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International Journal of Pavement Engineering

ISSN: 1029-8436 (Print) 1477-268X (Online) Journal homepage: http://www.tandfonline.com/loi/gpav20

Macro–meso freeze–thaw damage mechanism ofsoil–rock mixtures with different rock contents

Kai Xing, Zhong Zhou, Hao Yang & Baochen Liu

To cite this article: Kai Xing, Zhong Zhou, Hao Yang & Baochen Liu (2018): Macro–mesofreeze–thaw damage mechanism of soil–rock mixtures with different rock contents, InternationalJournal of Pavement Engineering, DOI: 10.1080/10298436.2018.1435879

To link to this article: https://doi.org/10.1080/10298436.2018.1435879

Published online: 23 Feb 2018.

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InternatIonal Journal of Pavement engIneerIng, 2018https://doi.org/10.1080/10298436.2018.1435879

Macro–meso freeze–thaw damage mechanism of soil–rock mixtures with different rock contents

Kai Xing, Zhong Zhou, Hao Yang and Baochen Liu

Department of Civil engineering, Central South university, Changsha, China

ABSTRACTSoil–rock mixture is a typical discontinuous material and often used as a roadbed filler. Rock content is a key factor in this mixture’s properties. The damage pattern of soil–rock mixtures with different rock contents after freeze–thaw cycles is more complicated than that in normal state. The damage behaviour of soil–rock mixtures with different rock contents after freeze–thaw cycles is analysed in this study. Firstly, size-distributed subgrade coarse grained soil samples with different rock contents (35, 45, 55 and 65%) are prepared. The samples are subjected to freeze–thaw cycles periodically (24 h per cycle) for different times (0 and 10). Large-scale indoor triaxial tests are performed, and elastic modulus and shear strength are determined. Secondly, the macro-properties of the soil–rock mixtures with different rock contents are compared under normal and freeze–thaw states. Finally, indoor triaxial experiments are numerically simulated with Particle Flow Code software. Matched results are obtained, and the meso-mechanism of the soil–rock mixtures with different rock contents is elucidated. At the macroscale, the elastic modulus and shear strength of the soil–rock mixture decrease after the freeze–thaw cycles, and the decrement trends differ with different rock contents. At the mesoscale, the freeze–thaw cycles reduce the strength of soil–rock particles with different properties. The soil–rock mixture with 55% rock content exhibits the most severe damage among all mixtures; this mixture has the most soil–rock particle contacts because of its good compactness and skeleton structure.

1. Introduction

Coarse grained soils are excellent roadbed fillers and can sig-nificantly affect road quality. Actually, it’s a narrow definition of soil–rock mixture. When the rock content is low, the soil–rock mixture can be regarded as Coarse Soil, and when the rock con-tent is high, the soil–rock mixture can be regarded as Fine Gravel. As special engineering and geological materials, soil–rock mix-tures are widely distributed in the natural world and are highly complicated and discontinuous media, and also the interesting research topic (Yang et al. 2014, Zhang et al. 2016, Zhou et al. 2016, 2017, Wang et al. 2017). Resilient modulus is an important parameter in characterising the resilient behaviour of pavement materials (Bao and Abbas 2017). Mixture properties, such as elastic modulus and shear strength, exert significant effects on road operation. But, the physical and mechanical properties of mixtures differ from those of soil or rock. According to the inter-nal structure of a soil–rock mixture, Xu and Hu (2006) defined a soil–rock mixture as an extremely inhomogeneous and loose geotechnical material composed of rocks with high strength at a certain engineering scale, pore spaces and soil particles. In a soil–rock mixture, rocks are distributed in soil particles, and the mixture can be divided into rocky soil (rock < 30%), mixture soil (30% ≤ rock ≤ 70%) and gravel soil (rock > 70%) according to the rock content (You 2008).

