# Influence of Crushed Rock Properties on the Productivity of a Hydraulic Excavator

^{*}

## Abstract

**:**

## Featured Application

**The presented methodology is a relatively fast and accurate method that provides solid information of the influence of crushed rock properties on the productivity of a hydraulic excavator. The methodology has been tested in quarries of crushed stone but is also applicable to geotechnics, construction works, and other earthworks where hydraulic excavators are used.**

## Abstract

## 1. Introduction

^{3}/h) by monitoring two independent variables, engine speed and bucket cut depth (BCD), in an excavator working with loose dry sand. It has been found that BCD and engine speed can affect the fuel efficiency and productivity of a hydraulic excavator in a way that a half-filled bucket (50% BCD) can have an effect of 30% higher productivity, 24% saving on fuel (l/kg), and 62% more sand moved per hour, in addition to the amount of fuel consumed. Except for granulometric composition, the productivity of the excavator will indubitably depend on the water content of the material. A simple explanation of this is the fact that if the quantity of water is greater, the bucket filling factor will be lower because part of the constructional bucket volume is filled by water [28]. Furthermore, the moisture in some materials causes the appearance of stickiness, resulting in a longer dumping time of the bucket that is longer than the cycle time of the excavator. On the other hand, the moisture in coherent material directly influences the increase in the bucket fill factor.

## 2. Materials and Methods of Field Research

## 3. Calculation of the excavator’s Productivity

_{f})/T

_{c},

^{3}/h, V is the geometrical volume of the excavator bucket in m

^{3}, k

_{f}is the bucket fill factor, and T

_{c}is duration of the cycle in seconds.

#### Geometrical Volume of the excavator’s Bucket

## 4. Results and Discussion

#### 4.1. Factors Influencing Excavator Productivity

_{f}= V

_{a}/V,

_{a}is the actual volume of material in the bucket and V is calculated the geometrical volume.

_{m}, can be expressed by loosening factor k

_{l}with Equation (3):

_{m}= V

_{a}k

_{l},

_{l}= V

_{m/}(V k

_{f}),

_{l}is the loosening factor, V

_{m}is the measured volume of the bucket load, V is the geometrical volume of the bucket calculated by the measured angle of repose and ISO calculation procedure, and k

_{f}is the bucket fill factor.

_{l}= 1.55) and the mean swell factor from Table 2 (k

_{s}= 1.5), they are evidently similar. The loosening factor for overburden material at quarry Žervanjska is the same as the swell factor (k

_{l}= k

_{s}= 1.4). Figure 5 plots dependencies of fill factor on swell factor based on data shown in Table 2.

^{2}= 0.6483). All trend lines showed a decreasing trend, i.e., with increased swell factors, fill factors decreased. Based on the shown dependencies, it is possible to assume the bucket fill factor if the swell factor is known.

#### 4.2. Analysis of the excavator Productivity Determinants

_{Vm}—productivity calculated by field-measured volume of the material in the bucket and Q

_{ISO}—calculated by the ISO procedure of the bucket volume calculation, and Q

_{CECE}—calculated by the CECE procedure of the heaped bucket volume calculated by expression (5):

_{ISO,CECE}= (3600 V k

_{f}k

_{l})/T

_{C},

_{Vm}= b

_{1}x

_{1}+ b

_{2}x

_{2}+ … + b

_{n}x

_{n}+ Intercept

_{r}and d

_{80}have the most significant degree of correlation with all other variables, while d

_{50}correlates the least with all other variables. It was determined by conducted analysis that, between the combinations of two properties, largest influence on productivity of the excavator was a combination of the slew angle of excavator A

_{T}and the coefficient of uniformity of particle size distribution n.

_{T}and coefficient of uniformity n. It can be seen from standardized regression coefficients b* that coefficient of uniformity n has a larger influence on excavator productivity. The probability value of error p of the assumed regression model shows that the probability of error is less than 4.601%, from which it can be concluded that the dependence of the excavator productivity on analyzed material characteristics is significant given the usual significance level of 5%. The intercept of the regression plane on the z axis and coefficient n are also significant.

