J. Cent. South Univ. (2020) 27: 3436-3449

DOI: https://doi.org/10.1007/s11771-020-4557-x

Mechanical behaviors of interaction between coral sand and structure surface

FENG Ze-kang(冯泽康)¹, XU Wen-jie(徐文杰)¹, MENG Qing-shan(孟庆山)²

1. State Key Laboratory of Hydroscience and Hydraulic Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China;

2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: Based on the interface shear tests, the macro- and meso-mechanical behaviors of interaction between coral sand and different structure surfaces are studied, in which CCD camera is used to capture digital images to analyze the evolution of the interaction band and a particle analysis apparatus is applied to studying the distribution characteristics of particle morphology. This study proposes four-stage evolution process based on the shear stress-strain curve. During the shear process, coral sand particles slide and rotate within the interaction band, causing the changes in shear stress and vertical displacement. In addition, the effects of structure surface roughness on shear strength, volume change and particle breakage are illustrated that the greater the roughness of slabs is, the larger the shear stress is, the more obvious the contraction effect is and the more the particles break. Furthermore, the change in particle’s 3D morphology during the breakage will change not only their size but also other morphological characteristics with convergence and self-organization.

Key words: coral sand; direct shear test; interaction surface; particle morphology

Cite this article as: FENG Ze-kang, XU Wen-jie, MENG Qing-shan. Mechanical behaviors of interaction between coral sand and structure surface [J]. Journal of Central South University, 2020, 27(11): 3436-3449. DOI: https://doi.org/10.1007/s11771-020-4557-x.

1 Introduction

Coral sands, a collection of sand particles originating from bioerosion of limestone skeletal material of marine organisms, are mainly located in tropical and sub-tropical marine environments such as the South China Sea Islands [1-3], the Australian coast [4] and the Mediterranean coast [5]. As a special geotechnical material, coral sands originate from the remnants of marine organisms including remnant skeletal fragments of foraminifera, calcareous algae, mollusks, and crustaceans [6]. Coral sands not only have internal pores and irregular shapes but also are prone to breakage, which induces that the characteristics of coral sand are quite different from the quartz sand. Most of the constructions of marine infrastructure projects, coastal defense facilities and oil exploration are set up on the island reef fillings. The coral sands’ characteristics with low strength and fragile cause a significant number of difficulties and challenges to the construction and maintenance of marine engineering.

In recent years, with the development of marine engineering in various countries, the study of the physical and mechanical behaviors of coral sand has become one of the hotspots in geotechnical engineering. And, a considerable number of experiments have been performed in the laboratory. Regarding triaxial tests, DEHNAVI et al [6] and HASSANLOURAD et al [7] studied the mechanics behaviors of coral sands under different conditions (such as different confining stress and density), and the obtained results indicated that increasing the confining pressure would reduce its dilation angle, while increasing the initial relative density would increase its dilation angle. Using large-scale direct shear tests, WANG et al [2, 3] demonstrated that apparent cohesion of calcareous gravelly soil is significantly higher than that of quartz sand. To analyze the effects of stress drop-creep of coral sand, by using stress drop- relaxation, LADE et al [8] revealed that overcoming structuration by creep as well as stress relaxation, there would produce further plastic straining. ZHANG et al [9] demonstrated that the coral sand sample undergoes a process of dilatancy- contraction with the shear strain increasing based on large shear strain ring shear tests.

Recent research demonstrated that particle breakage could influence the strength and stress-strain behavior of soils [10], which also has a significant effect on the undrained shearing behavior of sands [11-13]. Since the polygonal corners and easily broken characteristic of coral sands, a series of tests have been conducted to study the effects of particle breakage. ARANGO [14] presented that particles begin to break when the yield stress point is reached under 1-D compression test. According to the high pressure one- dimensional creep tests, ZHANG et al [15] concluded that particle breakage results in particle morphology changes. The breakage of coral sand particles mainly causes their internal structure changes leading to rearrangement of particles [16], which is the main factor affecting the mechanical characteristics of coral sands.