As an important physical parameter of a soil–rock mixture, rock content decides the internal structure of the mixture and can directly affect the deformation and mechanical properties of the mixture at the macroscale. Previous research has shown that when the rock content is low (<30%), rocks scatter in the mixture and are surrounded with soil. This condition means that no skeleton is formed, and the soil presents a forced structure. In this case, the properties of the soil–rock mixture depend on soil. When the rock content is high (>70%), a sufficient amount of rocks form a skeleton structure, and soil fills the skeleton space. In this case, the properties of the soil–rock mixture depend on the interlock capacity and friction force of the rock skeleton structure. The actual rock content of most soil–rock mixtures is between 30 and 70%. Soil and rock in different proportions play respective roles and determine the properties of the soil–rock mixture together. The mechanical pattern is highly com-plicated. Dina et al. (2014) investigated the impact of recycling by-product plasterboard waste with an asphalt mixture by partly replacing the filler portion of the asphalt mixture. The results showed that different filler portions exert different effects on mixture properties. Saeid et al. (2014) presented the results of a laboratory study conducted to verify the moisture susceptibility of warm-mix asphalt mixtures containing sandstone aggregates with different contents.

© 2018 Informa uK limited, trading as taylor & francis group

KEYWORDSroadbed filler; soil–rock mixture; different rock contents; freeze–thaw cycle; large-scale triaxial test; contact amongst soil–rock particles; PfC

ARTICLE HISTORYreceived 26 april 2017 accepted 26 January 2018

CONTACT Zhong Zhou 623028341@qq.com, dazhong78@csu.edu.cn

2 K. XING ET AL.

shear dilatation to increase and shear contraction to decrease. Xu and Zhang (2015) conducted triaxial tests on mixtures with different rock contents and analysed the failure patterns of sam-ples through CT scanning.

The soil–rock mixtures are often regarded as roadbed filler. At several areas subjected short-time and repeated freeze–thaw cycles, the influence patterns of this kind of coarse grained soil filler are different from those of simple soil or rock (rock con-tent can decide the effect significantly), furthermore, the effect of short-time and repeated freeze–thaw cycles differ from that of permafrost. So far the damage like this hasn’t been consid-ered when designing the filler. Thus, the research of damage mechanism of soil–rock mixtures with different rock contents is meaningful, and the design can be improved to some extent. The previous research of freeze–thaw cycles mainly focuses on single soil or rock, not a soil–rock mixture. Kong et al. (2014) showed the experimental results to describe the soil freeze–thaw process using piezoceramic-based smart aggregate (SA) transducers. Xu and Hu (2006) completed the coupled analysis of the freeze–thaw damage and thermal stress fields of rocks in the cold region. Liu et al. (2015a, 2015b) concluded the researches of freeze–thaw damage influence of joint rock mass and established the rock damage constitutive model and related assessment criteria.

To sum up, research on the properties of soil–rock mixtures with different rock contents has been widely investigated under the normal state. Well-distributed soil–rock mixtures in most regions of southern China constantly undergo freeze–thaw cycles. Research on the influence of rock content on soil–rock mixtures in freeze–thaw state is few. Large-scale indoor triaxial experiments were conducted in this study, and the influences of different rock contents (35, 45, 55 and 65%) on the properties of soil–rock mixtures in the freeze–thaw state were analysed. The meso-mechanism of the internal influence of rock content was discussed through PFC numerical simulation.

2. Indoor triaxial experiment

2.1. Experiment design

The influence of rock content on soil–rock macro properties was investigated through soil–rock freeze–thaw experiments. The experimental rock contents were set to 35, 45, 55 and 65%. Deformation and shear strength were compared under normal and freeze–thaw states (cycle time: 10). With reference to the graded gravel size standard of passenger railway beds, the sam-ples were composed of sandy clay, gravel and stone crumbles. All rocks are weak weathering and unbroken. The One-way Hierarchical Compaction Method was taken, and for each sam-ple compaction was divided into 5 layers. An optimum moisture content of 6% and a compactness degree of 92% were set accord-ing to previous experimental data. The particle size distribution of the samples and density are shown in Tables 1 and 2.

