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Utilizing regression models to find functions for determining ripping production based on laboratory tests
Accepted Manuscript Utilizing regression models to find functions for determining ripping production based on laboratory tests Edy Tonnizam Mohamad, Danial Jahed Armaghani, Amir Mahdyar, Ibrahim Komoo, Khairul Anuar Kassim, Arham Abdullah, Muhd Zaimi Abd Majid PII: DOI: Reference:
S0263-2241(17)30471-2 http://dx.doi.org/10.1016/j.measurement.2017.07.035 MEASUR 4875
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
9 September 2015 18 January 2017 20 July 2017
Please cite this article as: E.T. Mohamad, D.J. Armaghani, A. Mahdyar, I. Komoo, K.A. Kassim, A. Abdullah, M.Z.A. Majid, Utilizing regression models to find functions for determining ripping production based on laboratory tests, Measurement (2017), doi: http://dx.doi.org/10.1016/j.measurement.2017.07.035
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Utilizing regression models to find functions for determining ripping production based on laboratory tests Edy Tonnizam Mohamad1, Danial Jahed Armaghani2*, Amir Mahdyar3, Ibrahim Komoo4, Khairul Anuar Kassim5, Arham Abdullah6, Muhd Zaimi Abd Majid7
1
Centre of Tropical Geoengineering (GEOTROPIK), Faculty of Civil Engineering, University Teknologi
Malaysia, 81310 UTM Johor Bahru, Malaysia. Email: [email protected]. 2
* Department of Civil and Environmental Engineering, Amirkabir University of Technology, 15914,
Tehran, Iran. Email: [email protected]. Tel.: +98 911 1574644 (Corresponding Author). 3
Department of Structure and Material, Faculty of Civil Engineering, Universiti Teknologi Malaysia
(UTM), 81310, Skudai, Johor, Malaysia. Email: [email protected]. 4
Chairman of South East Asia Prevention Research Institute (SEADPRI), Universiti Kebangsaan
Malaysia, 43600 Bangi, Selangor, Malaysia. Email: [email protected]. 5
Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi
Malaysia, 81310 UTM Skudai, Johor, Malaysia. Email: [email protected]. 6
Department of Structure and Material, Faculty of Civil Engineering, Universiti Teknologi Malaysia
(UTM), 81310, Skudai, Johor, Malaysia. Email: [email protected]. 7
UTM Construction Research Centre, Institute for Smart Infrastructure and Innovative Construction
(ISIIC), Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia. Email: [email protected].
1
Abstract The selection of suitable overburden loosening method has a crucial importance in several applications of geotechnical engineering. Factors such as rock properties and environmental constrains play a significant role in the selection of the needed equipment for overburden loosening. This paper presents several new models/equations for prediction of ripping production (Q) using rock material properties. To this end, three sites in Malaysia were selected and a total of 52 direct ripping tests were conducted in Johor state on sandstone and shale rock types. In addition, using the collected block samples, point load test, Brazilian test, slake-durability test, p-wave velocity test and uniaxial compressive strength test were also carried out in the laboratory. Numerous equations have been proposed to predict Q considering simple regression, linear multiple regression (LMR), and non-linear multiple regression (NLMR) models. Simple regression analysis indicated that the relationships between rock material properties and Q were meaningful and acceptable. Furthermore, both LMR and NLMR equations indicated similar performance capacity in predicting Q. Nevertheless; the use of NLMR equations resulted in prediction performance with higher accuracy in estimating Q compared to LMR equations. Keywords: Ripping production, Laboratory test, Simple regression analysis, Linear multiple regression, non-linear multiple regression.
