The load bearing capacity and deformation response of granular spoils under uniaxial compression are numerically and experimentally investigated, aiming to shed light on the performance of back filled waste spoils while controlling ground subsidence after coal extraction. In numerical study, the particles are assembled in PFC commercial code in light of the digitized real shape of spoils with image technique, which is proved to be consistent with the physical test. The results from numerical and laboratory experiments showed that the complete compressive process of spoils tended to have spatial and temporal characteristics. The load-strain curves of investigated specimens could be divided into three stages (stage I, rearranging stage; stage II, breaking stage; stage III, consolidating stage) and three zones (I, rearranging zone; II, interlocking zone; III, consolidated zone) from outside to inside. During stage I, the load increasing rate of smaller spoils is relatively low, but it increases faster than larger ones in stages II and III. In addition, spoils with Talbot’s gradation are greater than single gradations. The magnitude of the density in consolidated zone is maximum, indicating that it is the main part holding the overlying strata weight.
For underground coal mining, piles of granular spoils with irregular shapes and varied size are produced due to coal extraction, which consists of debris and waste rock materials. Conventionally, spoils are heaped up on ground surface, which not only occupies a certain amount of land, but also causes environmental pollution [
So far, many research efforts have been made to investigate the compaction characteristics of rock spoil. Michalski and Skarzynska [
The existing studies are mainly based on compression tests. The spoils are compacted in steel cylinder during the test. Since the value of elastic modulus of steel cylinder is great, the lateral movement or deformation of aggregated spoils is constrained during compaction. In this situation, the boundary condition applies to the spoils that can be deemed approximately as displacement constraint. Under this boundary condition, the interaction between spoils is strengthened. Accordingly, the breakage and load-carrying properties are overestimated. Unlikely, during the backfilling mining process of goaf, the boundary condition is weak when compared with the above test.
In order to investigate the mechanical properties, crushing and splitting of spoils had different gradation and particle sizes without lateral constraint. In this research, the unconfined compaction tests of spoils were carried out. To this end, PFC numerical modelling and laboratory tests were conducted to investigate the mechanical behaviour and breakage of spoils under unconfined compression. Firstly, the numerical modelling technique and results were present in Section
Here, commercial code, PFC, is used to numerically investigate the uniaxial compressive characteristics of granular spoils under unconfined crushing. PFC is based on the microscopic discrete element theory to simulate the movement and interaction of particles and it is capable of simulating irregular shaped particles for the analysis of rock mechanics problems. The PFC has been extensively used to study a wide range of rock mechanical phenomena [
There are two types of contact in loose spoils: one is in for the fraction effect between spoils as illustrated in Figure
The contact constitutive models of spoils: (a) the compression test model; (b) the unbonded model; (c) the parallel bonded model.
In PFC, the contact constitutive model of unbonded material is as follow:
Such material is normally used to describe particles without bonds, for example, sand, grain, and crushing rock. On the macroscale, the spoils are discrete and unbonded. Therefore, the unbonded material is chosen to define the contact constitutive relation among spoils.
The parallel-bonded model describes the mechanical behaviour of a finite-sized piece of cementation material deposited between two balls, which can transmit both forces and moments among particles. The total force and moment associated with the parallel bond are denoted by
When the bond is formed,
The new force and moment vectors associated with the parallel bond are found by summing the old values existing at the start of the time step with the elastic force and moment increment vectors. The new force vectors are calculated by
According to the Beam Theory, the maximum normal stress
If the maximum tensile stress exceeds the normal strength (
In order to assess the validity of the proposed model parameters, the calibration process should be performed. For purpose of parameters calibrating, random packing particles were generated within a rectangular container. Such sample was used for PFC simulations under a typical experiment condition. Then the parameters of model were modified to match the macroscopic mechanics of the rock, for example, stress-strain curve, the peak stress, and Young’s modulus. After calibration, the parameters can be acquired, as shown in Table
Values of microparameters of granular spoils.
