An analysis of full truck versus full bucket strategies in open pit mining loading and hauling operations

ABSTRACT This work analyzes two loading methodologies used in open pit: full truck and full bucket. The effect on production, fleet size and associated operating costs was simulated. The results indicate that when there is a shortfall in hauling fleet, the recommendation is full truck methodology. This recommendation, results in a lower fleet operating cost in addition to higher production than full bucket. However, for a surplus hauling fleet scenario, an exhaustive study is necessary. When the ideal coupling between equipment is exceeded, there is an acceptable range of waiting trucks before considering a change of methodology.


Introduction
The end of the so-called 'super cycle' of mining and the arrival of the Global Financial Crisis heralded an era in which marginal costs grew faster than the marginal increase in production [1].In this sense, loading and hauling operations become highly relevant because they represent approximately between 50% [2][3][4][5][6][7] and 60% of the total cost of material handling [2,3,7,8].
For unit operations of loading and hauling in surface mining, mining companies currently possess sophisticated fleet equipment management systems.These software packages seek to optimise the operation by maximising the productivity of the mine at the lowest possible cost.
However, the dynamic nature of mining operations and various factors can present situations in which there are no specific criteria or methodologies to follow for adequate decision-making.This is the case when the coupling between the loading equipment and the truck is not perfect.A very good example is the change of the characteristics of the geological units as the extraction progresses, requiring a potential additional 'half pass' to complete the truckload according to density differences that are found as exploitation progresses.Another example is the constant change in the number of loading and hauling units present in the system because of maintenance or repairs.In these cases, the decision is between completely loading the truck, considering the additional 'half pass' (full truck), or not fully loading the truck, saving the additional pass of the loading equipment (full bucket).

Full truck and full bucket
The full truck and full bucket terms appeared for the first time in the fleet equipment simulation tool TALPAC.TALPAC is a computational tool developed by the Runge Pincock Minarco company that uses the Monte Carlo simulation method to simulate the loading and hauling system in surface mining based on characteristic variable distributions [9].Nguyen and Golosinki [10] provided one of the first references to these terms indicating the meaning of each term in the TALPAC tool, further noting that this characteristic of the software can be used to investigate the different loading methodologies in terms of the performance of the fleet equipment.
TALPAC is one of the software most used in the Australian mining for the simulation of truck and shovel fleets [11].The goal of the simulation is to determine the productivity of the fleet and the costs associated with the material extraction, decreasing mistakes that could be made with the use of simple spreadsheets [12].For the configuration of the software, it is required to enter information regarding material density, models of the loader and truck, transport profile, shift system and operating costs, among others.Once this information is entered, the user can assign a statistical dispersion to the times that will be used in the simulation according to the expected results [13].
The mining industry uses different tools to manage its assets.A few tools are oriented towards measuring the use of mining assets and others towards measuring their performance.Typical goals of mine fleet management are the maximise mine production, minimise stockpile re-handle and achieve production target [14].In all cases of mining fleet management, it is important to determine the cycle times involved in mining extraction.The operational cycle times of the load and haul equipment are factors of relevant interest in this industry [9].Besides, the literature indicates that the cycle time of the hauling equipment includes the loading time, hauling time (full), dumping time, return time (empty), queuing, spotting and reversing [15][16][17][18].However, the loading time (shovel) in a basic cycle includes the bucket filling time, full bucket turning time, material dumping time, empty bucket turning time and bucket positioning time for filling [16,18,19].
A method for evaluating the productivity performance of the equipment is the so-called 'match factor' (MF).This is an indicator that relates operational times and the number of machines associated with mining [15,[20][21][22].Burt and Caccetta [15] define the MF as the relationship between the truck arrival rate and the service time of the loading equipment by means of Equation (1): where x i is the number of trucks of type i, x i is the number of loading machines of type i 0 , t i;i is the time required to load a truck type i and t X is the average cycle time for all trucks.
From the perspective of the efficiency of the equipment present in the loading and hauling systems, the MF can be classified into three different sets: • A coupling factor less than 1 (MF <1), which implies a surplus of the loading fleet (undertrucking) and, consequently, maximum utilisation of the hauling units and low utilisation of the loading units.• A coupling factor greater than 1 (MF> 1), which implies a surplus of the hauling fleet (overtrucking) and, consequently, maximum utilisation of the loading units and low utilisation of the hauling units.• A coupling factor equal to 1 (MF = 1), which corresponds to a perfect coupling in terms of the productivity and efficiency of both fleets.
The maximum productivity that a loading and hauling fleet can achieve is illustrated in Figure 1.
The mining exploitation usually required to replace part of the old equipment by new one, with greater productivity rates.This leads to obtain mixed fleet that generated economies of scale since larger tonnage of material can be hauling in a similar time required than old equipment [19,23,24].This produces new effects on the productivity performance of the system, varying the number of machines according to the interaction they have.Moreover, there are other variables involved in the operation that also determine the convenience of using different loading methodologies.
The productivity of a loading and haulage system is determined by the characteristics of the equipment, its associated times and characteristics of the material to be loaded and transported.In a simple shovel-truck model, the load units act as servers of the transport units, which receive or remain waiting for the service [25].Similarly, the different destinations (stockpile, dumps, crushers, fuel loading stations, etc.) act as servers for the transport units.Therefore, to establish the productivity of the equipment, the characteristics of the material to be transported, the technical variables of equipment design, their interaction and the times associated with the work cycles should be considered.
An important factor in the definition of the loading methodology to be used is the characteristic of the material to be transported.In fact, the total real capacity of the loading bucket is determined, among others, by the bulk density of the material to be loaded.The density of the material, however, depends on the rock geomechanical properties and the technical blast parameters.Therefore, because of the anisotropy that occurs in mineral deposits, constant analysis of these parameters in mining projects is important to determine the load methodology appropriate to the mine conditions.