1. Introduction For excavating the ground surface, three main methods, i.e., digging, ripping, and blasting are used to break or loosen the ground. 'Excavatability' is a term referring to the capability of a method in breaking up the ground into more manageable sizes. Primarily, the ground loosening mechanisms applied to surface excavation fall into two types: mechanical methods and blasting methods. The former comprises direct digging and ripping. Digging, which is done by the excavator where the ground is softer [1], refers to the cutting and displacement process that is performed using a blade or bucket. Whereas ripping refers to 2
breaking harder ground using dragging tines of a bulldozer. Ripping should be taken into account as the final mechanical method prior to blasting. Ripping is an economical and efficient way to be used in areas whose hard materials are homogeneous, with a predictable geology [2]. A number of rippability models are available in literature, which can be used for determining the rocks rippabilities. The models are classified mainly into two groups: direct and indirect models. Normally, the direct ripping runs are carried out in cases where the field consists of dozer. In the indirect models, material properties and rock mass are used to predict rippability [3, 4]. In cases where direct ripping runs are not applicable, it is recommended to make use of rock mass and material properties for the prediction of the rocks rippability; this mainly because such methods can be used easily [4]. In terms of rock material, several factors including physical properties and strength have been introduced as the most influential parameters on rippability in various studies. In the generation of a fracture mechanism during ripping, both compressive and tensile failures of rock are involved. According to Singh et al. [5, 6], effect of tensile strength on ripping production is slightly higher than compressive strength. Hardy and Goodrich [7] noted that in highly fractured rock masses with high intact strength, p-wave velocity can give a good indication of rippability. The degree and density of material compaction are the influential factors in the velocity of the seismic shock wave. A method of rock excavation based on point load strength of intact rock was developed in the study conducted by Franklin et al. [8]. Atkinson [9] proposed a model for ease of excavation in different rock types based on the velocity of longitudinal waves in the rock mass. McLean and Gribble [10] used the results of UCS and Schmidt hammer rebound number in predicting rocks’ rippability. Karpuz [11] and Basarir and Karpuz [3] proposed a rippability classification system for coal measures and marls for use in lignite mines. This was based on the seismic p-wave velocity, the point load index or uniaxial compressive strength, and the Schmidt hammer hardness. Moreover, Based on the P-wave seismic velocity for a wide variety of rocks, ripper performance charts have been proposed [12, 13]. In another study based on point load strength and the geological strength index (GSI), Tsiambaos and Saroglou [14] proposed a new classification in order to 3
ease the rock mass excavation. Summary of used rock material properties for excavation assessment by previous researchers is presented in Table 1. Although a number of models are available for prediction of excavatability, there is a lack of any world accepted model due to the limitations in applicability of any specific model to a specific geological environment. Moreover, lack of awareness or difficulties in determining input parameters in the past case studies could be another reason [14]. Therefore, there is still a need to propose a practical classification/model for predicting rock excavatability.
This study is aimed to develop several
models/equations for predicting ripping production (Q) based on results of rock material properties. To achieve this aim, sufficient direct ripping tests were conducted in various weathering zones. In addition, relevant rock material properties were determined in the laboratory.
2. Field and Laboratory Tests 2.1 Ripping Tests In order to achieve the aim of this study, 52 ripping tests were conducted on two rock types namely sandstone and shale with weathering zones in the range of slightly weathered to highly weathered. Bukit Indah, Mersing, and Desa Tebrau in Johor state of Malaysia were selected to perform the test, which their locations are shown in Figure 1. During conducting this study, the excavation works were under progress; as a result, the actual performance of ripping could be measured. During the study, these sites were being reduced down to the required platform level by using a ripping machine. To measure the penetration depth of ripper tine, the shank was painted every 10 cm with a different colour. Thus, by just observing the painted colour, the ripper depth will reflect the ease and efficiency of ripping in that run. The distance between the shank and the disturbed material boundaries was observed both during ripping and after ripping. The ripped material width was performed through measurement of the breakage that is observable from both right and left of the ripping line. To maintain consistency of 4
ripping result, the same class of ripper was used at all sites i.e. Caterpillar D9H (CAT D9). Main specifications of the CAT D9 are given in Table 2. The ripping assessment was carried out in one ripping run, with no consideration of the maneuvering time, in order to evade inconsistency of the ripper performance that may occur because of the operator performance. As a result, the ripping performance depended merely on the machine and the rock mass properties with no human factor. For the assessment of the ease of ripping, during the ripping operation, changes occurred in the shank position, depth, and loss of traction were taken into consideration.