Regarding the engineering projects constructed on the coral reef, there are usually some interaction faces between “soft” material (coral sand) and “hard” materials (such as coral reef, pile foundation, concrete foundation). As we all know, “soft-hard” interaction faces are one of the key influences affecting the deformation and failure of engineering constructions [17-20]. Various types of interface shear tests have been performed to study the shearing behaviors of soil-steel interfaces, such as the direct shear interface tests between steel-sand [21-26] or steel-soil [27-30], ring shear interface tests for soil and structure interaction [31, 32] and axisymmetric interface tests [33]; all of these tests were used to study the shear mechanical characteristics between the geo-structure and the quartz sand or soil. Compared with the general direct shear test of sand or soil, it is found that the shear stress, sliding displacement, volumetric strain and residual strength are all affected by the roughness of the structural surface. Similarly, the mechanics characteristic of interaction between coral sand and geo-structures is also worthy of attention and research. Although the above researches on coral sand direct shear or cyclic shear have been attracted considerable attention, the research on the mechanical properties of the contact surface between “soft” coral sand and other “hard” geo-structures with different roughness is still few; However, it is also important for engineering projects.

To study the mechanical behaviors of the interaction between coral sand- and hard structure, a series of direct shear tests of the interface are conducted in this study. Three different roughness structural slabs are selected, which represents three typical relative roughness conditions, to study the influence of the interface’s roughness on the mechanical behavior of contact face. Based on testing results, four stages of the shearing process development between coral sand and structure surface have been proposed. Through establishing the interaction band development mechanism, the macroscopic and mesoscopic physical and mechanical behaviors of the contact surfaces, the deformation characteristics of the interaction band, the particle breakage and the particle morphology changes are systematically studied.

2 Experimental

2.1 Characteristics of sand sample

In the South China Sea, hydraulic reclamation has been an important means for the construction of islands and reefs. As an important platform for oceanic resources exploitation, quantities of coral reefs have been constructed, and calcareous sand on the coral reef can be used as building foundations and backfill material for constructions. The sand samples in this study are obtained from the calcareous soil layer which covers the original reef flat. As illustrated in Figure 1, the coral sand is accompanied by a small number of seashells and dominated by thin-walled mollusk and echinoderm plate fragments and thick-walled foraminifera. Most of the coral sands are in spindle shape, and granular coral sand has the characteristics of high angular angle, porosity (including internal pores) and irregular shape, which results in low strength and fragility.

Figure 2 shows the particle size distribution of the coral sand. It can be seen that the coefficient of uniformity (C_u) is about 11.26, coefficient of curvature (C_c) is about 3.08, average diameter of particle D₅₀ is about 3.47 mm, and the specific density is 2.74 g/m³.

2.2 Test method and procedure

To study the mechanical behaviors of the interface between the coral sand and the structure surface, an interface shear apparatus (Figure 3) is used in this study, which mainly consists of soil container (or lower shear box), structure surface, observation window using plexiglass plate, airbag, loading control system (including vertical and horizontal load), data collection system and sensors (including displacement and load of vertical and horizontal). In the vertical direction, the normal stress is applied by using an airbag, which could control the stress to be stable during the whole shearing process. Furthermore, to ensure uniform loading of the structural slabs, four stress sensors and two diagonal distribution displacement sensors are used to ensure accurate results. In the horizontal direction, one stress sensor and one displacement sensor are used. The principal advantages of this equipment can be characterized as follows: normal constant stress is maintained by the airbag with nitrogen easily; structural slabs can be easily replaced to analyze the effects of different structural surface morphologies. Through the observation window, the fixed camera in front of the window is used to capture images every 0.1 mm of horizontal displacement during the shear tests. The size of interface between slab surface and the sample is 50 cm in length and 36 cm in width. The ranges of vertical and horizontal load system are both from 0 to 200 kN. And the maximum normal and horizontal displacements are 5 and 10 cm, respectively. As for the sensors of loading and displacement, the accuracy of measurement is controlled at 0.1%.

