Jun 28, 2015 - railtrack [13]. Although the literature is replete with the study of settlement induced by cyclic loadings [14], few studies have investigated the ...
ARMA 15-647
Numerical Study of Rock Aggregate Materials Under Various Loadings L. Zhu, N. Erarslan, D.J. Williams, M. Serati and M. Ghamgoshar The University of Queensland, Brisbane, QLD, Australia Copyright 2015 ARMA, American Rock Mechanics Association This paper was prepared for presentation at the 49th US Rock Mechanics / Geomechanics Symposium held in San Francisco, CA, USA, 28 June1 July 2015. This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and critical review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 200 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.
ABSTRACT: Cemented and uncemented aggregate materials form the main component of road pavements, and play a key role in pavement behaviour under vehicle-induced cyclic loads. In this paper, the Discrete Element Method (DEM) was used to simulate the response of these aggregate materials under various loading conditions. Initially, aggregates of five different shapes and four different sizes, assembled at a certain volume ratio, were subjected to compression tests under constant confining pressure. The results indicated that: (i) cracks initiate more easily in larger particles and in the angular rocks at sharper corners; (ii) shear cracks occur more frequently than tensile cracks; and (iii) more micro fractures are obtained with increasing the confining pressure. Additionally, four different cyclic loadings were applied to a simulated flexible pavement with a Cement Treated Base (CTB) layer to understand the impact of loading type on pavement behaviour. The results showed that: (i) settlement of the CTB layer increases significantly with increasing the stress amplitude and decreased with increasing vertical loading frequency for sinusoidal vertical loading; and (ii) more settlement occurs in the CTB layer under cyclic moving wheels carrying constant vertical loads than that caused by cyclic moving wheels carrying sinusoidal vertical loads both at the same mean stress.
1. INTRODUCTION The breakage of particles relies on multiple factors; namely, particle size distribution (PSD) [1], particle shape [2, 3], confining pressure [4, 5], and loading conditions [6]. Laboratory observations show that the fracturing of different types of particles depends heavily on their contact with neighbouring particles [7]. This has been visualised by numerical simulations of circular particle assemblies under compression [8] and inter-particle breakage of irregular aggregate assemblies having limited and arbitrary particle sizes [9, 10]. However, to better understand particle breakage caused by particle interactions, further study on various irregular particles having specified sizes and volume ratios should be performed. Field statistics and numerical simulations have indicated that particle breakage can also occur in pavements with an unbounded granular base layer [11, 12] and ballast railtrack [13]. Although the literature is replete with the study of settlement induced by cyclic loadings [14], few studies have investigated the effect of vertical loads carried by moving wheels on the settlement of CTB
reconstructed from real heterogeneous materials. Discrete element method (DEM) , a numerical method, can represent irregular particles and visualize the evolution of micro cracks easily. In this paper, therefore, an attempt is made to employ the DEM to study: (i) the interactions of irregular aggregates assembled at a certain volume ratio under compressive loading with different confining pressures, and (ii) settlements of CTB subjected to cyclic moving wheels exerting either constant vertical or sinusoidal dynamic loading.
2. NUMERICAL ANALYSIS 2.1. Simulation of Angular Particle Assemblies under Different Confining Conditions In the first part of this study, the Particle Flow Code (PFC) [15] was used to simulate the interaction of particles in different loading conditions. In PFC, two material representations are usually adopted: (i) clumps, and (ii) clusters. An angular rock particle represented as a clump cannot be disaggregated, while a cluster model allows it to break under loading. Herein, a cluster was used to represent angular rock, to allow it to break under loading.
The model was generated in a 100 mm by 200 mm box using the radius expansion method [15], with 89 particles having an approximate radius of 10 mm, 268 particles with a radius of about 5 mm, 1,400 particles with a radius of about 2 mm, and 4,481 particles with a radius of about 1.7 mm. The first three of these particle sizes was represented by clusters comprising smaller particles of radii 5 mm, 2.5 mm, 1 mm and 0.25 mm at volume ratios of 4:3:2.5:0.5. The 1.7 mm sized particles were represented as single particles of this size. The clusters were represented by four different particle shapes, as shown in Fig. 1, denoted 25, 24, 26 and 27. In reality the clusters would comprise sub-particles of different size, forming irregular shapes. These are simplified diagrammatically in the right-hand side of Fig. 1 as clusters comprising particles of a single size. The prefix “2” means that all particles in the cluster are connected to adjacent particles. The suffix numbers 5, 4, 6, and 7 refer to the total number of particles in the cluster. For the purpose of simulation, the density of all particles was set at 2,500 kg/m3, and gravity was applied in 100,000 steps.
2.2. Simulation of Cemented Rock Aggregates Pavement Layer under Different Moving Loadings To represent a real CTB material, a digital picture was taken of CTB and then processed using a purpose-written sub-routine within Matlab to obtain data that was imported into PFC to reconstruct the material’s microstructure in the numerical model using the hexagonal closed packing method (Fig. 2) [15].