2.2 Monitoring of Ripping Test in Sandstone In case of sandstone in slightly weathering areas, penetration depth was greatly dependent upon joint spacing. Similar to zone III, three out of seven lines were unrippable. Note that to determine the rippability, particularly in case of the joint spacing, the discontinuities condition is of a great significance. Findings showed that more than 0.34 m of joint spacing did not allow the shank to penetrate into these materials; although, in cases where there is less than 0.29 m of joint spacing, the shank can penetrate for up to 0.7 m. This is noticeable that the ripping line width increases with an increase in the penetration depth. In case of these materials with higher strength, the discontinuity characteristic, especially the joint spacing, has a significant effect on determination of the rippability of the material. In this sense, two other important factors are the direction of ripping and the joint fill material. In case of low discontinuity spacing material, the crushing mechanism was detected. For weaker material in the zone IV, the depth of penetration was dependent, mainly on two issues: the discontinuity characteristics and joint spacing. Those discontinuities filled using iron pan minerals with more than 4 cm in thickness did not allow the ripper shank penetration, hence not monitoring any production. Lifting and crushing mechanisms were detected in this medium strength material with wide joint spacing. The penetration did not occur in the
5
zone IV that was consisted of materials with joint spacing of more than 0.55 m, and five cm-thick iron pan. 2.3 Monitoring of Ripping Test in Shale In comparison with sandstone, shale is relatively easier to rip. In general, tine penetrates further into weaker material. In areas in which joint spacing is wider, higher resistance is observed, hence expecting lower productivity. In case of low strength material that had been as low as or less than 0.5 m of joint spacing, the ploughing and lifting mechanism was observed particularly within the weathering zone IV. As observed in higher strength shale within the zone IV and lower, direction of ripping and joint spacing have a great effect since they can be used to observe if the tine is capable of penetrating or not. These are comparable to sandstone with analogous weathering zone. The tine occasionally is not able to penetrate the material initially, especially when the material is stronger; although since the developments in the machine, weight of the machine associated with the tine's penetration strength has made the ripping process more easy with the joints assisting. Generally, the range of ripper depth was between 0 and 1.2 m, while that of the ripping width was between 0 and 1.6 m. With lower weathering zone, the ripping width and depth reduced, which indicated a relationship between the ripping depth and weathering zone. The materials tested by direct ripping are briefly shown in Table 2. Results obtained from the test are presented as well as the types of material with the corresponding weathering zones.
2.4 Laboratory Tests In order to establish several models for Q prediction, more than 70 sandstone and shale block samples were taken from the mentioned sites and then transferred to the laboratory. All sample preparation and
6
laboratory test procedures in this study are according to ISRM [26]. Tests conducted were uniaxial compressive strength test, Brazilian test, p-wave velocity test, point load test and slake-durability test. Sample preparation consists of cutting and trimming of rock cores to obtain test samples of specific shape and size. A total of 52 samples were prepared for each type of test. For the UCS test, samples were cores of 54 mm diameter and height about 2.5 times their diameter. The end surfaces of the UCS samples were also lapped. This is to achieve the required surface smoothness and to ensure that both end surfaces are perpendicular to the core axis. As the failed samples along fractures or defects may not characterize the intact rock strength, these samples were extracted and not counted in the data set. Disc-shaped samples, with 54 mm diameter and thickness of about 0.5 times diameter were used for doing the Brazilian test. Moreover, aggregates/lumps (40 to 60 gr each) were prepared for the slake-durability test. P-wave tests were conducted on the same sample prepared for UCS test before that. In addition, irregular lump specimens were used for conducting point load tests. As example, several equipment for conducting pwave velocity test, slake –durability test and UCS test are shown in Figures 3 to 5, respectively. Moreover, Figures 6 to 8 display the failed samples after conducting point load test, Brazilian test and UCS test, respectively. In total, a database comprising of 52 datasets was prepared from the laboratory tests for predicting Q. As a result, the established datasets have been used to propose several models by employing several techniques and then, introduced models are compared to each other for choosing the best model among them for predicting Q. In these models, the developed datasets including point load strength index (Is(50)), Brazilian tensile strength (BTS), second-cycle slake durability index (Id2), p-wave velocity (Vp), uniaxial compressive strength (UCS) were utilized as model predictors for purposed models. Basic statistical descriptions of the measured parameters in the sites and laboratory are given in Table 3. It is worth mentioning that all observations and tests conducted in this study are in accordance with ISRM [26] suggested method.
