StrengthCharacteristicsofSoil Rock Mixtureunder Equal Stressand Cyclic LoadingConditions
Fan Yongbo1, *, Oyediran Ibrahim Adewuyi 2, 3, Feng Chun 1
1Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
2Key Laboratory of Engineering Geomechanics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, People's Republic of China.
3Department of Geology, Faculty of Science, University of Ibadan, Ibadan, Federal Republic of Nigeria.
*Corresponding Author:Fan Yongbo
Soil rock mixture is a special geological material with non-uniform rock distribution, non-continuouscementation between rock and soil and size effect structural characteristics hence, possessing mechanical propertiesdifferent from rock or soil. Field survey indicated that surface layer of soil rock mixture above rock slope were almost unstable undercyclic loading, at the same time, the slope itself was stable. This phenomenon exceeded initialjudgments, thus it was important to study the mechanics characteristics of SRM under cyclic loading. Numerical simulation using continuum-based discrete element method (CDEM) was employed to study thestrength degradation and failure mechanism of soil rock mixture under different frequency, dynamic stress amplitude and duration.Results show thatthe peak stress gradually increased with the dynamic stress amplitude and frequency increasing, butdecreased with the percentage of rock increasing because the stiffness decreased greatly under cyclic loading. At thesame time, the elasticity modulus decreased gradually with the dynamic stress amplitude and increasing frequency.
Key words：Cyclic loading, Dynamic elasticity modulus, Frequency, Dynamic stress amplitude, CDEM, Strength degradation
The May 12, 2008 Wenchuan earthquake with the highest magnitude , involved fifty thousand landslide collapse and debris flows as a result of its long duration and strong vibration response. The destructive event had a large proportion of thelandslides (Figure 1) being soil rock mixture landslides [2, 3, 4, 5, 6]. As a special geological material, themechanical property of soil rock mixture (non-homogeneous materials) is different from those of either rock or soil. Through model tests undertaken by Zhao et al. , major damage phenomenon of colluvial landslidetriggered by earthquake was observed to be shallow collapse, consistent with the result of Wenchuan earthquake phenomenon, which indicated that the type of colluvial slope failure underearthquake loading was notsubjected to the slip band, but the strength of soil rock mixtureat the surface of the slope. Several research works have been carriedout [8, 9, 10] to study the behavior of rock subjected to dynamic loadingand fatigue (cyclic) loading. Results show thatthe elastic modulus gradually decreased with theincrease of the dynamic stress amplitude; the axial strain at failure increased at the same frequency as the confining pressure increased. Furthermore, other researchers [11, 12] investigated materials such as sand, salt and clay under cyclic loading conditions. With respect to salt, elasticmodulus was observed to decrease slightly during the first few cycles and tends to remain constant until failure. Experiments on sand [13, 14, 15] revealed that the higher thecyclic stress, the smaller the number of stress cycles. Equally of note are studies on the mechanical properties of soil rock mixture under equal stress loading conditions by laboratory andin-situ tests. Fan et al.  conducted the stress boundary loading test of soil rock mixture and obtained that the strength parametersof soil rock mixture was about 20 % lower than the strength parameters under the equal displacement boundary conditions. Also,Ouyang et al.  and Li et al.  undertook the equal stress loading experiment by flexible emulsion and obtained the strength parameters. However,the strength parameters of soil rock mixture under cyclic loadingconditions have not been reported. Thus, obtaining the strength degradation characteristics of soil rock mixture under cyclic loading hastheoretical value and practical significance.
2.1. Numerical ExperimentScheme
2.1.1. Rock percentage and size
In order to reasonably determine the percentage of rock and size for numerical simulation,four hundred and sevencolluvial slopes analyzed  (Table 1) were taken into consideration. The percentage of rock of almost 90 % of theslope was less than 40 % with more than half of theslopes being less than 25 %. Furthermore, Rücknagel et al.  selected10 %, 20 %, 30 % and 40 % as rock percentage. Hence for this work, rock percentage less than 40 % (10 %; 15 %; 20 %;25 %; 30 % and 35 %) was therefore selected for all cases as the percentage of rock in the soil rock mixture samples. With respectto rock size, Xu et al. indicated rock size between 2 cm and 20 cm based on observations of the Xiazari colluvial slopes composition. Furthermore, gravel particle size insoil rockmixtures should not be larger than 1/5 to 1/6 of the compaction mould diameter.Thus, for this experiment 2 cm wasselected as the rock size for the 300 mm diameter soil rock mixture sample.
2.1.2. Experiment scheme
All of the numerical calculations were implemented using the continuum-based discrete element method (CDEM), a numericalmethod which can simulate continuous or discontinuous deformation and asymptotic failure under static or dynamicloading conditions. To obtain the strength parameters degradation degree of soil rock mixture, a series of initial parameters are assumed as follows：cycle time (0.05s, 0.1s and 0.2s), dynamic stressamplitude (100-200kPa, with 20kPa interval) and confining pressure (0.1MPa). The curve ofdynamic stress amplitude versus time is illustrated in Figure 2 while with respect to initial parameters, parameters of rock and soil including density, young modulus, Poisson’s ratio, cohesion and angle ofinternal friction are all listed in Table 2.The numerical model (Figure 3) shows the top and bottom of the model with x and y directionconstraint, with application of the confining pressure around the model and cyclic loading (sine curve) at thetop of the model (green element is soil, red element is rock, blue element is water,red element at the top and bottom of the model is pressure head)
2.1.3 Introduction of CDEM
Continuum-based discrete element method (CDEM) [23, 24, 25], the method, which couples FEM and DEM, does FEM calculation in a single block and does DEM calculation on the interface of two blocks. It can model continuous and discontinuous deformation and kinetic characteristics, as well as the asymptotic process from continuum to dis-continuum while it also includes block and contact model. Block model consists of Linear elastic model, Plastic model, Block cutting model, Drucker-Prager model, Mohr-Coulomb model, Failure model, Creep model, etc. while Contact model consists of Linear elastic model, Brittle fracture model, Strain softening fracture model, and Fracture flow model. CDEM has been widely used in geotechnical engineering, mining engineering, structural engineering, water resources and hydropower engineering and so on.