Calculation of equipment performance
The number of buckets needed to load a transport unit is given in Equation (2): where N p corresponds to the number of buckets needed to load a payload truck C C with the loader bucket payload B C .This equation considers not only the capabilities of the equipment but also other operational factors and the material to be loaded.
The tonnage that a shovel can load by the bucket is given by Equation (3): where V C is the nominal capacity of the bucket (volume), F f is the bucket filling factor and φ esp is the bulk density of the material.
The actual performance of a loader ðP C Þ in tonnes per minute, considering the time of cycle per pass T C (minutes), is determined as shown by Equation ( 4): The determination of this last variable depends in turn on the in-situ density of the rock and its post-blast characteristics, that is, the volume of loose material divided by the in-situ rock volume [26].
Replacing B C in Equation ( 2) by Equation (3) yields Equation ( 5): If N p is not whole (which is most frequently the case), it must be decided whether to provide an additional pass to complete the load of the truck (full truck) or ultimately to be left with only the load of the minimum entire pass (full bucket).Then, N 0 p is defined as the number of whole passes with which it is decided to load the truck as described by Equation (6).
The productivity of the system will also be affected by this decision.If N 0 p N p , the productivity of the loader is determined using Equation ( 4).If N p N 0 p , the productivity of the loader in the last pass made is considered as B C Ã N 0 p ÀN p , and the productivity of the loader is determined by Equation ( 7): However, the effective load of the truck C 0 C is calculated by multiplying the entire number of shovels made N 0 p by the tonnage of each bucket as described by Equation (8).
Then, the productivity of the hauling equipment can be calculated by means of Equation ( 9): where P T is the productivity of the hauling equipment and t t is the transport cycle time.Equation (10) represents the productivity of the system P s of the loading and hauling.
where i is the unit of hauling that enters to the system.The sum of the productivity of the transport units entering the system must always be less than or equal to the productivity of the loader.With respect to a match factor, considering N 0 p , and the relation with the unit of hauling, this is calculated by Equation (11).
The cost of loading and hauling, however, in the two different strategies of equipment prioritisation is also affected according to the final decision.If the production costs are categorised in an ABC activity model (Figure 2), the costs per unit produced can be defined to compare the strategies.Botín and Vergara [1] proposed Equation (12) for the determination of the operational cost of the loading and hauling equipment in an ABC methodology.
where C nB is the cost of the nature of the activity, in this case, the cost of loading and the cost of transportation USD tons À Á ; I is the intensity of use of a resource relative to the activity to be estimated operational hours period ; Pr is the price of a unit of use of the resource

USD perational hours
; and P is the performance when executing the activity tons period .Then, the cost of de-fleet system could be calculated by Equation (13).
The costs of loading and hauling operations are determined by the cycle times associated with each operation and the tonnage achieved during the evaluation period.If the intensity of use of the resource and the base price are maintained, the final cost will be higher or lower according to the loading methodology.The performance variable P directly depends on the operating cycle time of the equipment under analysis, and this changes according to the loading methodology used.For the loading case, the full bucket methodology would provide a lower operating cost because the tonnage is increased from the perspective of the loader (only complete passes); however, for transport, the operating cost would be higher because the full capacity of the truck would not be used.The full truck load methodology, in contrast, achieves lower transport operating costs because the total capacity of the truck is used; however, the operating cost of the loading equipment increases with passes of only one-half of the capacity.
Finally, the total cost of the loading and hauling operations must be the parameter considered for the final decision on the loading methodology used.The continuous analysis of the load and haul fleet and its dynamic behaviour must be responded to with dynamic decisions that are adapted to each given situation during the exploitation of the mineral resource.Given this, better results in the search for added value to the project can be achieved.