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3. Estimation of Ripping Production In this section based on obtained laboratory tests, a series of analysis were conducted to Q. In this regard, initially; simple regression analysis was applied and several simple equations were proposed and then by using all laboratory results, linear and non-linear multiple regression models were developed for Q estimation. The following sections describe the mentioned analyses and their results in predicting Q.
3.1 Simple Regression To investigate the impact of the predictor or input parameters, simple regression analyses were carried out between Q and other parameters such as Is(50), Id2, BTS, UCS, and Vp. A variety of equation types, e.g., exponential, linear, power and logarithmic were conducted to achieve equations with higher capacity of performance. For the purpose of the present research, variance account for (VAF), coefficient of determination (R2), and root mean square error (RMSE) were computed in a way to control the capacity performance of all of the developed models:
(1)
VAF = [1-
(2)
RMSE =
(3)
where y′ and y stand for the predicted and measured values, respectively, ỹ denotes the mean of the y values, and N signifies the total number of data. If and only if VAF = 100, R2 = 1, and RMSE = 0, then the model is excellent. Table 4 displays the equations chosen for the prediction of Q by means of the input parameters mentioned earlier in addition to their performance indices. As it can be observed in Table 4, logarithmic, exponential, linear, logarithmic, and exponential equations provide the best results in the 8
prediction of Q by means of BTS, Is(50), Vp, Id2, and UCS, respectively. The R2 values of the developed equations were achieved as 0.504, 0.592, 0.574, 0.589, and 0.627, respectively. Figures 9-13 present the purposed relationships between Q and relevant parameters of the rock. The results revealed that these relationships are statistically meaningful but in order to get higher-performance models in practice for prediction of Q, multi-input parameters may be needed. In this regard, two modelling techniques i.e. linear multiple regression (LMR) and non-linear multiple regression (NLMR) analysis were also constructed and developed.
3.2 Linear and Non-Linear Multiple Regression Models The relationship between different variables can be extracted using regression analysis that is known as a commonly-applied statistical tool. This technique determines systematically the relationship between dependent variable (output) and independent variable (predictor) in the form of regression function [27]. According to Ceryan et al. [28], as long as inputs have acceptable correlations or determinations with output(s), the inputs are applicable as predictors to the predictive models. Multiple regression exists in two different types, namely linear and non-linear. In the following paragraphs, both types are explained. The LMR analysis determines values of parameters for a function, causing the function to best matched with a provided set of data observations. In this technique, the function is a linear (straight-line) equation. Conducting a least squares fit, LMR makes suitable solutions to engineering problems. It causes the construction of simultaneous equations by forming the regression matrix. The use of this technique results in having a number of coefficients suggested by the backslash operator [29]. In case of simple bivariate regression, in which there is a single independent variable, prediction of the dependent variable can be done by taking the independent variable into consideration using Equation (4): (4)
9
where a signifies constant, x and y stand for independent and dependent variables, respectively. This equation can be extended to a numerous-variable concept as presented in the following equation: (5) where
represent various independent variables for the prediction of y.