_{vm}= 354.3595 − 0.8297 A

_{T}+ 52.6848 n,

_{vm}= -1.0764 A

_{T}− 4.0188 A

_{r}+ 62.2419 n + 513.5846,

_{vm}= − 0.9973 A

_{T}− 6.8447 A

_{r}− 0.2520 d

_{80}+ 62.7602 n + 649.3469,

_{vm}= 6.44 A

_{T}− 223.01 A

_{r}-31.72 d

_{80}+ 22.45 X

_{c}+ 127.99 n + 10574.19,

^{2}is 0.995984, there is a reasonable suspicion that overfitting occurred in this model. Therefore, the estimation equation will very well approximate the initial data on which it is based. It is likely that it would not be as good as the general model by which Q

_{vm}could be estimated. Besides, the cross-correlation of the independent variables shown in Table 5 allows the rejection of independent variables. Testing the dependence of the productivity on the combination of the two studied properties already yielded a significantly small mean absolute deviation of the productivity calculated by the measured values. The smallest mean absolute deviation of productivity calculated using the two studied properties was obtained using the equation on the dependence of the productivity on the slew angle A

_{T}and coefficient of uniformity of the heap particle size distribution n. The obtained results indicate that excavator productivity is highly dependent on the material granulometric properties. It can be assumed that equation (7) is the best model for estimating Q

_{vm}.

## 5. Limitations and Future Directions

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Determination of rock size distribution parameters: (

**a**) digital image; (

**b**) rock particle size diagram.

**Figure 4.**SAE and ISO excavator bucket rating [32].

**Figure 8.**Multiple regression analysis of the dependence of the excavator productivity on the slew angle of the excavator and the coefficient of uniformity of the particle size distribution.

Quarry | Excavator | Material | Task | A_{T}[°] | V_{m}[m ^{3}] | A_{r}[°] | T_{c}[s] | n | X_{c}[mm] | d_{50}[mm] | d_{80}[mm] |
---|---|---|---|---|---|---|---|---|---|---|---|

Žervanjska | Liebherr R944C | Overburden (wet) | Heap shifting | 70 | 2.37 | 49 | 14.23 | 6.59 | 30.1 | 29.07 | 32 |

Zaprešićki Ivanec | Fiat—Hitachi EX355 | Blasted dolomite rock (wet) | Heap shifting | 60 | 2.28 | 48.6 | 13:49 | 3.87 | 1.305 | 1.242 | 1.3 |

Gradna | Renders RKE 2600 | Blasted dolomite rock (wet) | Truck- shovel | 35 | 2.23 | 44.0 | 22.70 | 1.51 | 34.024 | 25.7 | 50 |

Škrobotnik | Komatsu PC 340 NLC | Blasted dolomite rock (wet) | Crusher- shovel | 130 | 1.95 | 23.5 | 20.14 | 1.274 | 128.984 | 96.08 | 280 |

Hruškovec | CAT 330D | Blasted diabase rock (wet) | Truck- shovel | 171 | 2.09 | 39.5 | 27.62 | 1.318 | 91.896 | 67.6 | 152 |

Špica | CAT 336E | Blasted limestone rock (dry) | Truck- shovel | 98 | 2.05 | 29.2 | 18.09 | 1.485 | 217.461 | 162.4 | 295 |

Očura | Liebher R944C | Blasted dolomiterock (dry) | Truck- shovel | 110 | 2.03 | 44.1 | 28.21 | 1.581 | 67.766 | 54 | 92 |

_{T}—slew angle of the excavator; Vm—measured volume of material in the bucket; Ar—angle of repose; Tc—mean duration of the excavator cycle; n—coefficient of uniformity of the particle size distribution; Xc—characteristic particle size; D50—50% of particles are smaller than this dimension.