Figure 1 Image of coral sand with different size

The testing processes are performed as follows:

1) Structural face selection. In this study, three different morphology structural surfaces (smooth steel slab, SmS; rough concrete slab, CoS; and sawtooth steel slab, SaS) are used to conduct the interface shear test, as shown in Figure 4. According to the geometric characteristics and distribution law of the surface irregularities of the structure, the surface roughness of the structure can be divided into two types: “random type” and “regular type” [34]. Based on this, for the “regular type”, the SmS is applied to simulating the retaining wall and piles, while the SaS is applied to simulating the diaphragm wall and drilling piles. In the contrast, the CoS, the “random type”, is created random bumps by hand to simulate the grounds of random fluctuations in engineering.

Figure 2 Grain size distribution of studied sands

Figure 3 Schematic diagram of apparatus (1-Track; 2- Horizontal-displacement sensor; 3-Observation window; 4-Soil container; 5-Horizontal load sensor; 6-Structure surface; 7-Vertical-displacement sensor; 8-Airbag; 9- Upper slab; 10-Hydraulic control system; 11-Vertical hydraulic cylinder; 12-Vertical load sensor; 13-Data collection system; 14-Bracket Base; 15-Hydraulic cylinder)

2) Preparation of samples. To eliminate particle size effect, sand samples pass through a sieve (sieve opening 20 cm) to remove gravel particles >20 cm (Figure 2). And then put the sand sample into the lower shear box. To reach the required density, the mold is tapped for layered compaction, and then make each layer interface rough. Sand sample is compacted using a rubber hammer to avoid particle breakage. The moisture content is (20±1)% for all the tests. During the process, a uniform black speckle is placed on the side of the viewing window to capture the migration changes of the marked points. Sand sample is relative loose in the tests due to the blow-fill formed by coral sand is not consolidated and compacted.

Figure 4 Different morphology structural surfaces:

3) Consolidation. After the preparation of samples, the contact surface is driven down to contact with the sand sample through the vertical loading system. Then the nitrogen is slowly filled into the airbag until up to the desired normal pressure and kept constant, which is to ensure that coral sand could fill the groove and make full contact with the contact surface. Consolidation is completed until the vertical displacement sensor no longer changes. After that, the displacement and stress of the acquisition system are set to zero.

4) Shearing. After the desired normal stress is applied, the lower shear box moves horizontally at a constant rate of 2 mm/min, until a total displacement of 30 mm is achieved while the upper structure surface is maintained stationary. Moreover, the sample is photographed through the observation window throughout the shearing process and the particles of the shear band after the shear test are recovered. In the whole process, displacement and stress information are collected by the sensors and transmitted to the computer by the data collection system.

3 Results and analysis

3.1 Roughness analysis of structure surface

In the practices, the morphology of the contact surfaces may greatly depend on engineering problems, such as the interaction between soil and steel [35], and the interaction between the island reef and the blow-fill structure. Different morphologies may influence the mechanical response characteristics of the contact face under external loads, and the roughness is one of the most important factors in the shear process.

In recent researches, different definition methods of roughness were proposed, which used many roughness parameters including the centerline average roughness R_a [36], width, depth and angle of grooves [37, 38]. Considering the roughness of surface and average diameter of sand, UESUGI et al [39] proposed the normalized roughness parameter R_n. Based on the definition, the parameter has been widely used by other researchers [40, 41].

By studying the relative roughness proposed by UESUGI et al [39] firstly, TOVAR-VALENCIA et al [42] modified normalized roughness parameter as follows:

                             (1)

where R_n is relative roughness, a measure of the relative surface roughness with respect to the particle size; R_max,avg is the average of all values of maximum roughness, which is measured within a moving window:

                      (2)

For the moving window size, L_m is equal to D₅₀ in this test. The reason why the new definition method is more reasonable is because of the consideration of moving step size x, the horizontal distance between two consecutive data points. Therefore, the moving window (L_m) is calculated as a variable defined continuously rather than discretely over the travel length. And n is the number of measurements for R_max;i over the entire measurement of travel length. Figure 5 shows the definition of the roughness parameter R_max,i.