As a solution to some problems arisen in geotechnical engineering fields, the LMR technique has been employed extensively. In [27], an LMR equation is introduced for predicting the rock fragmentation that may occur due to blasting operations. The rock material's shear strength parameters (i.e., c and ϕ) were predicted by Armaghani et al. [30] by means of the LMR technique. An equation was also developed by Hajihassani et al. [31], using the LMR technique in order to estimate the ground vibrations occurred due to quarry blasting. A commonly-used approach for achieving a non-linear relationship between dependent and independent variables is the use of non-linear multiple regression (NLMR). Contrasting the conventional linear regression, NLMR is capable of predicting a model with arbitrary relationships between the input and output variables [32]. The line of the best fit is a line minimizing sum of squares of deviation of various data points from the line. Note that both linear and non-linear relationships, for instance, power and exponential, can be applied to the NLMR technique. In the context of geotechnical engineering field, NLMR establishes mathematical formulas in a way to predict the dependent variables based on identified independent variables. NLMR was also employed by Yagiz et al. [32] and Gong and Zhao [33] to predict the TBM performance. In another project, Yagiz and Gokceoglu [34] introduced an NLMR equation that could estimate the rock brittleness. However, Shirani Faradonbeh et al. [35] developed the NLMR model to predict the back-break occurring due to blasting. In this research, based on the results of laboratory study, both LMR and NLMR techniques are taken into account for developing multiple novel equations for the UCS prediction. To this end, as recommended in literature (see [32] and [36-38]), five datasets were randomly chosen for training and testing in such a way 10
that multiple regression models could be developed. The use of some data for testing is an idea for the evaluation of efficiency of the developed model. Although Swingler [39] recommended the use of only 20% of the whole datasets for testing purposes, the Looney's [40] suggestion was 25%. As a result, in the present study, 42 out of 52 datasets (i.e., 80%) were randomly selected for development of the models, and 10 other datasets (20%) were applied to testing the models. Based on the established datasets, five LMR equations have been developed to propose Q as presented in Table 5. In developing these models, Is(50), BTS, Id2, Vp and UCS were considered as model inputs and then the Q values were estimated as a function of the relevant rock properties. In Table 5, coefficient of determination values, ranging from 0.681 to 0.751 were obtained for developed LMR models. Additionally, R2 values of 0.622, 0.785, 0.490, 0.796 and 0.530 were achieved for testing of five different sets, respectively. Apart from LMR models, NLMR equations were also proposed to predict Q considering the same datasets of the LMR analyses. These equations were mainly developed using simple regression functions. Table 6 shows proposed NLMR equations for Q prediction and their performance capacities in terms of R2 of training and testing datasets. Considering training datasets of the developed NLMR equations, R2 values vary between 0.688 and 0.768, while a range of 0.504-0.830 was obtained for testing datasets. Although results indicate similar performance capacity for both LMR and NLMR models in predicting Q of various weathering zones, NLMR equations can provide higher-performance prediction compared to LMR models.
More discussions regarding the selection of the best LMR and NLMR models are
presented in the next section. It should be mentioned that SPSS 16 as a statistical software package was used for constructing the simple regression, linear and non-linear multiple regression [41].