Xu et al. (2007) established a conceptual meso-model of soil–rock mixtures through a digital picture-processing technique combined with the finite element method. The results of their large-scale direct-shear experiment and numerical simulation proved that rock content exerts a significant influence on the internal stress field of a soil–rock mixture and changes the deformation and failure patterns. Wang and Li (2014) regarded the soil–rock mixture as a composite material consisting of rocks, soil and a rock–soil contact layer and believed that the primary reason for soil–rock mixture failure is the mismatch in the elastic properties of rock and soil. This mismatch leads to the sliding of the rock–soil contact layer. Wang et al. (2015) developed an atomistic simulation framework based on the classical molecular dynamics (MD) method to study moisture-induced damage at the asphalt–aggregate interface. The interface stress–separation curve under tension obtained from MD simulation resembles the failure behaviour measured from pull-off strength at the macroscopic scale. Xu and Hu (2008) believed that the strength of a soil–rock mixture involves two stages. In the first stage, soil enters the plastic state and is destroyed. In the second stage, due to increasing deformation, some rocks are destroyed, whereas some rocks move. Rock movement creates a connection amongst rock particles that were not contact with one another originally. You and Tang (2002) and He (2004) designed large-scale in situ experiments and reported that a change in rock content significantly affects the properties of soil–rock mixtures. Shear strength improves when the rock content is sufficiently high. The failure pattern is also controlled by rock content.

Owing to the development of computer techniques, numeri-cal simulation provides a new and helpful method for rock and soil analysis. You (2001) performed experiments on soil–rock mixtures with different rock contents by using FLAC software and pointed out that shear strength and elastic modulus increase with higher rock content. Particle Flow Code (PFC) is suitable for simulating soil–rock mixtures because of its excellent calculation method for discrete materials. He (2004) conducted a compres-sion–shear experiment by using PFC, and the results showed that the effect of rock content cannot be ignored. Li (2009) sim-ulated soil–rock mixtures with different rock contents through PFC, matched the relationship between shear strength and rock content and analysed the related parameters at the macro–meso scale. Wang (2010) investigated the factors that influence the properties of soil–rock mixtures by combining experimentation and numerical simulation and analysed the effect of rock content on stress–strain curves, strength, deformation and failure prop-erties. Jin et al. (2015) designed large-scale numerical triaxial experiments on soil–rock mixtures by using the discrete element method (DEM) for irregular particles. The researchers analysed the mechanical properties of soil–rock mixtures with different rock contents through computed tomography (CT) scanning. The results showed that an increase in rock content causes peak strength, residual strength, elastic modulus, failure strain and

Table 1. Particle-grading of samples with different rock contents.

Rock

Sieving quality percentage(%)/mm

60 40 20 10 5 2 1 0.5 0.25 0.07535% 100.00 98.25 87.75 75.50 65.00 49.40 35.10 24.70 15.60 7.8045% 100.00 97.75 84.25 68.50 55.00 41.80 29.70 20.90 13.20 6.6055% 100.00 97.25 80.75 61.50 45.00 34.20 24.30 17.10 10.80 5.4065% 100.00 96.75 77.25 54.50 35.00 26.60 18.90 13.30 8.40 4.20

INTERNATIONAL JOURNAL OF PAVEMENT ENGINEERING 3

Based on previous work (Wang et al. 2007, Qi et al. 2008, Yang et al. 2015), it’s found that the damage of freeze–thaw cycle tends to be stable and obvious enough for experimental research after 10 cycles. The samples with different rock contents of 35, 45, 55 and 65% were subjected to 0 and 10 freeze–thaw cycles. Eight groups were studied, and each group included three parallel sam-ples (total sample number of 24). Each freeze–thaw sample was set up in a self-made equipment and underwent freeze–thaw cycles (every freezing period: 12 h, −11 °C; every thawing period: 12 h, 10 °C) (see Figure 1). In freezing process, samples were frozen from three sides and no water supply. The temperature

setting was based on the weather data of Changsha, Hunan in China which is a typical area subjected to frequent freeze–thaw cycles in winter. Undrained shear tests were subsequently con-ducted at different confining pressures (50, 100, 200 and 300 kPa) in a large-scale dynamic–static triaxial apparatus (TAJ-2000). The applied mode on axial direction is strain-controlled (strain ratio: 0.5 mm/min) (see Tables 3 and 4).

2.2. Experiment results

In the indoor triaxial experiments, 96 stress–strain curves of the 24 samples were obtained under different confining pressures of 50, 100, 200 and 300 kPa. For the normal state, the samples marked as 1 (rock content: 35%), 5 (rock content: 45%), 6 (rock content: 55%) and 10 (rock content: 65%) were selected. For the freeze–thaw state (cycle time: 10), the samples marked as 14 (rock content: 35%), 18 (rock content: 45%), 21 (rock content: 55%) and 24 (rock content :65%) were selected. The stress–strain curves of the eight groups are provided in Figure 2.