Source | Material | Fill Factor | Swell Factor |
---|---|---|---|

John Deere | Wet Earth, Loam, Sandy Clay Loam | 1.2 | 1.2–1.43 |

Natural Bed Clay, Damp Sand, Sand & Clay, Lime Rock w/Fines | 1.1 | 1.05–1.33 | |

Rock and Earth--25%/75%, Dry Clay, Dry Earth, Topsoil | 1.0 | 1.25–1.56 | |

Rock and Earth--50%/50% | 0.95 | 1.29–1.38 | |

Rock and Earth--75%/25% | 0.9 | 1.25–1.42 | |

Dry Sand | 0.9 | 1.11–1.13 | |

Broken limestone | 0.8 | 1.63–1.70 | |

Caterpillar | Moist loam or sandy clay | 1.0–1.1 | 1.2–1.43 |

Sand and Gravel | 0.95–1.1 | 1.11–1.15 | |

Hard, Tough Clay | 0.8–0.9 | 1.34–1.43 | |

Rock—Well Blasted | 0.6–0.75 | 1.49 | |

Rock—Poorly Blasted | 0.4–0.5 | 1.67–1.80 | |

Komatsu | construction application | ||

Excavating natural ground of clayey soil, clay, or soft soil | 1.1–1.2 | 1.22–1.43 | |

Excavating natural ground of soil such as sandy soil and dry soil | 1.0–1.1 | 1.25–1.46 | |

Excavating natural ground of sandy soil with gravel | 0.8–0.9 | 1.18–1.41 | |

Loading blasted rock | 0.7–0.8 | 1.49–1.80 | |

mining application | |||

Excavating natural ground of clayey soil, clay, or soft soil | 1.0 | 1.22–1.43 | |

Excavating natural ground of soil such as sandy soil and dry soil | 0.95 | 1.25–1.46 | |

Excavating natural ground of sandy soil with gravel, Loading blasted rock | 0.9 | 1.18–1.80 | |

Volvo | Earth/Sandy Clay | 1.0–1.1 | 1.2–1.375 |

Hard and Compacted Clay, Sand/Gravel | 0.95–1.1 | 1.11–1.43 | |

Rock—well blasted | 0.75–0.95 | 1.49 | |

Rock—averagely blasted | 0.6–0.75 | 1.58 | |

Rock—poorly blasted | 0.4–0.6 | 1.67–1.80 | |

Liebherr | Clay and sticky material, clay, sandy loam, moist material | 1.1 | 1.1–1.43 |

Sand, sand gravel mixture, moist | 1.0–1.1 | 1.1–1.15 | |

Hard dry clay | 0.9 | 1.24–1.43 | |

Rock, well blasted | 0.85 | 1.49 | |

Rock, poorly blasted | 0.6–0.7 | 1.67–1.8 | |

Rock, deteriorated, layered shale, not blasted | 0.5–0.7 | 1.33–1.79 | |

Underwater digging of sand, gravel & sand-gravel mixtures | 0.85 | - |

Quarry | Excavator | Material | Vm [m ^{3}] | V [m ^{3}] | k_{f} | k_{l} |
---|---|---|---|---|---|---|

Žervanjska | Liebherr R944C | Overburden (wet) | 2.37 | 1.89 | 0.9 | 1.39 |

Zaprešićki Ivanec | Fiat—Hitachi EX355 | Blasted dolomite rock (wet) | 2.28 | 1.77 | 0.8 | 1.61 |

Gradna | Renders RKE 2600 | Blasted dolomite rock (wet) | 2.23 | 1.73 | 0.8 | 1.61 |

Škrobotnik | Komatsu PC 340 NLC | Blasted dolomite rock (wet) | 1.95 | 1.46 | 0.8 | 1.67 |

Hruškovec | CAT 330D | Blasted diabase rock (wet) | 2.09 | 1.72 | 0.8 | 1.52 |

Špica | CAT 336E | Blasted limestone rock (dry) | 2.05 | 1.71 | 0.8 | 1.50 |

Očura | Liebher R944C | Blasted dolomite rock (dry) | 2.03 | 1.83 | 0.8 | 1.39 |

Quarry | Excavator | A_{T}[°] | A_{r}[°] | Q_{Vm}[m ^{3}/h] | Q_{ISO}[m ^{3}/h] | Q_{CECE}[m ^{3}/h] |
---|---|---|---|---|---|---|