3.3 Evaluation of the Results
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In this section, the way to evaluate the performance of the developed models is discussed in terms of predicting Q for different weathering zones. Performing simple regression revealed the need for developing the Q predictive models with higher accuracy by means of multi-input parameters. Therefore, the LMR and NLMR models were developed. To this end, all 52 datasets were randomly divided into five datasets. Then, 5 LMR and 5 NLMR equations were developed using the constructed datasets. As mentioned before, in order to check the prediction performance of the developed models, R2, VAF and RMSE were considered and computed for training and testing datasets. Table 7 demonstrates the results obtained from R2, RMSE, and VAF of the developed LMR and NLMR models in case of five randomly chosen datasets based on training and testing. As it can be seen in Table 7, the results related to the performance indices are very similar; which makes it very difficult to select the best models. As a solution to this problem, in [36], a simple ranking method was introduced, in which a ranking value was computed and assigned separately to each training and testing dataset (see Table 7). Each of the performance indices was ordered in its own class; then, the highest rating was assigned to the best performance index. For instance, for the LMR technique, R2 values of the training datasets were 0.723, 0.687, 0.738, 0.681, and 0.751, respectively. As a result, their ratings were assigned as 3, 2, 4, 1, and 5, respectively. In case of all performance indices besides the NLMR predictive models, this procedure was iterated. Next, the ratings obtained for each of the datasets (training and testing) were separately summed up. For instance, the rating values of LMR training dataset 1 were 4 for RMSE, 3 for R2, and 3 for VAF; therefore, the performance rating was calculated as 10 (see Table 7). The concluding step to the selection of the best models is computing the total rank through summing up the rank value of each dataset (training and testing) as presented in Table 8. As it can be observed in this table, model 2 exhibits the best results in case of both NLMR and LMR methods. As it is observable by taking into consideration both training and testing datasets, the prediction performance of the selected NLMR dataset is more efficiently than that of the LMR dataset. The selected LMR and NLMR equations in predicting Q of various weathering zones are shown as follows:
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(6)
(7) Figures 14 and 15 present the developed relationship between the predicted Q and the measured one using LMR and NLMR methods, respectively. As it can be seen in these two figures, the NLMR method with R2 values of 0.708 and 0.793 for training and testing data, respectively, is the best Q predictive model.
4. Conclusions In this paper, several field and laboratory, tests were conducted in order to develop the predictive equations for estimating ripping production. 52 ripping tests were performed in three sites on weak rock types, i.e. sandstone and shale in various weathering zones ranging from slightly weathered to highly weathered using Caterpillar D9H machine (CAT D9).
For evaluation and prediction of ripping
production, several block samples were taken from the sites and various laboratory tests i.e., Brazilian, point load, slake-durability test, uniaxial compressive strength, and p-wave velocity were also conducted. By performing simple regression analysis, it was found that predictors and the Q have acceptable and meaningful relationships. Since each mentioned predictor has good relationship with the Q, multiple regression i.e. linear and non-linear models were also generated to achieve the best accurate results. In this regard, all datasets were divided to five randomly selected datasets and then 5 LMR, and 5 NLMR equations were developed to estimate ripping production. Considering model performance indices and using simple ranking method, the best LMR and NLMR equations were chosen among all constructed models. The obtained performance indices results of NLMR model are slightly higher than LMR model. The R2 equal to 0.708 and 0.793 for training and testing datasets, respectively suggests the superiority of the NLMR technique in predicting Q, while this value was obtained as 0.687 and 0.785 for LMR model. 13
It should be noted that the proposed equations in this study are designed for ripping production of shale and sandstone rock types; therefore, the use of the proposed equations for estimating Q of the other rock types is not recommended.
Acknowledgement The authors would like to extend their appreciation to the Government of Malaysia and Universiti Teknologi Malaysia for the FRGS grant No. 4F406 and for providing the required facilities that made this research possible.
