Cycle time is defined as the time required for any equipment to complete one cycle of operation. For a truck, cycle time comprises the time to spot and load, travel to the dump site, maneuver, spot and dump, and drive back to the loading point, also inclusive of predictable delays and unpredictable waiting times (Lineberry, 1985) [11] [12] .

Principally, cycle time is a direct measure of process and equipment performance in waste material transport for open-pit mining and other processes [13] [14] .

Cycle time analysis was conducted starting with identification of the activities to be analyzed, for which the cycle times of seven activities were determined and recorded. In accordance with Samwel Victotmanyele (2017) [13] , the total cycle time for the truck was appointed as per Equation

T c t = t q + t s p + t l d + t f h + t d p + t h g + t e h (1)

where t q : queuing time at the excavator, t s p : spotting time, t l d : loading time, t f h : full haul time, t d p : dumping time, t h g : hanging time and t e h : empty haul time.

Road conditions affect the technical and economic performance of open pit mine dump truck. The road of the open-pit mine is classified by its character. Relevant characters include:

Structure: paved and unpaved;

Movement direction: one lanes, two or more lanes in traffic;

Time using: permanent and temporary;

Location: bench road, ramp, surface, dump road.

Rolling resistance is defined as the force required to maintain a vehicle at a steady speed on the ground level, and is a function of not only the gross vehicle mass and driving characteristics, but also the type and conditions of the tires and the road surface on which the vehicle is operated [9] . The characteristics of the road pavement are expressed as a coefficient of the rolling resistance.

Empirical estimations of the rolling resistance are based on tire penetration, and it turns out that 0.6 percent increase in rolling resistance per centimeter of tire penetration into the road typically result in 1.5 to 2 percent minimum resistance [9] .

Figure 1 shows that rolling resistance for mine haul road depends on road conditions. Calculations of the rolling resistance are categorized as shown in Table 1.

According to B. Purevtogtokh (2018), the average value of the road rolling resistance in the direction of the load section j is defined as follow.

w l j = l 1 ∗ w 1 + l 2 ∗ w 2 + ⋯ + l n ∗ w n l 1 + l 2 + ⋯ + l n = ∑ i = 1 n l i ∗ w i ∑ i = 1 n l i , N/kN (2)

The average value of the road rolling resistance in the direction of the empty section j is set as:

w e j = w l j ∗ 1.25 , N/kN (3)

At the same time, the average slope of the road in the load and empty section j is specified as:

i j = l 1 ∗ i 1 + l 2 ∗ i 2 + ⋯ + l n ∗ i n l 1 + l 2 + ⋯ + l n = ∑ i = 1 n l i ∗ i i ∑ i = 1 n l i , ‰ (4)

where

w i : the rolling resistance of the road in the load of direction;

l i : the length of the road section i for traffic j, km;

i i : the slope of the road section i for traffic j, ‰.

Meanwhile, the total resistance of the movement is described as:

W j = P l 1 ( w l 1 + i l 1 ) ∑ l l 1 + P e 1 ( w e 1 + i e 1 ) ∑ l e 1 L 1 , N (5)

where: P l 1 , P e 1 : the weight of the dump truck in the load and empty direction, tons;

w l 1 , w e 1 : the rolling resistance of the road in the load and empty direction, N/kN;

l l 1 , l e 1 : the length of the road in the load and empty direction, km;

i l 1 , i e 1 : the slope of the road in the load and empty direction, ‰;

L 1 : the total distance of road.

It is essential to develop a methodology to optimize the utilization regime in connection with the increase in the volume of transport. Consequently, a scientific assessment of the organizational level, operating conditions and quality characteristics should be conducted; otherwise it is impossible to maximize the efficiency of the dump truck.

Multiple linear regression analysis is a statistical method used for determining a formula that explains the prediction of a dependent (unknown) variable by its relationship to a set of independent (known) variables. A weighting is assigned to each independent variable to reflect the portion of its impacts on the value of the dependent variable; thus, the weighting is referred to as the coefficient of the variable in the equations [15] [16] .

Multiple R. Multiple R is the Correlation Coefficient, illustrating the strength of the linear relationship. For instance, a value of 1 signifies a perfectly positive relationship while a value of 0 expresses no relationship between a certain independent variable and the dependent variable. Multiple R is the square root of R squared.