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6.5 | 3.3 | 11 | 1.25 | 10 | 1 |
The shape of spoils is irregular polygon shapes, and interlocking of fragments is the main part bearing axial loading. It is important for simulation to construct model whose shape is consistent with real spoils’. To model the mechanics behaviour of the waste spoils as the backfilling material, pictures of fragments were firstly taken in laboratory (Figure
The modelling processes of spoils.
The walls are often used as boundaries in PFC, for one fragment; if the boundary of model is a smooth curve, many short straight walls should be used to reproduce the profile. During the model construction, stochastic polygons (the number of edges of polygons are 4–8) are used as the simplified outlines of spoils (Figure
After the model construction, spoils were freely settled and then compressed by the wall. The velocity of loading wall was 2 × 10−6 m/step. The complete load-strain curve is shown in Figure
The mechanical properties of spoils: (a) load-strain curve of spoils under unconfined compression; (b–d) the distribution force chains in spoils during different compressing stages.
At the beginning of compaction, stage I, as shown in Figure
With the increasing of load, confining pressure is applied to central spoils by marginal ones. Therefore, the force chains in the centre are apparently stronger than before, and a relative stable interlocking structure is formed.
During loading stage III, the spoils in the centre of sample are highly crushed under the great load, and the porosity decreases as shown in Figure
According to the above description, it can be seen that the compaction mechanic properties vary in different loading stage.
The mechanical properties of spoils are influenced not only by the lithology of parent rock, but also the gradation which can be represented by the bulk density. The concept curve of the ideal gradation that could produce the best mechanical performance was firstly developed by Fuller and Thompson [
In 1923 Talbot and Richart developed the equation for the maximum density line as shown by (
It was further developed and validated for various aggregate types for asphalt mixtures [
Talbot’s grading curve maximum density lines (for various
It is considered that the compactness is better when
In this research, the gangue was taken from the stope of a coal mine in Chongqing, China; its lithology is argillaceous sandstone. In order to acquire granular spoils, the gangue was broken and sifted by sieves into seven continuous size ranges in the laboratory. The particle sizes of single gradations are 5–10 mm, 10–16 mm, 16–20 mm, 20–25 mm, 25–31 mm, 31–40 mm, and 40–50 mm. The above preparing process of testing material is shown in Figure
The preparation of gradual spoils in different size ranges: (a) massive gangue; (b) crushed spoils; (c) spoils in different gradations.
It is known that the crushed spoils without any confining pressure tend to expand horizontally. In order to adapt such movement, spoils were separately put into woven bags according to particle dimensions and sealed at the start of the test. Each bag was a specimen which had single gradation. Based on (
Unconfined compressing experiment of spoils.
(a) Material compaction test machine; (b) data acquisition system; (c) hydraulic pressure system.
Since horizontal expansion commonly took place during compaction, the area of contact face between indenter and specimens was continually changing. So the stress cannot be calculated accurately. In this paper, load-strain curve is used to describe the loadability of spoils hereafter. The complete load-strain curves of specimen with single gradation under unconfined compression are typically shown in Figure
The complete load-strain curves of spoil samples: (a) single gradation; (b) Talbot’s gradation.
It can be seen from Figure
The load-strain curves of three spoil specimens with Talbot’s gradation are shown in Figure
The stress schematics of spoils with single gradation and Talbot’s gradation are shown in Figure
Stress schematics of spoil samples with (a) single gradation and (b) Talbot’s gradation.
It is considered that, for materials with greater density, a larger amount of compaction energy is received to achieve the required density criteria. The accumulation of energy results in a high degree of particle breakage. The effect of increased interlocking leads to force raising. When the inner stress exceed the strength, the loadability generally falls with particle breakage under a given density. In this case, however, it implies that the friction angle for a given density can increase with particle breakage under varying gradations. This is due to the higher levels of densification generated by greater amounts of particle breakage.