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[28] Ceryan N, Okkan U, Kesimal A (2013) Prediction of unconfined compressive strength of carbonate rocks using artificial neural networks. Environ. Earth. Sci. 68(3):807-819 [29] Khandelwal M, Monjezi M (2013) Prediction of backbreak in open-pit blasting operations using the machine learning method. Rock Mech Rock Eng 46(2):389-396 [30] Jahed Armaghani D, Hajihassani M, Yazdani Bejarbaneh B, Marto A, Tonnizam Mohamad E (2014b) Indirect measure of shale shear strength parameters by means of rock index tests through an optimized artificial neural network. Measurement 55:487-498 [31] Hajihassani M, Jahed Armaghani D, Marto A, Tonnizam Mohamad E (2014) Ground vibration prediction in quarry blasting through an artificial neural network optimized by imperialist competitive algorithm. Bull Eng Geol Environ doi: 10.1007/s10064-014-0657-x [32] Yagiz S, Gokceoglu C, Sezer E, Iplikci S (2009) Application of two non-linear prediction tools to the estimation of tunnel boring machine performance. Eng. Appl. Artif. Intel. 22(4):808-814 [33] Gong QM, Zhao J (2009) Development of a rock mass characteristics model for TBM penetration rate prediction. Int J Rock Mech Min Sci 46(1):8–18 [34] Yagiz S, Gokceoglu C (2010) Application of fuzzy inference system and nonlinear regression models for predicting rock brittleness. Expert Syst Appl 37(3): 2265-2272 [35] Shirani Faradonbeh, R, Monjezi, M., Jahed Armaghani, D (2015). Genetic programing and nonlinear multiple regression techniques to predict backbreak in blasting operation. Engineering with Computers, DOI 10.1007/s00366-015-0404-3 [36] Zorlu K, Gokceoglu C, Ocakoglu F, Nefeslioglu HA, Acikalin S (2008) Prediction of uniaxial compressive strength of sandstones using petrography-based models. Eng. Geol 96(3):141-158 [37] Jahed Armaghani D, Tonnizam Mohamad E, Hajihassani M, Yagiz S, Motaghedi H (2015a) Application of several non‑ linear prediction tools for estimating uniaxial compressive strength of granitic rocks and comparison of their performances. Eng Comput DOI 10.1007/s00366-015-04105
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[38] Jahed Armaghani D, Mohamad ET, Hajihassani M, Abad SANK, Marto A, Moghaddam MR (2015b) Evaluation and prediction of flyrock resulting from blasting operations using empirical and computational methods. Eng. Comput doi: 10.1007/s00366-015-0402-5 [39] Swingler K (1996) Applying Neural Networks: A Practical Guide. Academic Press, New York [40] Looney CG (1996) Advances in feed-forward neural networks: demystifying knowledge acquiring black boxes. IEEE Transactions on Knowledge and Data Engineering 8 (2):211–226 [41] SPSS Inc. (2007). SPSS for Windows (Version 16.0). Chicago: SPSS Inc List of Tables: Table 1 Summary of the used rock material properties for excavation assessment Table 2 Specification of Caterpillar D9 Table 3 Monitored ripping tests at Bukit Indah site in different weathering zones Table 4 Summary of the measured parameters and their details Table 5 Selected equations to predict Q Table 6 Proposed LMR equations for 5 randomly selected datasets to predict Q Table 7 Proposed NLMR equations for 5 randomly selected datasets to predict Q Table 8 Results of performance indices for each model and their rank values Table 9 Total rank values for developed predictive techniques
18
List of Figures: Figure 1. Location of studied areas Figure 2. Ripping process at Bukit Indah site by a CAT D9 ripper Figure 3. Equipment for conducting p-wave velocity tests Figure 4. Equipment for conducting slake –durability tests Figure 5. Equipment for conducting UCS tests Figure 6. Failure due to conducting point load test Figure 7. Failure due to conducting Brazilian test Figure 8. Failure due to conducting UCS test Figure 9. Relationship between point load strength index and ripping production Figure 10. Relationship between Brazilian tensile strength and ripping production Figure 11. Relationship between slake durability index and ripping production Figure 12. Relationship between p-wave velocity and ripping production Figure 13. Relationship between uniaxial compressive strength and ripping production Figure 14. Measured and predicted values of Q by LMR equation for training and testing datasets Figure 15. Measured and predicted values of Q by NLMR equation for training and testing datasets
19
20
21
22
23
24
25
26
27
28
Table 1 Summary of the used rock material properties for excavation assessment Property Reference Vp X X
UCS
Is(50)
Rn
TS
A
Caterpillar [16] Atkinson [12] X X Franklin [11] X Bailey [18] Weaver [19] X X Church [15] X Kirsten [20] X Muftuoglu [21] X X Abdullatif et al. [22] X X Smith [23] Anon [24] X Singh et al. [9] X X X X (PL Bozdag [25] X T) Karpuz [14] X X X MacGregor et al. [26] X X Pettifer and Fookes [27] X Kramadibrata [28] X X X Hadjigeorgiou and Poulin [1] X Basarir and Karpuz [3] X X X X X X X Basarir et al. [4] 11 10 9 3 1 2 Popularity (No.) Remarks: Vp: p-wave velocity, UCS: uniaxial compressive strength, Is(50): point load strength index, Rn: Schmidt hammer rebound number, TS: tensile strength, A: abrasiveness.