R squared. R squared (r²) is the Coefficient of Determination, representing the proportion of the variance for a dependent variable that is explained by the independent variables included in a regression model. For instance, R squared value of 80 %describes that 80 percent of the variations of the value of y fall on or closed to the regression line (the mean) are explained by the value of x; thus, implying that 80 percent of the values calculated are fit to the model.

Adjusted R square. Adjusted R-square (adjusted R²) shows how well the data points fit the regression line, but adjusts for the number of terms in a regression model.

Standard Error of the Regression. Standard Error of the Regression is an estimate of the standard deviation of the error μ, which is not similar to the standard error in descriptive statistics. The standard error of the regression is the precision that the regression coefficient is measured; if the coefficient is large compared to the standard error, then the coefficient is probably different from 0.

Observations. Observations report the number of observations in the sample.

In order to minimize the amount of road sections, a summary of the road parameter must be checked to ensure the road conditions for possible tractive forces, define the speed of movement and the time as well as the efficient usage frequency. Afterwards, the principle road scheme is simplified in accordance with associated parameters.

Before the road is simplified, following road conditions must be taken into account.

· Summarized roads must be a same type of road section (bench road, ramp, surface road, dump road).

· Pavement and structure of road must be the same.

· Road gradient and rolling resistance are nearby for dump trucks operating in the same regime.

· The speed of the dump truck is nearby.

· Safety conditions must be the same.

The R radius curved sections is converted to the slope of straight section. The curved sections of radius R are defined as the curve resistance according to the equation:

Δ i R = 30 ∗ 200 − R 200 , ‰ (per mille) (6)

where: R: turn radius, m.

The radius R curve in section j is defined according to the equations:

i j = i ′ j + Δ i R , ‰ (7)

where: i j : slope of the j section curve converted into slope, ‰;

i ′ j : Slope of the j section curve, ‰.

The road has to be subdivided into sections of the road, namely bench road (BR), ramp (R), surface road (SR), dump road uphill (DRU), and dump road (DR).

For each section of road, the average length, the average slope and the average rolling resistance are defined. In addition, the amount of charge is considered.

For example; weighted average length of the bench road:

L B R = ∑ L B R j ∗ Q j ∑ Q j , km (8)

Weighted average slope of the bench road:

i B R = ∑ L B R j ∗ i B R j ∑ L B R j , km (9)

Weighted average rolling resistance of the bench road:

w B R = ∑ L B R j ∗ w B R j ∑ L B R j , N/kN (10)

where; L_BRj: length of bench road in j section, km;

I_BRj: slope of bench road in j section, ‰;

Q_j: quantity of transport load by section j, tn/m³;

W_BR: rolling resistance bench road in j section, N/kN (‰).

The current study observes every road section and dump truck movement. Subsequently, the data is analyzed via multiple mathematical regression models using mathematical statistical methods. The data regarding five bench roads, three ramps, three surface roads, three dump uphill roads and three dump roads are combined and calculated and accordingly the measurement of “UkhaaKhudag” open-pit mine has been summarized. The results show the estimated ranges obtained via Microsoft Excel application as outlined in Table 5.

The Microsoft Excel program compares statistical calculations with of regression models: linear, quadratic and exponential. Factors are validated by the F-test. Table 6 shows comparisons of road moving time regression models in each section in the loaded direction.

Table 7 shows comparisons of road moving time regression models in each section in the empty direction.

By comparing the regression models described in each road section, the models with greater correlation coefficient and smaller standard errors are selected; therefore the prediction models are acquired.

For the modeling variables: L: the length of the section on the road, km;

i: the grade of the section on the road (‰);

w: rolling resistance of the section on the road, N/mN (m-mega).

Bench road in loaded direction

T = 21.12 + 140.50 ∗ L + 0.043 ∗ i − 279.68 ∗ w (25)

Road length and grade have a direct effect on moving time of cycle whereas rolling resistance has an indirect effect.

Figure 4 and Figure 5 prove that the regression model described in the direction of the bench road is similar to the value of the actual measurement.