Figure 5 Definition of roughness parameter R_max,i

For the same roughness profile, R_n increases for decreasing soil particle size. Increasing value of R_n is associated with enhanced interlocking at the interface, which results in greater interface shear strength. Through scanning structural surface and establishing the surface model, roughnesses of three different slabs are calculated based on the new definition of roughness. The R_n of the SmS (Figure 4(a)), CoS (Figure 4(b)), and SaS (Figure 4(c)) used in this study are 0, 0.17 and 2.67, respectively. Notely, the R_n of SmS is considered to be 0 in this study because there are no obvious grooves and bulges on the surface compared with other two slabs.

3.2 Mechanical behaviors of interaction face with different roughnesses

Based on the test results, the shear stress-shear strain and vertical displacement-shear strain development curves obtained by interface shear tests under different normal stresses between coral sand and different morphological slabs are plotted, as shown in Figure 6.

It can be seen that the development of the stress-strain (τ-ε) curves are similar under the different vertical pressure and different morphology. And the whole process can be divided into four stages:

1) Initial particle adjustment stage

Since only the vertical pressure is applied to consolidate, the contact between the particles and the slab is not dense enough and local stress concentration would occur (such as contact between the convex portion of the contact surface and the sands) during this stage. So, when the shearing process begins, the internal structure of the sample would be adjusted, which causes contact between particles and contact surface more closely. Meanwhile, it could also be seen from the normal displacement curve (body deformation) that it is the compaction stage.

Figure 6 Stress-strain relationship (a) and vertical displacement-strain relationship (b) under different slabs (red: interaction with SmS; blue: interaction with CoS; purple: interaction with SaS; A, B, C, D resent feature points in four stages)

Interacting with different slabs under the same vertical pressure, the trends of both of stress-stain curve and vertical displacement-strain curve are approximately the same. The shear stress increases gradually, and the curve is parabolic, in which the displacement in the vertical direction decreases and contraction occurs. On the other hand, interacting with the same slab under different vertical pressures, the higher the vertical pressure, the larger the shear stress, the faster the increasing rate, the more rapid the vertical displacement, and the more obvious the effect of the contraction.

2) Elastic deformation stage

The stress-strain curves present linear characteristics in this stage, in which the stress increases sharply as the strain increases and the internal structure of particles is adjusted strongly. To resist larger external loads, the particles slide and rotate along the structural surface, causing the shear stress to rise rapidly, which also weakens the effect of the contraction, and even begins to show dilatancy especially under lower vertical pressure.

Interacting with different slabs under the same vertical pressure, the larger the value of R_n, the larger the shear stress, which is more obvious under high vertical pressure. When it is applied with the SaS, the movements of the particles are mainly dominated by the rotation, and the bite cooperation between the particles is the strongest, resulting in a large increase in shear stress (Figure 7(a)). When interacting with CoS, the movements of particles include both sliding and rolling; the sliding friction resistance with the structural surface is lower, and the shear stress is decreased (Figure 7(b)). When it is applied to a SmS, only the sliding between the sand particles and slab is dominant during the shearing process. Compared with the sliding movement, the rolling of particles has to overcome greater resistance. Therefore, at this time, the shear stress is the lowest, and only some of the particles are broken (Figure 7(c)).

3) Initial yield stage

In this stage, the shear stress grows slowly with the shear displacement increasing, in which the internal structure of the sample is finished step by step and some particles begin to break. Under lower vertical pressure, the concentrated stress is not enough to crush the coral sand, and the dilatancy of sands occurs due to the process of the particles continuing to rotate. In the contrary, under higher vertical pressure, the strength of the coral sand itself could not resist the concentrated stress and the fracture begin to occur, in which no dilatancy but the effect of contraction is weakened.