Fig. 2. Real specimen image (left) and DEM specimen representation (right)
Fig. 1. Irregular rock aggregate assemblies
For simplicity, a linear contact model was adopted in the simulation, in which the shear interaction is controlled by a frictional law and the contact interface does not resist relative rotation [15]. The ratio of normal bond strength to shear bond strength was assumed to equal to 1.0. The tensile strength of a particle was assumed to follow the relationship [12]:
max (r ) max 1mm (r ) 1
of 5.0×10-4 mm/step. Then, the materials in the box were compressed under stresses of 1 MPa, 2 MPa, 3 MPa, 4 MPa and 5 MPa, as would typically be applied experimentally. This was achieved by automatically controlling the velocities of the lateral walls through a numerical servo-mechanism sub-routine. The compressions under the applied stresses were performed by moving the top platen down with a final constant speed of 0.5 m/s obtained from sectional acceleration. Although the final loading rate is unreasonably high in the lab tests, it is slow enough for PFC simulation [16]. Cracks were then recorded during the two simulating sections: (i) the process of confining pressure adjustments, and (ii) cracks accumulated during the compression tests.
(1)
with the tensile strength of a particle of maximum radius 1 mm max 1mm assumed equal to 3×107 N. The normal stiffness and shear stiffness of all particles were assumed to be 1×108 N/m. The friction coefficient between particles forming the same cluster was assumed equal to 0.7, and the tightness of the packing factor of the cluster was assumed to be 0.99. The friction coefficient of clusters representing angular rocks was also assumed to be equal to 0.7. Particle compressions were performed by two different confining conditions. Firstly, materials were put into a box with fixed lateral confining walls and a top platen that could move up and down. In this condition, strain-control was adopted and the top platen was moved down at a rate
The heterogeneous composite material was composed of three phases: aggregate, binders and interface between aggregates and binders [17]. Therefore, each phase needed an independent set of material parameters. A linear contact bond model was employed with contact normal bond strength between particles representing cement and rock aggregates 0.8×107 N, with the ratio of contact normal bond strength to contact shear bond strength of 1.0. The contact normal bond strength and contact shear bond strength between particles representing cement was set to 1.0×107 N. The contact normal bond strength and contact shear bond strength for particles representing aggregate was set to 5.0×107 N. All particles in this model were of contact normal stiffness 1.0×108 N/m, shear stiffness of 1.0×108 N/m, radius of 1 mm, density of 2,500 kg/m3; and particle friction coefficient of 0.7 [12]. A field cross-section of pavement base course material is hard to obtain. For simplicity, therefore, the material micro-structure presented in Fig. 2 was assumed to be a field cross-section of CTB material, and moving loads were applied above it to simulate its mechanical performances under moving loads from vehicles. The
width and height of this cross-section were 250 mm and 100 mm, respectively. An undegradable asphalt layer above the CTB layer was represented by 9 rows of clumped particles having a radius of 2 mm and density of 2,500 kg/m3 [12]. A 250 mm by 50 mm layer comprising unbounded particles of radius 2 mm was placed under the CTB layer as a subgrade. In addition, a ball with a radius of 15 mm was assumed to represent a loaded wheel. The loaded wheel was moving forward with a constant translational speed of 100 m/s, spin speed of 0.1 rad/s. For understanding the effect of load amplitude and waveform on settlement, four types of vertical loading were considered: two were constant loadings of 2.0×107 N and 2.5×107 N, and the other two were dynamic loadings of 3.14×107 |sin (2πt)| N and 3.14×107 |sin (4πt)| N. The loaded wheel was generated at the left boundary of the pavement section and was run to the right of the pavement section (Fig. 3). It was deleted when it reached the right boundary of the pavement section, and then a new wheel with the same parameters was again generated at the left boundary of the pavement section [12]. The entire loading scenario was automatically controlled by a subroutine and stopped when 200 passes of the loaded wheel were completed. During the loading phase, the settlement of the CTB was monitored by recording the vertical position of the particle in the centre of the CTB layer.
were more shear cracks than tensile cracks, and (iii) breakage occurred in the larger particles first. The compression tests showed that multiple cracks formed during the process of adjusting the confining pressure due to the particle arrangement and shearinduced failure (Fig.5). In general, more particle breakage occurred with the higher confining pressure. Besides, this trend changed with the continued compression steps as the number of stress-induced cracks decreased with the second loading series. However, increasing number of cracks trend was obtained again with further loading steps. It may show the settlement and plastic damage is obtained more with the first loading application. Then materials gains some strain hardening then softening follows the hardening with further loading. The dominant cracking mechanism for particle breakages in all loading configurations was again shear fracturing.
3.2. Settlements of Cemented Rock Aggregates Pavement Layer under Different Moving Loadings Continued settlement was observed in the CTB layer following both static vertical loading and dynamic vertical loading (Fig. 6). It was observed that: (i) increased vertical load amplitude causes more settlement, (ii) more settlement is induced by constant vertical loading than by sinusoidal loading under the same mean stress, (iii) settlement increases with decrease in the frequency of vertical sinusoidal loading, and (iv) settlement increases with the number of completed passes of a moving wheel. Under all loading scenarios initial sudden settlement was followed by a relatively slow increase in settlement, followed by a deceleration in settlement as failure is approached. Material damage is greatly affected by stress amplitude, frequency and wave type, in agreement with the published results of Janssen on thermoplastics [18].