Table 2. the average density of samples with different rock contents (g/cm3).

Rock content �s - rock

�s - soil

�s - mixture

35% 3.46 2.61 2.8645% 3.45 2.67 2.9755% 3.44 2.65 3.0365% 3.46 2.66 3.13

Figure 1. triaxial test equipment and parallel samples.

Table 3. Parameters of the taJ-2000 dynamic–static triaxial apparatus.

Sample size (mm)Maximum axial load

(kN)Maximum confining

pressure (MPa)Axial deformation velocity (mm/min)

Maximum axial dis-placement (mm)

Volume change meas-uring range (ml)

Φ 300 × 600 2000 5.0 0.01–100 300 10,000

Table 4. Sample design in the freeze–thaw experiments with different rock contents.

Experimental design Parallel sample tab Freeze–thaw cycle time

Group1 (35%) 1 2 3 0group2 (45%) 4 5 6 0group3 (55%) 7 8 9 0group4 (65%) 10 11 12 0group5 (35%) 13 14 15 10group6 (45%) 16 17 18 10group7 (55%) 19 20 21 10group8 (65%) 22 23 24 10

4 K. XING ET AL.

(a) 35% - normal (b) 35% - 10 freeze–thaw cycles

(c) 45% - normal (d) 45% - 10 freeze–thaw cycles

(e) 55% - normal (f) 55% - 10 freeze–thaw cycles

(g) 65% - normal (h) 65% - 10 freeze–thaw cycles

Figure 2. Stress–strain curves of samples with different rock contents.

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bound water in the soil–rock mixtures. When the temperature is low enough, water in the pore is transformed to be ice and its volume expands, causing compression to the particles. Then, these particles move to balance again. When the temperature rise again after freezing for a period, ice melts gradually but the local plastic deformation of some particles can’t be recovered, which forms new pore between particles. A serial of freeze–thaw cycles causes the damage repeatedly in soil–rock mixtures, and the internal structure becomes weaker and weaker. Finally, when the cycles are enough, the internal structure becomes very loose and lots of pores occur, making the elastic modulus decrease. Meanwhile, the closely connected particles disconnect after freeze–thaw cycles, which leads to the loss of shear strength.

The change trend of elastic modulus was analysed. The curves in Figure 3 show that the elastic modulus of the soil–rock mixture samples with rock contents ranging between 30 and 70% increased with gradually increasing rock content and

Experimental data analysis showed that the soil–rock mix-ture in the tests was a strain-softening material. When the con-fining pressure was low, strain softening was obvious. When the confining pressure was sufficiently high, the extent of sof-tening was small. Increased rock content in the samples led to increased static strength (σ1–σ3)f and initial elastic modulus of the mixture. This result means that a complete skeleton is formed in the soil–rock mixture when the rock content is high, and sample failure requires considerable external energy. The elastic modulus of the rock skeleton was stronger than that of soil. For the same sample, increased confining pressure resulted in increased static strength (σ1–σ3)f and elastic modulus E. This result proves that the restraint caused by high confining pres-sure is significant.

The static strength (σ1–σ3)f and elastic modulus E of all sam-ples with different rock contents under different confining pres-sures (50, 100, 200 and 300 kPa) are shown in Tables 5 and 6 according to the stress–strain curves obtained in the triaxial tests. Notably, secant modulus was regarded as elastic modulus when the axial strain approached one-third of the strain at the strength peak.

2.3. Comparison of deformation and shear strength under normal and freeze–thaw states

Soil–rock mixture samples in the normal state were compared with those in the freeze–thaw state (cycle time: 10) through indoor triaxial experiments. The properties of the soil–rock mix-ture, including deformation and shear strength, decreased after the freeze–thaw cycles, and samples with different rock contents had different decrement values.

The freeze–thaw cycle is divided into two phases: freeze and thaw, whose effect is related with water including free water and

Table 5. Static strength of soil–rock mixtures with different rock contents.

Freeze–thaw cycle time Rock content (%)

Static strength (kPa)

Confining pressure 50 kPa

Confining pressure 100 kPa

Confining pressure 200 kPa

Confining pressure 300 kPa

0 35 210 252 341 4510 45 238 280 385 4900 55 254 322 432 5340 65 275 335 451 55410 35 159 200 294 42110 45 166 217 323 45110 55 178 228 331 47310 65 198 247 355 484

Table 6. elastic modulus of soil–rock mixtures with different rock contents.