Žervanjska | Liebherr R944C | 70 | 49 | 600 | 573 | 491 |

Zaprešićki Ivanec | Fiat—Hitachi EX355 | 60 | 48.6 | 608 | 584 | 488 |

Gradna | Renders RKE 2600 | 35 | 44 | 354 | 357 | 302 |

Škrobotnik | Komatsu PC 340 NLC | 130 | 23.5 | 349 | 413 | 356 |

Hruškovec | CAT 330D | 171 | 39.5 | 272 | 290 | 239 |

Špica | CAT 336E | 98 | 29.2 | 408 | 478 | 399 |

Očura | Liebher R944C | 110 | 44.1 | 259 | 263 | 224 |

A_{T} | A_{r} | n | X_{c} | d_{50} | d_{80} | |

A_{T} | 1 | −0.5 | −0.43 | 0.47 | −0.31 | 0.57 |

A_{r} | −0.5 | 1 | 0.61 | −0.85 | 0.32 | −0.97 |

n | −0.43 | 0.61 | 1 | −0.53 | 0.25 | −0.59 |

X_{c} | 0.47 | −0.85 | −0.53 | 1 | −0.39 | 0.95 |

d_{50} | −0.31 | 0.32 | 0.25 | −0.39 | 1 | −0.39 |

d_{80} | 0.57 | −0.97 | −0.59 | 0.95 | −0.39 | 1 |

_{T}—slew angle of the excavator; A

_{r}—angle of repose; n—coefficient of uniformity of the particle size distribution; X

_{c}—characteristic particle size; d

_{50—80 %}of particles are smaller than this dimension

N = 7 | R = 0.88628382; R^{2} = 0.78549901; Adjusted R^{2} = 0.67824851; F (2,4) = 7.324 P < 0.04601; Std. Error of estimate: 81.529 | |||||
---|---|---|---|---|---|---|

b * | Std.Err. of b * | b | Std.Err. of b | t (4) | p−Value | |

Intercept | 354,3595 | 110.2472 | 3.21423 | 0.032458 | ||

A_{T} [°] | −0.265315 | 0.256894 | −0.8297 | 0.8034 | −1.03278 | 0.360057 |

n | 0.738543 | 0.256894 | 52.6848 | 18.3258 | 2.87490 | 0.045245 |

^{2}—Coefficient of determination; Adjusted R

^{2}—Adjusted coefficient of determination; F (2,4)—F-distribution; p−Probability value of error; b—regression coefficients; b*—standardized regression coefficients

**Table 7.**Multiple regression analysis of dependence of the excavator productivity Q

_{vm}on analyzed determinants.

Mark Equation | Regression Summary for Dependent Variable: Excavator Productivity in Loose State of Material Q _{vm} (m^{3}/h) | Mean abs. Deviation (m ^{3}/h) |
---|---|---|

(7) | R = 0.886284; R^{2} = 0.785499; Adjusted R^{2} = 0.678249; F (2,4) = 7.324;p < 0.04601; Std. Error of estimate: 81.529 | 54.75 |

(8) | R=0.909546; R^{2}=0.8272741; Adjusted R^{2}= 0.6545482; F (3,3) = 4.7895;p < 0.11534; Std. Error of estimate: 84.479 | 44.98 |

(9) | R = 0.910839; R^{2} = 0.829628; Adjusted R^{2} = 0.488884; F (4,2) = 2.4348;p < 0.31172; Std. error of estimate: 102.76 | 47.19 |

(10) | R = 0.999665; R^{2} = 0.999331; Adjusted R^{2} = 0.995984; F (5,1) = 298.63;p < 0.0439; Std. error of estimate: 9.1082 | 2.82 |

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**MDPI and ACS Style**

Kujundžić, T.; Klanfar, M.; Korman, T.; Briševac, Z. Influence of Crushed Rock Properties on the Productivity of a Hydraulic Excavator. *Appl. Sci.* **2021**, *11*, 2345.
https://doi.org/10.3390/app11052345

**AMA Style**

Kujundžić T, Klanfar M, Korman T, Briševac Z. Influence of Crushed Rock Properties on the Productivity of a Hydraulic Excavator. *Applied Sciences*. 2021; 11(5):2345.
https://doi.org/10.3390/app11052345

**Chicago/Turabian Style**

Kujundžić, Trpimir, Mario Klanfar, Tomislav Korman, and Zlatko Briševac. 2021. "Influence of Crushed Rock Properties on the Productivity of a Hydraulic Excavator" *Applied Sciences* 11, no. 5: 2345.
https://doi.org/10.3390/app11052345