Bench road in empty direction

T = 101.37 + 66.31 ∗ e L + 0.0004 ∗ e i − 147.25 ∗ e w (26)

The model indicates that an increase of 179.7 seconds movement time results

in one unit increase of the road length. Furthermore, one unit increase of pavement road leads to a decrease of 399 seconds movement time.

Ramp in loaded direction

T = − 36.99 + 134.67 ∗ L + 0.79 ∗ i + 121.69 ∗ w (27)

The regression model reveals that one unit increase of the rolling resistance causes an increase of 121.69 seconds movement time. One kilometer increase of the road length contributes to an increase of 134.67 seconds movement time. In the meantime, one unit increase of the road slope per mille conduces to an increase of 0.79 seconds movement time.

In summary, three factors included in this model significantly impact the cycle time.

Figure 6 reflects the similarities between the regression model described in the direction of ramp and the value of the actual measurement.

Ramp in empty direction

T = − 5 + 64.74 ∗ L − 0.29 ∗ i + 52.44 ∗ w (28)

The regression model demonstrates that one unit increase of the rolling resistance and the length of the road lead to the increase of the movement time for 52.44 and 64.74 seconds respectively.

As evidenced in Figure 7, the differences in the values of the errors have a higher value compared with the other figures.

Surface road in loaded direction

T = − 217.12 + 23.23 ∗ e L − 6.67 ∗ e i + 239.17 ∗ e w (29)

Surface road in empty direction

T = − 34.25 + 17.25 ∗ e L − 6.12 ∗ e i + 62.36 ∗ e w (30)

The regression models shown in Figure 8 and Figure 9 are drawn from

related exponential functions. It is obvious that the road pavement has larger influence on the movement time. Hence, the pavement should be highly considered as the surface road length increases.

Dump road uphill in loaded direction

T = − 25287.04 − 256924.76 ∗ L 2 − 1.03 ∗ D 2 + 570.85 ∗ L ∗ D       + 160942.16 ∗ L − 156.76 ∗ D (31)

Dump road uphill in empty direction

T = + 578.552 − 13619.027 ∗ L 2 − 0.1684488 ∗ D 2 − 288.4464 ∗ L ∗ D       + 2913.8509 ∗ L − 95.6335 ∗ D (32)

The regression models portray the values of the slope while main resistance factors on the road are expressed in the term of D;

D = ( i + w ) / 10 (33)

where: i: the grade of the section on the road (‰);

w: the rolling resistance of the section on the road, N/kN.

Figure 10 and Figure 11 manifest that the difference between the calculations and actual measured values varies from 0.32 to 0.55 in the loaded direction and 0.34 to 0.52 in the empty direction; however, the proportion is comparatively small.

Dump road in loaded direction

T = 254.87 + 72.88 ∗ L − 1457.53 ∗ w (34)

Dump road in empty direction

T = − 1040.43 + 448.69 ∗ L 2 − 16221.3 ∗ w 2 + 1304.72 ∗ L       − 8663.95 ∗ L ∗ w + 9209.55 ∗ w (35)

The turning radius and the slope of the dump road are relatively small, for this

reason, the regression model should be determined by including only two variables: rolling resistance and the road length.

The regression models emphasize that one unit increase of rolling resistance is attributed to a reduction of 1457.53 seconds movement time in loaded direction. Simultaneously, one kilometer increase of the road length is the cause of an increase in the movement time for 72.88 seconds and 36.25 seconds in the loaded direction and the empty direction respectively. As a result, it is necessary to define the road exactly as the length increases. Figure 12 and Figure 13 show the comparison of the calculated and measured values of the defined models in the loaded and empty direction.

This section measures the waiting time of the excavator, spotting time, loading

time, dumping time, and dumping spot time. The experimental measurement exemplifies the combination of Excavator R9250 and Truck CAT785, and the results are displayed in Table 8.

It is affirmed that waiting usually takes longer time than most of the other processes. Moreover, the difference between the minimum and the maximum records of the waiting time appears extremely large. Thereby, it is necessary to optimize the combination of trucks and shovels.

Corresponding to Table 9, the difference between the actual and mathematical model of the mean time is 0.82 seconds. Regarding the errors, the absolute error of 0.82 seconds with the relative error of 2.51 percent confirms the probability value of the mathematical models. Table 10 shows the total cycle times of the dump trucks.