Freeze–thaw cycle time Rock content (%)

Elastic modulus (MPa)

Confining pressure 50 kPa

Confining pressure 100 kPa

Confining pressure 200 kPa

Confining pressure 300 kPa

Confining pressure 0 kPa

0 35 8.67 10.47 13.78 16.54 6.430 45 9.99 12.08 16.59 20.32 7.200 55 11.34 14.32 18.90 23.57 8.550 65 13.54 16.03 21.41 26.85 9.7510 35 6.07 7.96 11.58 15.22 4.4810 45 7.29 9.97 13.85 18.49 5.0310 55 8.62 11.03 16.07 21.21 6.2110 65 10.16 13.34 17.77 23.90 6.97

Figure 3. Decrement curve of elastic modulus with rock content.

6 K. XING ET AL.

high when the rock content was small. With a gradual increase in rock content, the decrement decreased. However, when rock content was 65%, the value increased compared with that for rock content of 55%. This phenomenon is due to the fact that for samples with a low rock content, the amount of soil particles is large in the mixture. Their elastic properties are more easily affected by external factors, such as freeze–thaw, than those of rocks. For samples with a rock content of 55%, the rock pro-portion was balanced, and soil particles filled the pore space in the skeleton formed by rocks, which in turn made the sample integrality ideal and the decrement small. For samples with a rock content of 65%, their increasing decrement may be attributed to the fact that although the sample skeleton with a rock content of 65% was highly integrated, the amount of soil particles was small, and large pore spaces existed amongst the rock particles which cannot be filled by sufficient soil particles. When loaded and compacted, the large pore spaces disappeared, which caused the modulus to decrease significantly.

The values of shear strength parameters are listed in Table 7. The curve in Figure 4 shows the change of shear strength. In the normal state, cohesive force and friction angle increased with increasing rock content. In the freeze–thaw state, the trend was basically similar, and the only difference was that shear param-eters decreased slightly for 55% rock content and continued to increase for 65% rock content. Freeze–thaw cycles caused shear strength to decrease to a certain degree. For cohesive force, the decrement values were 4.10, 5.16, 8.05 and 6.09%; for fric-tion angle, the decrement values were 19.41, 24.35, 26.99 and 21.64%. After the freeze–thaw cycles, the decrement in cohesive force became minimal, whereas the decrement in friction angle became obvious because the soil–rock mixture samples in this experiment belonged to a material with weak cohesive force and strong friction angle. The decrement in the samples with a rock content of 55%, regardless of cohesive force or friction angle, was the peak value in the experiments.

3. Freeze–thaw macro–meso damage research

The primary reason for the change in the macro-properties of the soil–rock mixture was the change in the internal meso-structure. The effect of rock content on the properties of the soil–rock mix-ture was analysed based on the proportion and distribution of soil and rock at the mesoscale. Figure 5 shows that for samples with low rock contents of 35 and 45%, the amount of soil particles

was basically linear. After the freeze–thaw cycles (time: 10), the moduli of all samples decreased, and the decrement values were 30.33, 30.14, 27.37 and 28.51% corresponding to rock contents of 35, 45, 55 and 65%, respectively. The decrement value was

Table 7. Shear strength of soil–rock mixtures with different rock contents.

Freeze–thaw cycle time

Shear strength parameters 35% 45% 55% 65%

0 C (kPa) 34.44 35.84 37.53 38.41φ(°) 36.12 44.32 50.54 56.29

10 C (kPa) 33.03 33.99 34.52 36.07φ(°) 29.11 33.53 36.90 44.11

(a) Cohesive force

(b) Friction angle

Figure 4. Cohesive force and friction angle curves with rock content.

(a) 35% (b) 45% (c) 55% (d) 65%

Figure 5. Soil–rock mixtures with different rock contents.

INTERNATIONAL JOURNAL OF PAVEMENT ENGINEERING 7

rock contents, which was directly due to the meso-structure. The relationship function between rock content and elastic modulus damage was matched through Matlab in Figure 6:

where CR is the rock content of the mixture and ΔE = (1 – E10/E0) × 100% is the decrement in elastic modulus after freeze–thaw cycles (time: 10).