Rotation of particle may have more influence on the dilatancy of the sample than the sliding or motion of the particles. Compared with SaS, the CoS is limited in groove volume though low normal relative roughness. So the dilatancy effect of interaction between coral sand and CoS is the most significant.

4) Plastic yield stage

After the initial yield stage, the shear band (contact band) has been generated. At the same time,due to particle breakage and internal structural adjustment in the contact band, the strength of sands within contact band is low, so that the deformation mainly occurs along the contact band, and the stress and the volume remain stable. Since the fine particles generated after the particle breakage could fill the pores, the particles between the contact band are more compact, so that no strain softening occurs after the peak shear strength.

Figure 7 Sketch map of coral sand movement evolution in shear band:

Interacting with different structure surfaces, the greater the relative roughness, the higher the value of the residual strength, which is approximately equal to the peak shear stress. Meanwhile, in addition to the vertical stress of 100 kPa, the vertical displacement has been constant under other stress conditions. This is mainly because the particles are broken under high normal stress and the structural adjustment between the particle is basically completed. But under low normal stress (100 kPa), the particle breakage is relatively small, and the pores between the particles still allow the particles to continuously adjust and develop.

Overall, at the beginning of the shearing process, the coral sand particles in the shear band rotate and roll, and the structure is continuously adjusted, which induces the dilatancy. With the shearing process progressing to the yield stage, some coral sand particles are broken, and the coral sand in the shear band develops towards a more stable and compact state, so the contraction occurs.

On the other hand, it is also important to consider the different mechanical response characteristics depending on interaction with structural surfaces of different roughness. Figure 8 shows the law of the fitting curves of the shear strength of the interaction face between coral sand and three different contact surfaces. The stress- strain curve satisfies the linear relationship, and corresponding internal friction angles of the smooth steel slab, rough concrete slab and sawtooth steel slab, the internal friction angles of the interactions are 34.7°, 36.6° and 42.2°, respectively. The interaction between the structural surface and the coral sand is mainly caused by the coral sand sliding or rotating along the structural surface. If the roughness of slab is larger, the particles mainly rotate along the contact surface, resulting in the shear stress increasing and the corresponding internal friction angle increasing correspondingly.

Figure 8 Fitting curves of shear strength of interaction face between sand and three different slabs

3.3 Evolution of interaction band

During the test, a CCD camera system (with resolution: 2448×2050; max. fps:15) is used to capture the digital image of the contact band. For every 0.2% increase in strain, pictures are taken with the camera until the shear stops, which ensures enough images of the whole process. After that, digital image correlation (DIC) method is used to obtain the displacement and strain information of the sand in the shearing process, and an opensource code named as NCORR [43] is applied to process digital images.

To analyze the evolution of the interaction band between coral sand and the structure surface during the shearing process, the test of the rough concrete slab-coral sand interaction face under 300 kPa is selected. Figure 9 shows deformation of the interaction at different stages, corresponding the four points (A, B, C, D) in Figure 6(a). First of all, non-uniformity and discontinuity deformation of sands occur within the interaction band, which resulted from not only the non-uniformity of the internal structure of the sand particles, but also the unevenness of the slab, causing the inhomogeneity of stress and deformation within the interaction band.