Case study
The methodologic steps for the evaluation in the software are as follows: Step 1: Selection of equipment.The equipment selected for this study consists of a Caterpillar 7495 electric shovel and Caterpillar 797 F truck.This choice was based on their high popularity in Chilean mining operations.Step 2: Determination of the characteristics of the material to be loaded and transported such that N p is not whole.
Step 3: Generation of routes and assignment of operating costs and times associated with the cycles of the loading and hauling equipment.
Step 4: Simulation of full truck and full bucket methodologies over a given time.
Step 5: Analysis of the full truck and full bucket methodologies varying the number of trucks.
The capacities of the selected units are 56 m 3 for the shovel and 201 m 3 for the truck.The technical characteristics of the equipment are assumed as indicated in the technical specifications provided by the manufacturer.
The case study considers the following characteristics of the material: an in-situ density of the rock of 2.4 t/m 3 , a bulk factor of 1.33 and a fill factor of 100%.Given this, the bulk density of the material to be loaded and transported is 1.8 t/m 3 .
The route generated considers a total length of 4.8 km.This route considers loading as the starting point with a dump as the final destination; the characteristics of each one of the route sections are summarised in Table 1.The restrictive operating speeds of the trucks are as follows: 30 km/h in the loading and unloading areas, 30 km/h along curves and 40 km/h on negative slopes.
The operating costs associated with the load and haul system correspond to the purchase and operation of both equipment fleets.The unit cost for the purchase of the equipment is 23 M USD and 5.5 M USD for the shovel and truck, respectively.Both units consider a linear depreciation of 10% and an operating life of 100,000 h.The residual value of both units corresponds to 10% of the investment.The operating costs of the equipment correspond to 320 USD and 526 USD dollars per operative hour for the shovel and truck, respectively (Table 2).
The shift system used for the case study reflects the reality of the large mining industry in Chile.Two shifts of 12 h per day are considered; in addition, annual work losses of 6 and 8 scheduled and unscheduled shifts are included, respectively.The non-operative and operative delays of the loading and hauling system are also considered, 0.5 h and 1 h, respectively, per shift.
The variable inputs to represent the real mine operation were stablished with real data (Supplementary Material S 1 ).The time, load and availability distributions associated with the load and haul operation are indicated in Table 3.For simplifying the study, all normal distribution variables are considered.In addition, selection data are limited to 1% and 99% probability for all variables.For the case of the shovel, being only 1 unit, a fixed mechanical availability of 85% is considered with a 6-s delay time for the first pass.Loading is considered for only one side of the shovel.