Elastic modulus is an important parameter in evaluating the deformation property. In the normal state, the elastic modulus of the soil–rock mixture linearly increased with increasing rock content, which proves that rocks play a key role in the value of elastic modulus. After the freeze–thaw cycles, the rock effect was similar, but the decrements differed. When the rock content was below 55%, the less the rock content was, the larger the damage was. When the rock content exceeded 55%, the more the rock content was, the larger the damage was. The damage of elastic modulus was the smallest when the rock content was 55%. Soil elastic properties suffered from much more damage from the freeze–thaw cycles than the rock elastic properties did. On the one hand, the samples with a low rock content exhibited a sig-nificant soil proportion, substantial soil particles and extensive damage. On the other hand, with increasing rock content, the rock skeleton determined the elastic modulus. Thus, high rock content led to considerable damage on the entire rock skeleton. When the rock content was approximately 55%, the sample struc-ture was sufficiently tight because of the rock skeleton and the filling effect of soil particles. The tight and integrated structure could resist the weakening effect of the freeze–thaw cycles. The elastic modulus damage was therefore the smallest.

was large, whereas that of rock particles was small and scattered in the soil part. Soil properties are important to soil–rock mix-tures. For the samples with a moderate rock content value of 55%, the proportions of rock and soil were basically the same, and rock particles formed the primary skeleton where soil particles filled in. The entire structure was very tight. The properties of soil and rock determined the mixture’s properties. For the samples with a high rock content of 65%, the amount of rock particles was large, and some of them were in contact with one another, which led to a highly integrated skeleton structure. The amount of soil particles was small, which caused the fill effects to be severe, and a large amount of pore space was created amongst rocks. Thus, the samples with a rock content of 65% were not as tight as the samples with a rock content of 55%. Rocks mainly determined the mixture’s properties.

The influence of freeze–thaw cycles starts from the meso-struc-ture. There are three types of particle contacts including soil–soil, soil–rock and rock–rock, and bonds only exist between first two types of contacts. The water distributes evenly between particles. When freeze and thaw occur alternately, expanded ice presses particles and the bond structures of some particles are destroyed or weakened. After ice melts, the structures can’t be recovered. The properties of soil and rock are different significantly, so the soil–rock bond contacts are damaged most seriously, which leads to that the surface of soil and rock will be key factor to the destruction. The effects of freeze–thaw cycles to soil–rock mixtures are more serious than ones to soil or rock. In the tests, the control variable method is chosen and make sure that the other factors such as porosity, moisture content and cracks (the stones come from same resource) are same except soil–rock bond contact. And the rock content determines the distribution and numbers of soil–rock contacts.

As shown in Table 8, the indoor triaxial tests revealed that all of the macro-properties of the soil–rock mixture regardless of the rock content decreased to some extent after the freeze–thaw cycles. Nevertheless, the damage condition differed for different

Figure 6. the relationship between rock content and elastic modulus damage.

Table 8.  the data of degradation with different rock contents after freeze–thaw cycles.

Rock content 35% 45% 55% 65%ΔC (%) 4.09 5.16 8.02 6.09Δφ(%) 19.41 24.35 26.99 21.64ΔE (%) 30.33 30.14 27.37 28.51

Figure 7. the relationship between rock content and cohesive force damage.

Figure 8. the relationship between rock content and friction angle damage.

8 K. XING ET AL.

failure patterns of the mixture. For the samples with a low rock content, the contacts amongst soil particles were the major type. For the samples with a high rock content, the contacts amongst rock particles were the major type. The damage for the same type of contacts after the freeze–thaw cycles was small because both types of contacts belonged to the same material. By con-trast, soil–rock contacts with two types belonging to different materials suffered from much damage caused by the freeze–thaw effect. For the samples with a rock content of 55%, the soil–rock contacts were the most extensive because of their tight structure. After the freeze–thaw cycles, the damage of these parts of the meso-structure was obvious, and the decrement in shear strength was significant.

To sum up, the meso-structure of soil–rock contact in the mixture determined macro deformation and shear strength. For the samples with a rock content of 55%, soil–rock contacts were distributed on the average, and contact damage was severe.

