Discrete element parameter calibration and the modelling of dragline bucket filling

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Abstract

The Discrete Element Method (DEM) is useful for modelling granular flow. The accuracy of DEM modelling is dependent upon the model parameter values used. Determining these values remains one of the main challenges. In this study a method for determining the parameters of cohesionless granular material is presented. The particle size and density were directly measured and modelled. The particle shapes were modelled using two to four spheres clumped together. The remaining unknown parameter values were determined using confined compression tests and angle of repose tests. This was done by conducting laboratory experiments followed by equivalent numerical experiments and iteratively changing the parameters until the laboratory results were replicated. The modelling results of the confined compression tests were mainly influenced by the particle stiffness. The modelling results of the angle of repose tests were dependent on both the particle stiffness and the particle friction coefficient. From these observations, the confined compression test could be used to determine the particle stiffness and with the stiffness known, the angle of repose test could be used to determine the particle friction coefficient. Usually DEM codes do not solve the equations of motion for so-called walls (non-granular structural elements). However, in this study a dynamic model of a dragline bucket is developed and implemented in a commercial DEM code which allows the dynamics of the walls to be modelled. The DEM modelling of large systems of particles is still a challenge and procedures to simplify and speed up the modelling of dragline bucket filling are presented. Using the calibrated parameters, numerical results of bucket filling are compared to experimental results. The model accurately predicted the orientation of the bucket. The model also accurately predicted the drag force over the first third of the drag, but predicted drag forces too high for the subsequent part of the drag.

Introduction

In open cast mining, the overburden needs to be removed in order to mine the ore below. This overburden can vary from topsoil to hard rock. The bulk of the costs involved in open cast mining can be attributed to overburden removal.

Draglines are very economical and represent the most popular of all overburden removal devices. They are usually used in combination with scrapers to reduce the amount of re-handle. A dragline is a crane-like structure with a large bucket of up to 100 m3 in volume, suspended by steel ropes (Fig. 1). The bucket is dragged through the overburden and once the bucket has been filled, it is hoisted up. The base of the dragline pivots and the overburden is dumped elsewhere. The overburden usually needs to be blasted before the dragline can be used.

Draglines are designed to operate 24 h a day for 360 days a year. The cost of the loss of production due to dragline down time has been estimated at 8000 Australian dollars an hour [8]. Many dragline breakdowns can be attributed to the design of the bucket. The buckets either fail or overload the machine and cause failures in the dragline boom and main structure.

The filling of a bucket is a complex granular flow problem. Instrumentation of equipment for quantifying certain parameters of the operation is difficult and expensive. It is possible to use small-scale (usually 1/10th scale) experimental rigs to evaluate bucket designs [10], [23] but they are expensive and there are questions regarding the validity of scaling [21], [22]. To scale-up results from model experiments is problematic since there are no general scaling laws for granular flows [6].

Numerical models and simulations have become an important design tool in engineering. Although numerical simulations seldom totally replace experiments, they allow designers to investigate a far wider range of options in a relatively short time and usually at much lower cost than using experimental investigations. A sensitivity analysis to determine the influence of specific parameters on the performance can be done more easily and comprehensively. Expensive experiments can then be used after numerical investigations to “fine tune” the design [17].

The Discrete Element Method (DEM) has been used to predict the behaviour of granular materials for the last two decades. A DEM code was first developed by [7] to simulate rock fracture mechanics. Today, there are commercial DEM codes available in both two and three dimensions. DEM is based on the simulation of the motion of granular material as separate particles. Calculations performed during a DEM simulation alternate between the application of Newton’s second law to the particles and a force-displacement law at the inter-particle contacts. DEM has the advantage that it can easily be used for the simulation of granular flow subjected to large deformations and free boundaries. With the development of faster computers, the number of particles that can be simulated has increased, allowing for more accurate material representation and the modelling of large industrial processes. The main problem with DEM is how to specify the micro-parameters (particle size, shape and contact parameters) so that the flow on macro-level of thousands of particles behaves in the same way as real granular flow. Laboratory experiments [11] or in situ tests [3] are necessary to determine these parameters before any useful modelling can be performed and valid predictions can be made.

