1. In land development projects earthmoving constitutes a major part of the operations, involving a considerable portion of the total expenditure. Operations generally include the construction or improvement of roads and watercourses and the arrangement and re-arrangement of an area within a specific network of roads and watercourses.
For the realization of earthmoving projects a choice is made from suitable equipment, which is to some extent determined by an estimate of the total cost. In this study the minimum cost is assessed for a job that can be carried out by bulldozers, dragline excavators and dumpers, referred to in Dutch as 'dry' earthmoving to distinguish it from hydraulic work. It is taken that the work must be completed within a certain time. It is ascertained how the minimum cost and the relevant equipment are affected by a change in the job time specified and the conditions expected during the execution of the job. By comparison, the cost of hydraulic earthmoving (by suction dredges) is also calculated. Because of the size of the job it is assumed that it can be carried out by one suction dredge, thus eliminating in this case the commitment to complete it within a particular time. Cost calculations have been made for two schemes prescribing (unalterable) volumes of earth to be excavated and dumped, as well as the dumping location (+ and - chart).
The emphasis of the first earthmoving scheme is on 'dry' earthmoving, i.e. by excavators, haul units and bulldozers; the second scheme is carried out by suction dredges. In the latter scheme only indispensable levelling is done by bulldozers Or dragline excavators and ditches are dug by excavators. Sectional division of the two schemes are identical. The ultimate surface elevations and ditch capacities are different. The existing and new situations are shown in Figures 11 and 12.
2. To calculate the cost of a job a continuous and a discrete method are employed. In the former it is assumed that a fraction of a machine can perform an element or a sub-element of the job. In the latter method only a complete set of equipment can be operated with.
3. For the planning and calculating of an earthmoving scheme various design and computation techniques have been devised, which more or less minimize the volume of earth to be moved. The results of an earthmoving computation show the volumes of earth to be excavated and to be dumped as well as their sites (cut and fill balance). Based on these data the transport schemes (dry earthmoving Figures 8, 9; hydraulic earthmoving Figure 11) can be devised. The necessary computations for devising a transport scheme have been made by computer. When computing the transport scheme for dry earthmoving the procedure selected made it, because of the vast number of data, impossible for the problem to be processed in one operation.
The transport scheme has been obtained by dividing the whole area into sections, in which the number of points did not exceed the capacity of the computer. This division into sections was based upon a transport scheme for a considerably reduced number of cut and fill points. The reduced number of points was obtained by adding the volumes per point for a certain number of points (of cut and fill) and to locate the total in the balance point.
4. To find the cost of earthmoving with various machines a number of computer programmes have been evolved, in which the output-determining factors of the machines have been taken into account. By this procedure the operational conditions can be included in the computation process, if both the qualitative and the quantitative data and their influence on the output determining factors are known.
The programmes for excavators combined or not combined with haul units are based on the formulas 5 and 11 -18; for the bulldozers on formula 22. For hydraulic earthmoving a programme was devised, which includes data on pump, engine and soil type. The computation of the period for completing the job and of the cost based on formula 23 have been included.
5. For dry earthmoving the transport lines (Figures 8 and 9) with relevant volumes have been divided into a number of groups (Figure 10). Per group the cost was calculated for all equipment employed. The results of the computations were arranged in a matrix (Table 15). This matrix includes the period of completion and the cost per machine or machinery combination for each group.
By applying linear programming, for a particular period the minimum completion cost of a job was calculated and the relevant equipment was determined. The computations were made for a continuous as well as for a discrete method. For the execution of the project under different conditions the output determining factors of the machines were reduced by 15 % and 30 % (Tables 12 and 13).
For hydraulic earthmoving the transport distances were divided into distance classes. Per distance class the volume of earth to be dumped was indicated (Table 8). For each distance the time needed to move earth over this distance was computed. The total time of completion was obtained by adding the periods of completion per distance. By multiplying the total time of completion by the cost per time unit the total cost was computed.
6. The results of the computations for dry earthmoving are shown in Figure 12. These suggest that in making an estimate the conditions expected must be known if they affect the output determining factors of the machine, because they may have a large influence on the total cost. For example: compared with the most favourable situation (A-a,a) there has been found to be an increase in cost of approximately 40 % in the case of a reduction of the output determining factors of the machines by 15 % (B-b,b). The change in cost results from a change in the number and types of machines employed; the assignment of machines to the various elements of the job can be changed. When the numbers and types of machines are re-assigned, the influence of a change in allowed job time on the estimate of cost proves to be less important in the selected example than the influence of a change of work conditions. A change in the allowed job time in this case also results in a change in the number and types of machines employed and in the assignment of the machines to the various elements of the job.
If conditions during the operations are less favourable than those assumed in the estimate, failure to adapt the equipment to the job may cause the allowed job time to be exceeded, the contractors having to pay a penalty in consequence.
The determination of the minimum cost in the discrete method proves in most cases to be time consuming. For this reason only the first discrete solution found by the computer is supplied. In the computations various cost-determining factors (e.g. damages and repairs) are not included. These cost can be introduced however, in the cost job time matrix and thus be incorporated in the optimization process.
7. In hydraulic earthmoving, given the type of machinery and types of soil, the output is determined by the transport distance and the possible concentration of solids in the discharge line (Tables 16, 17 and 18). An increase of the transport distance tends to cause a less performance through a reduction of the mixture output (increase in resistance). If transport distance is increased, it is also possible that the concentration of solids in the liquid should be reduced to prevent exceedance of the critical speed. Apart from the limitations at the suction and discharge side of the suction dredge the concentration of solids is also
determined upon the requirement that the output of solids must be coped with at the dumping site (time needed to couple or uncouple the piping). The limitations at the suction and discharge side of the suction dredge affect the maximum concentration at the suction side, the maximum allowable underpressure, and the critical speed. Because of the mentioned limitations hydraulic earthmoving cannot be applied to all allowed job times (Tables 20 and 21).
Table 23 shows the cost of completion with the dredge machinery required. With the procedures selected the cost of hydraulic earthmoving is of the same order as that of operations with dry earthmoving (Figure 12) under favourable conditions (in both cases exclusive transport cost of equipment).