Furthermore, from Figure 9, it can be seen that the interaction band thickness changed with shear process. At the initial stage (Figure 9(a)), the thickness of the interaction band is about 11.38 mm which is 3.28 times the D₅₀ of the coral sand. Local stress concentrations push the particles to adjust and fill the pores. With internal adjustment of the particle structure near the contact surface, particles are sorted, reorganized and bite densely, the shear stress increases rapidly and the vertical displacement decreases. At elastic stage, the width of the interaction band increases to 18.98 mm which is 5.47 times D₅₀ of the coral sand (Figure 9(b)). The particles begin to move along the structural surface, including sliding and rolling along the surrounding particles and slabs in this stage. The particles of the local area together resist sliding friction and rolling friction, and the shear stress increases rapidly with strain, meanwhile the effect of contraction decreases even begin to dilate under low vertical pressure. While at the initial yield stage, the thickness of the interaction band turns to decrease to about 13.29 mm which is 3.83 times D₅₀ of the coral sand (Figure 9(c)). The adjustment of the particles structural within the interaction band is completed almost, and a part of particles begin to break, causing the fine particles generated by the breakage to continue to fill the pores, meanwhile the volume change tends to be gentle. So, the thickness of the interaction band is gradually reduced. In the end, at the yield stress stage, the width of the interaction band turns to be about 10.63 mm which is 3.06 times D₅₀ of coral sand (Figure 9(d)). After a series of structural adjustments and particle breakage, due to the particle breakage and local deformation, the interaction band is formed and concentrated in a narrow range, in which the volume is substantially constant and the interaction band is small in thickness and tends to be stable.

Figure 9 Displacement increment every horizontal displacement 1 mm in interaction band of digital image:

During the whole shearing process, the thickness of the shear band changes continuously. The shear band is narrower at the initial stage, and then thickens and reaches 5.47 times, which is as the same as the previous research [44]. As the shearing process evolves, the thickness of the shear band becomes narrower at the yield stage, and eventually stabilizes at about 3 times, which is mainly due to the fact that the coral sand begins to break at the yield stage and D₅₀ becomes smaller. At the same time, coral sand breakage causes not only the change of particle gradation, but also the coral sand structure being constantly adjusted, which results in the displacement in the shear band at different period to be discontinuous (Figure 9).

4 Particle meso characteristic analysis

The macroscopic mechanical characteristics of the granular material particles are affected by meso-structure changes. In Part 3, it is obvious that coral sand particles move and rotate in the shear band, and its stress-strain relationship undergoes four stages. The following part will demonstrate the results of coral sand meso changes, including the particle breakage index and morphology evolution.

4.1 Analysis of particle breakage index

Particle breakage affects the mechanical properties of soil and sand, which is an important parameter for studying strength and deformation [45, 46]. In the process of coral sand-structural surface shearing, since the strength of the coral sand itself is insufficient to overcome the shear stress, the sand particles will break, which changes the original morphology, gradation and strength characteristics of the coral sand within the interaction band. To study the particle breakage characteristics of the coast sand, after the shear test, the sand in the interaction band with 1 cm width is sieved. Figure 10 shows grain size distribution of the sand, before and after the tests of the rough concrete slabs-coral sand interaction shear under the vertical stress of 300 kPa.

Figure 10 Alteration of grain size after interface shear test

To analyze the particle breakage characteristics, HARDIN [10] pointed out that when the gradation curve of the soil reaches a steady state, the particles no longer break, and an index of the particle breakage is as provided follows:

                                (3)

where B_r (relative value of breakage) is the quantitative value of particle breakage; B_t (total value of breakage) is the area enclosed between the gradation curves before and after shearing; B_p (potential value of breakage) is enclosed area of the initial particle grading curve and particle size 0.075 mm.

Figure 11 illustrates the relative breakage index (B_r) of particles breakage under different slabs. As for the interaction of the same slab under different vertical pressures, the relative breakage index increases with the vertical stress increasing. The higher the vertical stress is, the stronger the constraint around the particles and self-locking ability between particles are, which will result in an increase of the stress concentration at the convexity position of the particles causing the particles more likely to break. Furthermore, the small particles generated in the particle breakage will fill the pores, which also reflects the above results: the higher the vertical pressure, the more significant the contraction effect. On the other hand, regarding the interaction with different slabs under the same vertical pressure, the larger the R_n, the larger the relative breakage index. Due to the fact that the rougher the contact surface, the more intense the rotation between the particles, as shown in Figure 7, which results in increasing of particle breakage. During the rotation of the particles, the particles in the long axis direction bite and resist each other. When the external load exceeds its strength, breakage will occur.

