Evaluation of the particle breakage of calcareous sand based on the detailed probability of grain survival: An application of repeated low-energy impacts

doi:10.1016/j.soildyn.2020.106497

Soil Dynamics and Earthquake Engineering

Volume 141, February 2021, 106497

https://doi.org/10.1016/j.soildyn.2020.106497 Get rights and content

Highlights

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Various-sized fragments and residual grains under impact load are analyzed.
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Breakage modes under impact load are analyzed in a holistic approach.
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The difference between relative grain breakage and actual amount of grain breakage is found.
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Relationship between detailed probability of grain survival and particle breakage of samples is established.

Abstract

The detailed probability of grain breakage influences the micromechanical behaviours of granular soil under repeated impact loads. This study investigated grain breakage in single-sized and multi-sized calcareous sands under repeated low-energy impact loads. By introducing the dye tracing and particle image segmentation methods in impact tests, various-sized fragments and residual grains were distinguished and further quantitatively analysed. The experimental results showed that the probability of grain survival decreased with the increase in the repeated cycles of impact (total input work); large grains played a more important role in the latter breakage stage as the repeated cycles of impact increased. Compared with the commonly used index B_g, the breakage index B_s based on the detailed probability of grain survival was much closer to the actual amount of grain breakage for single-sized samples and was slightly larger than B_g for multi-sized samples. The detailed probability of grain survival and the indexes could be used for investigating mechanisms of grain breakage under repeated impact loading.

Graphical abstract

Detailed probability of grain survival (S_i) and breakage in multi-sized granular soil and the corresponding three modes of grain breakage under impact load.

Introduction

Grain breakage plays an important role in the mechanical behaviour of granular soil under repeated impact loads and is an emerging topic in geotechnical engineering [[1], [2], [3]]. Abundant evidence shows that grains crush under repeated impact loads, such as vehicle wheel loading [4], explosions [5], underground engineering [6], pile driving and loading tests on piles [7,8]. These grain breakages further influence the behaviour of the structure in granular soils; for example, the grain breakages around piles obviously decrease the lateral friction of piles and result in the piles sinking fast in granular soils [7,9]. Calcareous sand is a typical granular soil that is crushable and widely distributed in tropical marine areas between latitudes N30° and S30°, such as the South China Sea, Red Sea, west continental platform of Australia and Bass Strait [[10], [11], [12]]. Therefore, the investigation of the breakage of calcareous sand under repeated impact loads is necessary for civil, transportation and mining engineering applications in distributed regions [[13], [14], [15], [16]].

To date, many studies have focused on grain breakage under repeated low-energy stress. Understanding the progressive growth of crack-like defects, breakage modes, and the breakage probability of a single grain is fundamental for finding the mechanisms of grain breakage under repeated low-energy impacts [[17], [18], [19]]. In tests on a single particle, the particle is usually compressed diametrically between two polished rigid plates, while the displacement and force on the particle are recorded [[18], [19], [20]]. The results showed that the particle size, initial void ratio, angularity, mineralogy and single particle tensile strength, humidity and loading conditions all affect particle damage [[21], [22], [23]]. In the tests on an assembly of several grains, except for the factors for a single grain, failure models heavily account for the coordination (numbers of contact points) [24]. Contact points and contact force networks inside an assembly have been studied by many authors through the use of phototechniques (such as computed tomography and high-speed microscope cameras) [24,25], which greatly promote research on the link between grain breakage and the macromechanical behaviour of granular soil. However, the numbers of grains in these studies are usually in a countable range, the grain size in these assemblies is limited in a small span, and the grains are usually in a theoretical condition that doesn't have substantial intraparticle voids or internal defects. The detailed probability of grain breakage in the multi-sized assembly of grains with intra-particle voids is not highly researched in laboratory tests.

The different crushing characteristics among grains of different sizes, the interaction between adjacent grains, and the influence of particle progeny make it difficult to grasp the rule of grain breakage in an assembly of grains [2,26,27]. One useful way to grasp the rule of grain breakage is to determine the detailed probability of grain breakage and the survival probability in an assembly of grains [28]. This knowledge is fundamental to understanding the energy dissipation induced by position adjustment and grain breakage, the change in the coordination numbers under impact loads, and the interaction among different-sized grains [14,[28], [29], [30]]. However, until now, the detailed probability of grain breakage used in numerical simulations has been relatively arbitrary and has not been verified by systematic experimental data for a multi-sized assembly of grains [30,31]. Furthermore, in previous experimental studies, most relevant studies on a multi-sized assembly of grains are breakage-result-based studies. The grain breakage effect on soil behaviour is based on the final results of grain breakage. The result between the pressure (P) and void ratio (e) is further used in computing the stress and deformation of the soil when the loads from structures are applied [7,[32], [33], [34]]. However, breakage-result-based studies impede advances in researching the micromechanical behaviours of granular soil under loads from structures [22,35,36]. Therefore, quantitatively discerning detailed fragments and obtaining the detailed probability of grain breakage (or survival) are also useful in understanding the detailed behaviour of grain breakage and the mechanism of soil-structure interaction in granular materials.