4. PFC numerical simulation

As a newly developed DEM software, PFC is widely used in geo-logical numerical simulation. PFC utilises the Newton motion equation as a solving method, replaces elements with particles and simulates large deformation. These advantages make PFC suitable for simulating discrete soil–rock mixtures. Combined with PFC software, numerical indoor triaxial tests were con-ducted in this study (see Figure 9).

The numerical sample size was similar to the size of the indoor triaxial test samples, and the sample is a Φ 300 × 600 mm cyl-inder sample whose particle size was set according to the real distribution curve. Given that computer calculation is limited, the particle size was simplified as follows: particles with radii below 5 mm were regarded as 5 mm particles, and the remaining particles were retained as real distribution. Samples with different rock contents were generated based on the grading distribution curves, and the particle numbers differed (rock content of 35%:

The relationship function between the rock content and shear strength of the soil–rock mixture was matched through Matlab in Figures 7 and 8:

where CR is the rock content of the soil–rock mixture and ΔC = (1 – C10/C0) × 100% and Δφ = (1 – φ10/φ0) × 100% are the decrements in cohesive force and friction angle after freeze–thaw cycles (time: 10), respectively.

In the normal state, the strength of the soil–rock mixture linearly increased with increasing rock content. After the freeze–thaw cycles, shear strength decreased, but the decrement extents differed for samples with different rock contents. When the rock content was below 55%, the less the rock content was, the smaller the damage was. When the rock content exceeded 55%, the more the rock content was, the smaller the damage was. When the rock content was 55%, the damage of shear strength was the largest. Many contacts were observed amongst soil, rock and soil–rock particles. The failure behaviour of the soil–rock mixture always appeared at the soil–rock contact layer because of the mismatch between the elastic properties of soil and rock. At the mesos-cale, the properties of the soil–rock contact layer determined the

(a) 35% (b) 45% (c) 55% (d) 65%

Figure 9. numerical simulation samples with different rock contents.

Table 9. Parameters in the PfC numerical simulation model.

Particle parameters Wall parameters

Contact normal stiffness (kn/Pa)

Contact tangential stiff-

ness (ks/Pa) Friction factor Damping

Load wall nor-mal stiffness

(kn/Pa)

Load wall tangential stiff-

ness (ks/Pa)

Side wall nor-mal stiffness

(kn/Pa)

Side wall tangential stiff-

ness (ks/Pa) Friction factor5e6 1e6 0.5 0.7 1e7 1e6 1e6 1e6 0.5

Figure 10. matched stress–strain comparison of indoor and numerical experiments.

INTERNATIONAL JOURNAL OF PAVEMENT ENGINEERING 9

The internal crack development after experiments were com-pleted is shown in Figure 11. For the samples with a rock content of 35%, the amount of soil particles was substantial, and crack distribution was average for each area. When the rock content increased, the crack distribution showed increased centralisation. Most cracks centred around rock particles, which proves that the soil–rock contact layer is the weakened zone because of the property mismatch on both sides of contact. When the sample was loaded, the soil–rock contact layer slid and led to the failure of the soil–rock mixture. For the samples with a rock content of 55%, the good filling effect resulted in numerous the soil–rock contacts, and cracks mainly appeared. For the samples with a rock content of 65%, rock contacts were numerous, soil–rock contacts decreased and cracks also decreased.

Coordination number, which is defined as the average contact number around a lone particle, is an important parameter in evaluating contact distribution in PFC simulation. In the numer-ical simulation, the data of the coordination number of samples after different freeze–thaw cycles were written. The coordination numbers of samples when the triaxial experiments were com-pleted are listed in Table 10. This data can express the samples’ internal particles’ connections. The value is smaller, the contacts are less, and the connections of the sample are more loosen. So the results showed that after the freeze–thaw cycles, the entire structure of the samples loosened, and the properties of the con-tact layer amongst particles weakened, which in turn led to the failure of connections amongst particles and reduced contact number. The particle contacts of samples with a rock content of 55% decreased the most because contacts between soil and rock particles were the easiest to be damaged.

5. Conclusion

Large-scale indoor triaxial experiments were conducted in this study to investigate the effect of rock content on the properties of soil–rock mixtures in the freeze–thaw state. The changes in the properties of the soil–rock mixtures with different rock contents after freeze–thaw cycles (time: 10) were analysed. The influence of the freeze–thaw cycles on the meso-structure of the soil–rock mixture samples with different rock contents was explored and proven by PFC numerical simulations. The following conclusions were obtained:

(1) The stress–strain curves of the soil–rock mixture were similar under normal and freeze–thaw cycle states.