Figure 11 Evolution of relative breakage index under different slabs

4.2 Evolution of particle morphology

The morphology of the particles has a large effect on the physical and mechanical properties of the particle geometry [47-49]. Particle morphology affects the degree of particle breakage, and particle breakage also affects the development of particle morphology. To study the evolution of the particle’s morphology due to the particle breakage during interface shearing with different slabs, a particle morphology observation system, Microtrac PartAn series [50] is used in this study. It is mainly composed of observation equipment, feeding equipment, lighting equipment, calibration equipment. The feeding device is responsible for vibrating the stacked particles by vibration to make them uniformly pass through the observation area without overlapping. When the particles leave the feeding system, the vibration of the feeding device causes tumbling, so that the particles fall freely under the action of gravity, accompanied by their own tumbling, and finally fall into the lower collecting basin. The illuminator is responsible for the continuous, uniform illumination of the particles on the falling path. The observation camera is responsible for recording the image of the entire particle drop. The falling process of the particles will cause the change of the distance between the observation camera and the particles. To correct the effect of this phenomenon on the observation results, the calibration rod should be placed at the feeding port position before the experiment to calibrate the pixel size on the falling path. After obtaining the particle images, the particle parameters are measured by the number of pixels and some morphology parameters of the particles can be obtained, such as the FEFER particle size, sphericity and so on.

The FERET particle size represents the distance between 0° and 180° of all parallel lines tangent to the projected image of the particle, where FERET length is equal to the diameter of the minimum circumscribed circle and FERET width is equal to the diameter of the maximum inscribed circle (Figure 12(a)).

The coral sand particles are polygonal and irregular in shape, and the aspect ratio (L/W ratio) can reflect the 2D morphological characteristics of the coral sand particles. The larger the aspect ratio is, the more the particles appear as spindles or rods. Aspect ratio is expressed as the ratio of the minimum FERET diameter (F_min) to the maximum FERET diameter (F_max), which can be written as:

                            (4)

Compared with the 2D projection morphology, which is highly random and the result can only represent the topographical features of a sample particle in a certain projection direction, the sphericity refers to the ratio of the equivalent projection perimeter of the particle to the projected image of the particle, which is mainly reflecting the 3D shape of the particles, the relationship among the length, width and thickness of the particles.

Figure 12 Schematic representation of particle size parameter:(A: Equal area circle; B: Particle; C: Equal circumference circle; F_max: maximum of FERET; F_min: minimum of FERET)

In this study, a ratio of the equal area circle diameter (D_a) to equal circumference circle diameter (D_p) is defined as:

                               (5)

Figure 13 shows the histogram distribution of the aspect ratio (L/W). Overall, the aspect ratio of coral sand is mainly distributed between 1.5 and 2.5, indicating that the shape of coral sand particles is irregularity mostly. The aspect ratio before and after shearing changes significantly, in which the aspect ratio less than 1.5 increases continuously after shearing, that is, the length decreases continuously. This result reflects that the change of coral sand mainly occurs in the length direction which means that stress concentration together with wear and tear occurs first in the length direction during motion. Furthermore, the greater the roughness of the contact surface is, the more obvious the aspect ratio changes, which also reflects that the greater the roughness is, the more significant the particle breakages.

Figure 13 Histogram distribution of aspect ratio under vertical stress of 300 kPa

In addition to the change in aspect ratio in 2D, the statistical law of sphericity reflects the variation of the particles in 3D. Figure 14 demonstrates that the sphericity of the particles is closer to 1 after shearing, and corresponding to the SmS, CoS and SaS, the average sphericity values are 0.895, 0.893 and 0.892, respectively. Similarly, the greater the roughness, the greater the sphericity, which can also be explained by particle breakage. The results show that the greater the roughness, the fewer the particles at 0.85, and the more and more at 0.95, which can be inferred from that change in the length direction is the largest, resulting in a smaller sphericity in three dimensions.