In order to accurately model dragline bucket filling, both the granular material and the bucket dynamics must be accurately modelled. A dragline bucket is suspended by ropes and the motion of the bucket is influenced by the forces acting on it (gravity, rope forces and the interaction forces with the soil). The path followed by the bucket and the bucket’s orientation is not known in advance or manipulated by the operator, as in the case of hydraulic excavators for example. The dragline operator positions the bucket on the ground and then the bucket is dragged in the general direction of the drag ropes at constant rope speed.

In a DEM model, structures such as buckets are modelled using walls. DEM codes calculate the behaviour of the particles based on the forces acting on them, but most DEM codes do not solve the equations of motion for the walls. In some DEM codes, the translational and rotational velocity of the walls cannot be changed during the simulation, or the velocity can only be pre-programmed as a function of time. In dragline bucket modelling the velocity of the walls (bucket) needs to change according to the forces acting on it and it cannot be pre-programmed.

The DEM codes by Itasca give the user access to almost all internal variables via the built-in programming language, FISH. This feature makes it possible to obtain the resultant force and moment caused by particles on a wall. The resultant force and moment vectors can then be used to solve the equations of motion for each wall and update the velocity of each wall accordingly. In this paper, this option is used to model the dynamic behaviour of a dragline bucket.

Commercial DEM codes include general purpose codes such as PFC2D, PFC3D, UDEC, 3DEC ([14]), EDEM ([9]), Newton [1], Elfen ([24]), Bulk Flow Analyst [2] and codes for specific applications such as Chute Analyst ([20]) and Chute Maven ([4]). In this paper, PFC3D is used.

Discrete element modelling of dragline bucket filling has never been directly compared to experimental results. Cleary [6] modelled dragline bucket filling and trends were shown and qualitative comparisons made, but no experimental results were presented.

This paper addresses the challenges in the DEM modelling of dragline buckets, namely accurate modelling of material properties and the modelling of the bucket dynamics. The experimental setup and numerical model are described followed by a comparison between the experimental and numerical results.

Section snippets

The Discrete Element Method

Discrete Element Methods are based on the simulation of the motion of granular material as separate particles [7]. Using the soft particle approach, each contact is modelled with a linear spring in the contact normal direction (secant stiffness kn) and a linear spring in the contact tangential direction (tangent stiffness ks) as depicted in Fig. 2. Frictional slip is allowed in the tangential direction with a friction coefficient μ. The particles are allowed to overlap and the amount of overlap

Experimental setup

A scale dragline model was build to obtain data which could be used to validate the numerical results. The drag forces, the bucket trajectory (path) and the bucket’s orientation during a filling cycle were recorded.

The bucket was a 1:18 scale model of a 61 m3 bucket ([26]). The bucket had a length and width of roughly 300 mm and a fill height of 175 mm (Fig. 3). The size of the drag bed was determined by the size of the bucket used. The width and height were chosen to minimise boundary effects.

Material calibration

This section discusses the methods used to determine the granular material parameters. In order to fully describe the cohesionless material in PFC3D, the following material properties were needed:

  • particle shape distribution,

  • particle size distribution,

  • density,

  • normal and shear stiffness and

  • friction coefficient.

Bucket dynamic model

PFC3D has two main element types, namely, walls and balls (spheres). The balls are used to simulate the granular materials and the walls are used to simulated rigid bodies. PFC3D is a command-based solver that relies on the user to define the simulation setup and parameters. Built into the solver is a programming language called FISH, which can be used to control and/or modify the simulation in real-time.

PFC3D does not solve the equations of motion for the walls. Walls can only be given a

DEM model setup

The modelling of large systems is still a challenge [25]. Even with parallel processing becoming available, clever modelling can reduce the computation times without loss in accuracy.

Bucket filling

Each experiment was repeated three times to ensure the results were reliable and repeatable. The bucket position, orientation and drag force were recorded for each test. The results showed that the bucket behaviour is predominantly two-dimensional with very little rolling and yawing motion. [23] also observed that the flow of material into the bucket is mostly two-dimensional and the motion of a dragline bucket can be accurately modelled taking into account only the bucket translation in the

Conclusion

A procedure to determine the micro parameter values for the DEM modelling of cohesionless granular material was presented. The particle size, shape and density were directly measured and modelled. The particle stiffness and friction coefficient were determined by confined compression tests and angle of repose tests. It was found that the compression test is mainly dependent on the particle stiffness and the particle friction coefficient had no significant effect on the results. From this test,

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