This paper explores the grain breakage and survival probability in a series of single-sized and multi-sized calcareous assemblies of grains under repeated low-energy impacts. First, dye tracing and particle image segmentation methods are adopted to quantitatively discern fragments and unbroken grains in each size range. Then, the probability of grain survival in each size range is analysed by excluding the interference effect of the fragments. This is followed by the evaluation of grain breakage of samples by the probability of grain survival. This study provides methods and indexes to reveal the actual grain breakage in granular materials, which facilitates the understanding of the phenomenon and mechanisms of grain breakage under repeated low-energy impacts.

Section snippets

Description of the problem

The grain breakage of sand under loading is usually evaluated by contrasting the grain size distribution (GSD) of particles before and after grain breakage, as shown in Fig. 1a. Based on the shift of the GSD, many commonly used breakage indexes, including B_g proposed by Marsal [36], B_r proposed by Hardin [38], and B_e and B proposed by Einav [39,40], are useful for quantitatively describing the amount of grain breakage for engineering applications [14]. However, due to the coexistence of

Test materials

The calcareous sand used in the study, obtained from the South China Sea, contained more than 94% CaCO₃ by weight. The specific gravity of calcareous sand was approximately 2.78. Two types of natural single-sized calcareous sand, Group A (1–2 mm) and Group B (0.25–0.5 mm), and two types of coloured calcareous sand, Group C (rich in coarse grains) and Group D (rich in fine grains), were tested under repeated low-energy impacts. The physical properties of the different calcareous sand samples are

The probability of grain breakage and survival in each size range

Using the methods described above, the probability of grain breakage and survival in each size range can be obtained. The detailed GSDs of the sand samples under repeated impacts of 800 cycles are shown in Fig. 4 as an example. For the convenience of description, grains that are retained in the initial size range (that do not pass through the initial sieve) are called “residual grains”; grains that pass through the initial sieve are called “fragments”. For example, blue coloured calcareous

Conclusions

A series of repeated low-energy impact tests were carried out to investigate the detailed probability of grain breakage and survival in several groups of single-sized and multi-sized calcareous sand samples. Based on the present study, the following conclusions can be drawn.

(1)
The breakage mode of calcareous sand is increasingly complicated due to the sharp edges and intragranular pores of the grains in single-sized and multi-sized sand samples. However, various-sized fragments and residual grains

CRediT authorship contribution statement

Yu Peng: Data curation, Writing - original draft. Xuanming Ding: Conceptualization, Methodology. Yu Zhang: Validation. Chenglong Wang: Data curation, Validation. Chunyan Wang: Writing - review & editing.

Declaration of competing 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.

Acknowledgements

This work is supported by the National Natural Science Foundation of China with grant numbers 51878103 and 41831282.

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Technical NoteEvaluation of the particle breakage of calcareous sand based on the detailed probability of grain survival: An application of repeated low-energy impacts

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Description of the problem

Test materials

The probability of grain breakage and survival in each size range

Conclusions

CRediT authorship contribution statement

Declaration of competing interest

Acknowledgements

Soil Dynam Earthq Eng

Soil Dynam Earthq Eng

J Terramechanics

Int J Impact Eng

J Rock Mech Geotech Eng

Soil Dynam Earthq Eng

Soil Dynam Earthq Eng

Soil Dynam Earthq Eng

Powder Technol

Powder Technol

Powder Technol

Eng Geol

Soils Found

Soils Found

Eng Geol

Eng Geol

Comput Geotech

Int J Miner Process

Powder Technol

Comput Geotech

J Mech Phys Solid

Int J Miner Process

Powder Technol

Soil Dynam Earthq Eng

Powder Technol

Construct Build Mater

Technical Note
Evaluation of the particle breakage of calcareous sand based on the detailed probability of grain survival: An application of repeated low-energy impacts