.9705 4 24 Br= 3 10− W 3 10− 0.9705 0.9428 × P ×
By substituting Equations (5) and (6) into Equation (4), a model for calculating the relative breakage index of coral gravelly sand that can reflect the influence of ω and plastic work and can describe the evolution law of particle breakage. The model is as shown in Equation (7) below:
6 0.14695ω 2.4087 10 2ω+1.5437 Br = 8 10− e W− × − (7) × p The relative breakage index of the coral gravelly sand are calculated by Equation (7) established in this paper and compared with the measured relative breakage index value obtained by the experiment. The applicability of Equation (7) in the calculation of the relative breakage index of coral gravelly sand was evaluated by comparing the calculated and measured values, as shown in Table7. It can be seen from Table7 that the calculated value obtained using Equation (7) is relatively close to the actual value, and the ratio of the calculated value to the measured value is between 0.72 and 1.10, which means that the calculated value obtained by Equation (7) has a high accuracy and will provide a good reference for the prediction of the relative breakage index of coral gravelly sand in actual projects with high practicality. In addition, the particle gradation, shape, density, loading condition, etc. of coral gravelly sand also affect the relative breakage index. Relevant research on the mathematical basis of the equation for calculating the relative breakage index needs to be carried out from the variation in the relative breakage index with various parameters and the correlation of mathematics; this will provide a theoretical basis for establishing an empirical formula that is generally applicable to the evaluation of the relative breakage indices of various types of coral gravelly sand.
Table 7. Comparison between the calculated value and measured value of Br.
Deviation Confining Water Content Calculated Measured (Calculated Sample Pressure ω (%) Value Value Value/Measured σ (kPa) 3 Value) 50 0.50% 0. 57% 0.88 100 1.06% 0. 96% 1.10 6 200 2.23% 2.24% 0.99 400 4.31% 4.68% 0.92 50 0.85% 0.91% 0.94 100 1.81% 2.18% 0.83 12 200 3.14% 3.97% 0.79 400 5.68% 6.16% 0.92 Coral gravelly sand 50 1.23% 1.33% 0.93 100 1.92% 2.18% 0.88 18 200 3.44% 3.92% 0.88 400 5.98% 6.28% 0.95 50 1.58% 2.19% 0.72 100 2.47% 2.69% 0.92 24 200 3.92% 4.14% 0.95 400 6.59% 9.21% 0.72 J. Mar. Sci. Eng. 2020, 8, 634 23 of 25
6. Conclusions The main conclusions of this paper are as follows:
(1) Coral gravelly sand with a relative density of 70% and different water contents undergo contraction during the triaxial shear process under confining pressures of 200 and 400 kPa, and the deviatoric stress at 15% of the axial strain is taken as its peak stress, which is the main reason for the peak friction angle being smaller than the friction angle in the end state. (2) The water content (ω) has less impact on the internal friction angle of coral gravelly sand. As the ω increases, the internal friction angle increases slightly (<1◦) and then decreases with the increasing ω, and (the overall change is within 3◦). The apparent cohesion is more sensitive to changes in the ω, which increases almost linearly with increasing ω. Therefore, when designing and constructing projects involving coral gravelly sand, the impact of rainfall and seawater tides on the project should be considered. (3) When the water content (ω) of the sample is small, the pore water mostly exists in the form of bound water and capillary water, and the free water content is relatively small. As the ω of the sample increases, the capillary water content is the highest and grows the fastest among the three pore water types, followed by bound water and free water. (4) The increase in free water content is the internal cause of the internal friction angle of coral gravelly sand with the water content (ω) greater than 11.1% continuously decreasing with increasing ω. The capillary water content is the main factor impacting the apparent cohesion of coral gravelly sand, and there is a positive correlation between the two.
(5) As the water content (ω) increases, the median particle diameter (d50) gradually decreases, and the relative breakage index (Br) increases with increasing ω. The median particle diameter (d50) is negatively correlated with the relative breakage index (Br) and the linear relationship between the two is obvious except for individual discrete points. (6) There is a power function relationship between the relative breakage index of the coral gravelly sand and the plastic work. Through statistical analysis of the test data, a calculation model was established to allow for reasonable predictions of the relative breakage index of the coral sand based on the water content (ω) and stress process.
Author Contributions: Conceptualization, Y.W. and X.W.; methodology, X.W.; validation, X.W.; formal analysis, X.W. and J.-H.S.; investigation, J.-H.S.; resources, X.W.; data curation, X.W.; writing—original draft preparation, J.C.; writing—review and editing, C.-Q.Z.; visualization, X.-Z.W.; supervision, C.-Q.Z.; project administration, Y.W.; funding acquisition, Y.W. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Consultative Project by Chinese Academy of Engineering(2019-XZ-18), the National Natural Science Foundation of China (Nos. 41877271, 51908153), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA13010301), and Guangzhou City Technology and Science Program (201904010278). Conflicts of Interest: All the authors have read and approved this version of the article, and due care has been taken to ensure the integrity of the work. All the authors have no conflicts of interest to declare.
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