3.1. Results and Discussion
3.1.1. Characteristic of stress-strain curve
The stress-strain curve (Figure 4) was divided into three stages: initial linear elastic stage (compression between soilparticle), hysteresis loop stage (dislocation between rock and soil, short and decentralized crackappeared) and plastic stage (shear crack incorporated).
3.1.2. Failure type and characteristic
The type of failure observed was similar to those with static loading. So manyshort and decentralized cracks appeared with the cyclic loading increasing. Continuous loadingresulted in theshear crack incorporated and finally generated the single crack, eventually shearfailureappeared.
3.1.3. Strength degradation characteristic influencing factor
The relationship between peak stress, amplitude, cycle and percentage of rock is displayed in theFigure 5. The result of numerical simulation showed that the peak stress gradually increased with the dynamic stress amplitude increasing under the same frequency loadingcondition (Figure 5a). With the same dynamic stress amplitude, it was noted that the peak stress gradually decreasedwith the percentage of rock increasing. Comparing the three graphs (Figure 5a-c), it could also be seen that peak stress graduallyincreased with the same dynamic stress amplitude when frequency increased.Moreover, peak stress gradually increased with the frequency increasing (Figure 5b), which indicated that the soil rock mixture sample would fail under a higher stress. Meanwhile, peak stress gradually decreased with thepercentage of rock increasing under the same frequency, particularly when dynamic stress amplitude was higher. This tendency became more andmore obvious and was not consistent with observations under static loading conditions. Because under cyclic loading conditions, with thepercentage of rock increasing, the contact surfaces between soil and rock increased, sliding failureoccurred easily, then the force decreased, the sample would become loose. Thus, the stiffness decreased accordingly. A comparison of the graphsshowed that the peakstress gradually increased with the same frequency when dynamic stress amplitude increased.Furthermore, peak stress gradually increased with the dynamic stress amplitude increasing under the samepercentage of rock conditions (Figure 5c). At the same time, the higher the frequency, thegreater the peak stress.Under the samefrequency loading conditions, peak stress gradually decreased with the percentage of rock increasing. The graphsshowed clearly that peak stress gradually decreased with the percentage of rock increasing under the same frequency.
3.1.4. Deformation characteristics
The curve of elasticity modulus subjected to the frequency, dynamic stress amplitude and percentage of rock (Figure 6)showed that theelasticity modulus decreased gradually, with the dynamic stress amplitude increasingunder the same frequency, while, the higher the percentage of rock, the bigger the elasticity modulus.In all cases, elasticity modulus gradually decreased withfrequency increasing under the same dynamic stress amplitude loading conditions.
Numerical simulation about soil rock mixture under equal stress and cyclic loading conditions assessed a series of mechanicalcharacteristics of soil rock mixture. The results indicated that peak stress gradually increased with the dynamic stressamplitude and frequency increasing, but decreased with the percentage of rock increasing because the stiffnessdecreased greatly under cyclic loading, as higher loading frequencies imply less time for hysteresis loop energy dissipation, so they produce more damage to tested materials. The obtained results corroborated this trend. At the same time, the elasticity modulus decreased gradually with the dynamicstress amplitude and frequency increasing, with higher loading frequency and dynamicstress amplitudeimplying much more compression unit time.Thus, internal damage would be larger and elasticity modulus would be decreased.
Some elementary knowledge obtained from the numerical experiment about the soil rock mixture showed the complexities involved with the following three aspects deemed necessary. Firstly, the diameter distribution of stone should be considered; secondly, three dimension numerical models would exactly reflect the mechanical characteristics of soil rock mixture; and thirdly,it was necessaryfor comparisonwith experiment data with the same loading conditions.
The work presented in this paper was supported by the National Natural Science Foundation of China (11302229), 973project (2010CB731506) and the National Nature Science Foundation of China (51274185 and 51374196). The authors are thankful for the support. I thank Oyediran Ibrahim Adewuyi for his linguistic assistance during the preparationof this manuscript. Finally, I would like to thank the Editor-in-Chiefand three reviewers for their valuable comments onan earlier draft of this paper.
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Figure 1 the landslide of BeiChuan middle school (Quoted from Huang Runqiu)
Figure 2 the curve of the dynamic stress amplitude versus time (T=0.05s)
Table 1 the characteristics of percentage of rock distributionPercentage of rock（%） / <25 / 25~40 / 40~70 / >70
proportion（%） / 57.3 / 32.9 / 8.1 / 1.6
Table 2 physical and mechanical parameters of rock and soilMaterial name / Density
/kg·m-3 / Young modulus
/Pa / Poisson's ratio / Cohesion
/Pa / Angleof internal friction
rock / 3000 / 1.3e11 / 0.25 / 6e6 / 45
soil / 1580 / 1.5e6 / 0.35 / 1.5e4 / 25
Figure 3 the soil rock mixture sample with equivalent diameter 2 centimeter rock
Figure 4 Stress-strain curve of soil rock mixture under cyclic loading conditions
（a） （b） （c）
Figure5 The relationship between peak stress、amplitude、cycle and rock percentage
Figure 6elasticity modulus curve with amplitude（T=0.1s）