The comparison and discussion of numerical and experimental results are presented in this section. According to the numerical modelling and the compaction experiments, it can be found that the loading characteristics of granular spoils under unconfined compression have spatial and temporal characteristics. The detailed description is as follows.
The variety of loadability and breakage in different space and time are mainly caused by the force state evolution of spoils. So the force state can be used to reflect the spatial-temporal mechanical behaviour of spoils. The forces applied on spoils are When When When
The different force states of spoils result in the change of loadability. This is also the reason for the loading capability of spoils which tends to have spatial and temporal characteristics under compaction.
The best-fit curves of experimental data are presented as follows:
According to (
By taking the derivative of (
The fitting curve of load increasing rate.
It can be seen from Figure
(1) When
(2) When
(3) When
It also can be seen from Figure
In addition to the loadability variation with time, the spoils also tend to have spatial variation characteristic under unconfined compression. When the spoils are in stage II or III, different parts of specimen have various density and loadability. According to the force state of spoils, it can be divided into three zones. The zones distribute as concentric circular, from outside to inside; these zones can be defined as follows: I, rearranging zone; II, breaking zone; III, consolidating zone, as shown in Figures
The spatial characteristic of spoils under unconfined compression and the comparison of the consolidated zones. (1) Large particle size; (2) small particle size; (3) Talbot’ gradation.
The spoils in zone I are compacted in very low confining pressure, so they are easily dislocated and rearranged which ends in large deformation. For the spoils in zone II, it is under confining pressure applied by zone I, so the stability of carrying structure increases and the loadability significantly improves. By the act of greater confining force and axial load, there is a higher degree of particle breakage that occurs on particles of zone III. This situation results in reduction of porosity and increase of density. The fragments of various sizes solidify and form the consolidated zone where the loadability of relevant spoils further improved (Figure
In order to observe the consolidating zone, the loose spoils on the edge of specimens are stripped after the compaction experiments. It can be found that the spoils strongly consolidated in central part (zone III). The shape of zone is circular truncated cone with a high magnitude in density (Figure
In this research, numerical simulation and a series of laboratory experiments were carried out to study the unconfined compressive behaviour of spoils with different gradations for coal mine backfill. In numerical study, the particles were assembled in PFC according to the real shape of spoils which is obtained by image technique. Basing on the profile of spoils, numerical model was built and then compressed by the wall. Such method was proved to be consistent with physical experiments.
The compaction of simulation and experiments indicated that the load-strain behaviour of spoils was nonlinear and load-dependent. The complete load-strain process can be divided into three stages: rearranging stage (stage I); breaking stage (stage II); and consolidating stage (stage III). Stage I is characterized by large deformation and weak loadability; during stage II, spoils have formed stable interlocking structure and the rate of mechanics improves rapidly. In zone III, the central spoils highly crushed and consolidated, and its load bearing capacity increases fastest during this stage.
In addition, the gradation has a marked impact on the load-strain behaviour of spoils. During stage I,
In addition, the spoils under unconfined compression also have spatial characteristic. According to the force state, the spoils can be divided into three zones: rearranging zone (zone I); interlocking zone (zone II); and consolidating zone (zone III) from outside to inside. Among them, the consolidating zone has the highest value of density, so it is the main part to bear the overlying strata weight. Clearly, the uniaxial compressive strength of the parent rock constitutes one of the significant elements in determining the load behaviour of spoils.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge funding by National Natural Science Foundation Project of China (51474039, 51404046, and U1361205), Scientific Research Foundation of State Key Laboratory of Coal Mine Disaster Dynamics and Control (2011DA105287-ZD201302, 2011DA105287-ZD201302, and 2011DA105287-MS201403), Fundamental Research Funds for the Central Universities (106112015CDJXY240003), and Program Supported by the Basic Research of Frontier and Application of Chongqing (cstc2015jcy jA90019).