Figure 14 Histogram distribution of sphericity under vertical stress of 300 kPa

Overall, the breakage and morphology of particles changes before and after the test, which causes the structural adjustment of the meso structure and the four stages of the stress change in the macroscopic mechanical properties.

5 Conclusions

The mechanical behavior of the interaction between the coral sand and the structural surface is significantly different from that of sand. A comprehensive experimental investigation is conducted to probe the effects of important parameters including vertical pressure, roughness of slabs, particle morphology and particle breakage.

The shearing process of the interface between the coral sand and the structural surface undergoes four stages, namely, initial particle adjustment stage–elastic deformation stage–initial yield stage–plastic yield stage, in which the increasing trend of shear stress with strain changes from parabola to linear, and then to nonlinear growth, finally reached the peak of shear strength and tended to be stable.

Under the lower vertical pressure, the sand sample contracts firstly and then dilatates with shear processing. The contraction is induced by the initial grain adjustment, which results in more compact between particles and decreasing of the sample volume. And the dilatancy is resulted from the sliding and rolling of particles during the initial yield stage, which results in the increasing of the sample volume. In the contrast, the dilatancy is constrained and suppressed under the higher vertical pressure.

The normalized roughness (R_n) has an important influence on the shear stress and sample volume in the interface shear tests. The greater the R_n, the higher the shear resistance and the greater the friction angle of interface. In addition, particle breakage occurs during shearing process, and the greater the R_n, the more obvious the particle breakage. Meanwhile, particle breakage causes particle morphology changes. With the increasing of the R_n, the aspect ratio of the particles decreases and the sphericity increases, which reflects the convergence and self-organization of particle morphology.

The particles in the contact band mainly slide and roll, which depends on the interaction slab (R_n). Through digital images and DIC analysis, the shear band thickness changes with the evolution of the shearing process. The shear band first becomes thicker, which can reach to 5 times D₅₀ for the elastic period of coral sand-CoS interaction, and then becomes thinner, which is induced by particle breakage. Meanwhile, inside particles motion is discontinuous during different stages of shear process due to the particle breakage.

Contributors

FENG Ze-kang conducted series of tests, wrote the manuscript and analyzed the results. XU Wen-jie designed tests and also provided writing assistant for the manuscript. MENG Qing-shan gave suggestions about the experiment, and edited the manuscript.

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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(Edited by YANG Hua)

中文导读

珊瑚砂与结构面间相互作用的力学响应

摘要：基于接触面剪切试验，本文研究了珊瑚砂与不同结构面间相互作用的宏观和细观力学行为。试验中采用CCD相机捕获数字图像以分析接触带的演化，同时应用粒子分析仪研究试验前后颗粒形态分布特征。基于剪切应力-应变曲线，本研究提出了剪切过程中的四个演化阶段。在剪切过程中，试样剪切应力和垂直位移的变化是由于珊瑚砂在接触带内发生滑动和旋转而产生的；此外，结构表面粗糙度对剪切强度，体积变化及颗粒破碎的影响结果表明，结构面的粗糙度越大，峰值剪应力越高，体积收缩效越明显，颗粒破碎越显著。在破裂过程中，颗粒三维特征不仅发生尺寸变化，同时颗粒形态也表现为均一化和自组织变化。

关键词：珊瑚砂；直剪试验；接触面；颗粒形态

Foundation item: Project(2017YFC0805406) supported by the National Key Research and Development Program of China; Projects (51879142, 51679123) supported by the National Natural Science Foundation of China; Project(2020-KY-04) supported by the Research Fund Program of the State Key Laboratory of Hydroscience and Engineering, China

Received date: 2020-02-12; Accepted date: 2020-07-23

Corresponding author: XU Wen-jie, PhD, Associate Professor; Tel: +86-10-62782301; E-mail: wenjiexu@tsinghua.edu.cn; ORCID: https://orcid.org/0000-0002-5593-7576