54,545 particles; rock content of 45%: 43,440 particles; rock content of 55%: 39,311 particles; rock content of 65%: 32,276 particles). By writing the indoor triaxial experiment server and load program code, we simulated confining pressure by setting side walls, and load was simulated by establishing top and bottom walls. Particle contact, especially in the soil–rock contact layer, was simulated with the joint contact bond model in PFC, and the strength of the contacts was quantified as normal and tangential bond strengths. The bond strength was 0 for contacts amongst rock particles. The bond strength of contacts between rock and soil particles was half of that amongst soil particles.

The parameters of the soil–rock mixture material and experi-mental equipment in the numerical simulation test were marked based on existing PFC numerical simulation results (Shao and Chi 2013, Zhu and Hu 2016, Jin et al. 2017) and indoor triaxial experimental data (Table 9).

The stress–strain curves in the numerical simulation were matched by adjusting the values of normal and tangential bond strengths according to each stress–strain curve in the indoor triaxial experiments and based on the parameters listed in Table 9. To provide an example, the stress–strain curves of the samples with a rock content of 35% marked as No. 2 under different confining pressures are shown in Figure 10.

The PFC numerical simulation results basically matched the indoor triaxial test results, which proves the accuracy of the indoor triaxial tests. For the joint contact model, the normal bond strength value was same as the tangential bond strength value. In the numerical simulation samples, the normal and tan-gential strength values of the contact in the joint contact bond model were 174, 221, 382 and 352 Pa in the normal state (cor-responding to rock contents of 35, 45, 55 and 65%, respectively) and 119, 149, 252 and 249 Pa in the freeze–thaw state (corre-sponding to rock contents of 35, 45, 55 and 65%, respectively). The decrements were 31.6, 32.6, 34.0 and 29.3%. At the PFC meso-scale, for samples with a rock content of 55%, the damage on bond strength was severe, which caused the shear strength parameters to weaken significantly.

Figure 11. Internal crack development with different rock contents.

Table 10. Coordination number of numerical samples with different rock contents.

Freeze–thaw cycle time

Rock content

35% 45% 55% 65%0 2.46 2.54 2.71 2.6010 2.13 2.20 2.35 2.30

10 K. XING ET AL.

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When the confining pressure was low, the soil–rock mixture belonged to a strain-softening material, and the phenomenon of strain softening became obvious after entering the plastic state. When the confining pressure was high, the phenomenon of strain softening remained, but it was insignificant. The elastic modulus ranged between those of soil and rock.

(2) For the soil–rock mixture with different rock con-tents subjected to freeze–thaw cycles (time: 10), elastic modulus and shear strength were affected. As a typical discrete material, the soil–rock mixture was a material with weak cohesive force and strong friction angle. The decrement in cohesive force was small, whereas the decrements in friction angle and elastic modulus were large.

(3) The decrements differed for freeze–thaw soil–rock mix-tures with different rock contents. For elastic modulus, the decrement was obvious for the soil–rock mixture with a low rock content and small for mixtures with a high rock content. The decrement was the smallest for the soil–rock mixture with 55% rock content because of the preliminarily formed skeleton structure of rock particles and the good filling effect of soil particles. For shear strength, with gradually increasing rock content, the decrement initially increased then decreased. The decrement was the largest when the rock content was 55% because in such a mixture, the soil–rock layer contacts distribute widely and large contact numbers mean serious damage.

(4) At the mesoscale, the soil–rock mixture was an aggre-gate of rock and soil particles. The contacts amongst soil particles were major for the soil–rock mixture with a low rock content, whereas the contacts amongst rock particles were major for mixtures with a high rock con-tent. The degradation of the macro-properties of the soil–rock mixture was an indication of meso-contact failure amongst particles. The freeze–thaw damage between soil and rock particles was evident because of the mismatch between the elastic properties of the two particle types. Consequently, the influence of freeze–thaw on the soil–rock mixture with different rock con-tents differed.

Disclosure statementNo potential conflict of interest was reported by the authors.

FundingThe work was supported by the National Natural Science Foundation Project of China [grant number 50908234]; the Major State Basic Research Development Program of China [grant number 2011CB710604].

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