Results
We implemented this case study in the software Talpac version 11 on an Intel core i7-6500U PC with 2.5 GHz and 8 GB of RAM.We run the simulation with the incremental analysis method considering 1 shovel and a range of trucks since 1 until 25 units for full truck and the same characteristics for full bucket methodology.The software simulated in 16 s, 8760 h of operation for each case and with a total of 438,000 h of operation.
When comparing the results regarding the number of trucks, both methodologies provide relevant information.By applying the full simulation tool, the optimal number of trucks obtained is 14 for the full truck methodology.For the full bucket methodology, however, the optimal quantity is 18.This difference in the number of trucks is a reflection of the methodology to be used because, for the same tonnage to be extracted, the shovel in the full truck methodology will dispatch fully loaded trucks; however, in the full bucket methodology, it will not dispatch fully loaded trucks, and therefore, more trucks will be needed to meet the planned tonnage.
The annual production obtained by the different methodologies shows significant variances according to the number of trucks in the system.The full truck methodology at its optimal point (14 trucks) reaches an annual production of 59,218,376 tons.In contrast, the full bucket methodology in its optimal fleet of trucks (18 units) reaches an annual production of 64,746,671 tons.
Regarding cycle times, the full truck methodology presents an average time of 28.06 min.However, a cycle time of 27.15 min is achieved using the full bucket methodology.This result is because the truck loading time is greater in the full truck methodology because it requires an additional pass.
In relation to costs, for an optimal fleet, an average capital and operational cost of USD 1.15 per ton is obtained in the full truck methodology and USD 1.32 per ton in the full bucket methodology.Capital costs are higher in the full bucket methodology, which is the result of a greater number of trucks for the same production rate.The operating costs of the trucks are increased in the full bucket methodology because of the non-utilisation of the truck's total capacity.
To complete a sensitivity analysis of a system according to the number of trucks that interact in it and the final production obtained, an incremental simulation was conducted.This simulation consists of varying the number of trucks in the circuit and observing the impact on the MF, productivity and associated costs.
In relation to the MF (Figure 3), it can be observed that in the full truck methodology, the optimal fleet is achieved using 14 trucks, while in the full bucket methodology, it is achieved using 18 trucks.
Regarding the annual production of the fleet (Figure 4), for both methodologies, it was observed that with a truck shortage (less than the optimal amount), the annual production is higher in the full truck methodology.When the number of trucks that interact with the loading equipment exceeds the optimum, the full bucket methodology achieves a higher productivity.Total capital and operating costs (Figure 5) drastically decrease (between 1 and 3 trucks) for the full truck and full bucket methodologies.Subsequently, the decrease is more gradual, reaching a minimum cost of 1.13 USD/t when there are 11 trucks using the full truck method and 1.25 USD/t when there are 14 trucks using the full bucket method.After reaching the minimum capital and operating costs, the curves tend to gradually increase.
Comparing the capital and operating costs of both methodologies, a transition point is observed.The costs in the full truck methodology are lower than those of the full bucket methodology until the optimal fleet is reached in the latter (18 trucks); after this point, the costs in the full truck methodology are greater to those of the full bucket methodology.The production comparison between the full truck and full bucket methodologies shows a difference up to 19 trucks (Figure 6), resulting in a maximum difference of 5.3 million tons when there are 13 trucks available.With 20 trucks, the production of the full truck method is less than that of the full bucket method.
In the full truck methodology, the selected shovel can support five additional trucks, once the established optimum has been exceeded (19 trucks).If more units are added to the system, it is convenient to change the load methodology to full bucket because better annual production results are obtained.
The transport cycle times (Figure 7) show a similar behaviour in both methodologies for up to approximately 14 trucks.The cycle time in the full truck method is higher because of the time used for the additional pass that the loader must make.The cycle time in the full truck method significantly increases in the full bucket method.This is because the waiting time of the trucks in the loading area increases as the trucks continue to be sent to the loading equipment which exceeds its optimal capacity.
For the sensitivity analysis, we focus on the ideal match factor because, for this case of study, at this point, the fleet's performance is optimum (Table 4).For full truck methodology, the optimum number of truck is 14, while for full bucket is 18, in this condition, and for an under-trucking situation (MF<1), for both cases, full truck achieves better production than full bucket.About the cost (capital and operational) for ideal MF and when MF <1, full truck achieves again better result, this for two principal reasons, a less number of trucks required and the higher movement of material.Besides, in the range between ideal MF in both methodologies (14 for full truck and 18 for full bucket), always full truck methodology achieves better results in production and cost (capital and operational).Nevertheless, when the ideal MF is higher for full bucket methodology (>18 trucks), the production and cost are better in this methodology (full bucket).

Conclusions
The dynamic nature of large open-pit mining operations produces situations that deserve special analysis to assess the impact of decisions that engineers must make when facing these events.In a loading and hauling system, when a non-scheduled stoppage of the loading equipment occurs, one of the following must be chosen: remove from the system the trucks assigned to the stopped shovel or redistribute the trucks to the loaders that continue to work in the system.When opting for the latter, a saturation of the loading equipment will occur, and this will become a bottleneck in the system; therefore, the maximum productivity that can be achieved will be conditioned by this equipment.
The maximum productivity of the loading equipment will be achieved only when it makes a fully loaded bucket in a saturated state, that is, with trucks waiting to be loaded.However, there is an acceptable range of waiting or queuing trucks, in which the productivity of the transport equipment is still a priority, specifically, to fully load them.This last strategy (full truck), in the experience of the finning company expert, is the methodology most used by the industry for presenting better productive results in most cases.
The MF for the full truck methodology is achieved with a smaller number of trucks than that in the full bucket methodology.This means that the loading equipment in the full truck methodology can load less trucks because the loading time is greater than that of the full bucket methodology.Therefore, investments in mining projects will always be lower in the full truck methodology validating the preference of this methodology over the full bucket methodology.
According to the number of trucks in the system, there is a transition point at which once the operating cost in the full bucket methodology is exceeded, it will be less than that in the full truck methodology.Prior to this point, the full truck methodology will always be of lower cost, which explains its preference in mining operations.However, it is important to identify this transition point because of the effect it produces on operational results.
Finally, this study concludes that in the event of trucks queuing for the loading equipment, there is a point at which the full truck methodology must be changed to the full bucket methodology to achieve better productivity and lower costs.This demonstrates the need for greater analysis of mining systems, in particular, situations where decisions must be made to add value to the mining business.

Disclosure statement
No potential conflict of interest was reported by the authors.

Figure 3 .Figure 4 .Figure 5 .
Figure3.Effect of the increase in trucks on the match factor according to the full truck and full bucket methodologies.

Figure 6 .Figure 7 .
Figure 6.Production differences between the full truck and full bucket methodologies.

Table 1 .
Characteristics of the transport profile to be used in the case study.

Table 2 .
Operating costs USD per hour.

Table 3 .
Distribution of loading and hauling equipment times to be considered in the case study.