4. CONCLUSIONS The following conclusions are drawn from this research: Fig. 3. Numerical model for pavement under moving wheel
cracks occur more readily in angular rocks and usually start at the sharper corners;
3. RESULTS AND DISCUSSION
3.1. Particle Breakage in Rock Aggregate Assemblies
tensile cracks initiate first and are followed by shear cracks;
cracks increase with confining pressure and shear failure is the dominant failure type; and
the settlement of CTB layers is greatly affected by the stress amplitude, frequency and wave type of the vertical loading imposed by vehicles.
The following outcomes were observed from the compression tests of the angular rock assemblies under fixed lateral walls (see also Fig. 4): (i) cracks occurred more often in angular rocks and usually started at the sharper corners possibly due to huge induced stress concentration at the sharp corners, (ii) tensile cracks appeared first, followed by shear cracks; however, there
Fig. 4. Crack development within rock aggregate assemblies
Fig. 5. Crack development within rock aggregate assemblies
Fig. 6. Settlements with increasing number of completed passes of a moving wheel
10.
REFERENCES 1.
2. 3.
4. 5.
6.
7.
8.
9.
Hall, E., and B. Gordon. 1964. Triaxial testing with large-scale high pressure equipment. Laboratory Shear Testing of Soils. American Society for Testing and Materials, Philadelphia, Penn. Special Technical Publication STP-361, 315-328. Hardin, B.O. 1985. Crushing of soil particles. Journal of Geotechnical Engineering, 111:10, 1177-1192. Tang, C., H. Liu, W. Zhu, T. Yang, W. Li, L. Song, and P. Lin. 2004. Numerical approach to particle breakage under different loading conditions. Powder Technology. 143, 130-143. Vesic, A.B., and R.D. Barksdale. 1963. on shear strength of sand at very high pressures. Atlanta. Bagherzadeh-Khalkhali, A., A.A. Mirghasemi, and S. Mohammadi. 2008. Micromechanics of breakage in sharp-edge particles using combined DEM and FEM. Particuology. 6:5, 347-361. Erarslan, N., H. Alehossein, and D.J. Williams. 2014. Tensile Fracture Strength of Brisbane Tuff by Static and Cyclic Loading Tests. Rock Mechanics and Rock Engineering. 47:4, 1135-1151. doi: 10.1007/s00603013-0469-5. Aydin, A. 1978. Small faults formed as deformation bands in sandstone. Pure and Applied Geophysics. 116:4-5, 913-930. Lobo-Guerrero, S., L.E. Vallejo and L.F. Vesga. 2006. Visualization of crushing evolution in granular materials under compression using DEM. International Journal of Geomechanics. 6:3,195-200. Kou, S., H. Liu, P.-A. Lindqvist, C. Tang, and X. Xu. 2001. Numerical investigation of particle breakage as applied to mechanical crushing—Part II: Interparticle
11.
12.
13.
14.
15.
16.
17.
18.
breakage. International Journal of Rock Mechanics and Mining Sciences. 38:8, 1163-1172. Liu, H., Kou, S., and Lindqvist, P.-A. 2005. Numerical studies on the inter-particle breakage of a confined particle assembly in rock crushing. Mechanics of Materials. 37:9, 935-954. Zeghal, M. 2009. The Impact of grain crushing on road performance. Geotechnical and Geological Engineering, 27:4, 549-558. Vallejo, L.E., S. Lobo-Guerrero, and K. Hammer. 2006. Degradation of a granular base under a flexible pavement: DEM simulation. International Journal of Geomechanics. 6:6, 435-439. Lobo-Guerrero, S. and L.E. Vallejo. 2006. Discrete element method analysis of railtrack ballast degradation during cyclic loading. Granular Matter.8:3-4,195-204 Gnanendran, C., J. Piratheepan, J. Ramanujam, and A. Arulrajah. 2011. Accelerated laboratory pavement model test on cemented base and clay subgrade. ASTM Geotechnical Testing Journal. 34:4, 297-309. Itasca. 2008. Particle flow code in 2 dimensions (PFC2D) version 4. Minneapolis, MN, USA: Itasca Consulting Group, Inc. Cho, N, C.D. Martin, and D.C.Sego. 2007. A clumped particle model for rock. International Journal of Rock Mechanics and Mining Sciences. 44:7, 997-1010. Kim, H., M.P. Wagoner, and W.G. Buttlar. 2008. Simulation of fracture behavior in asphalt concrete using a heterogeneous cohesive zone discrete element model. Journal of Materials in Civil Engineering. 20:8, 552-563. Janssen, R.P., L.E. Govaert, and H.E. Meijer. 2008. An analytical method to predict fatigue life of thermoplastics in uniaxial loading: sensitivity to wave type, frequency, and stress amplitude. Macromolecules. 41:7, 2531-2540.