29
Table 2. Specification of Caterpillar D9 Specification
Value
Flywheel power
410hp/ 306kW
Operating Weight
47900 kg 4.24 m2
Ground contact area Maximum penetration force (shank vertical)
153.8 kN
Pry out force
320.5 kN
30
Table 3 Monitored ripping tests at Bukit Indah site in different weathering zones Material type Sandstone
Shale
Weathering zone II III IV II III IV
31
No. of ripping test 3 4 7 2 4 9
Table 4 Summary of the measured parameters and their details Parameter
Unit
Symbol
Category
Min
Max
Mean
Point load strength index
MPa
Is(50)
Predictor
0.15
3.93
1.39
Brazilian tensile strength
MPa
BTS
Predictor
0.83
4.12
2.35
%
Id2
Predictor
31.3
97.5
69.8
P-wave velocity
m/s
Vp
Predictor
1455
2994
2266
Uniaxial compressive strength
MPa
UCS
Predictor
8.35
67.5
24.4
Q
Output
45.9
1136.1
517.5
Second-cycle slake durability index
Ripping production
3
(m /h)
32
Table 5 Selected equations to predict Q Predictor
Equation Type
Is(50) BTS Id2 Vp UCS
Exponential Logarithmic Logarithmic Linear Exponential
Developed Equation
33
R2
RMSE
VAF
0.592 0.504 0.589 0.574 0.627
190.738 190.436 173.278 176.419 191.057
51.683 50.374 58.914 57.411 51.336
Table 6 Proposed LMR equations for 5 randomly selected datasets to predict Q
R2 Training
R2 Testing
1
0.723
0.622
2
0.687
0.785
3
0.738
0.490
4
0.681
0.796
5
0.751
0.530
Dataset No.
Proposed Equation
34
Table 7 Proposed NLMR equations for 5 randomly selected datasets to predict Q
R2 Training
R2 Testing
1
0.754
0.574
2
0.708
0.793
3
0.760
0.504
4
0.688
0.830
5
0.768
0.576
Dataset No.
Proposed Equation
35
Table 8 Results of performance indices for each model and their rank values Method
LMR
NLMR
72.302 68.699 73.817 68.055 75.056
Rating for R2 3 2 4 1 5
Rating for RMSE 4 2 5 1 3
Rating for VAF 3 2 4 1 5
Rank value 10 6 13 3 13
174.457 140.391 185.027 150.198 167.683
62.053 78.501 36.227 78.487 35.477
3 4 1 5 2
2 5 1 4 3
3 5 2 4 1
8 14 4 13 6
0.754 0.708 0.760 0.688 0.768
133.475 143.193 134.639 143.926 137.496
75.401 70.723 75.964 68.692 76.745
3 2 4 1 5
5 2 4 1 3
3 2 4 1 5
11 6 12 3 13
0.574 0.793 0.504 0.830 0.576
186.516 132.337 180.873 133.964 188.885
57.279 79.279 38.177 82.512 36.535
2 4 1 5 3
2 5 3 4 1
3 4 2 5 1
7 13 6 14 5
Model
R2
RMSE
VAF
Training 1 Training 2 Training 3 Training 4 Training 5
0.723 0.687 0.738 0.681 0.751
141.631 144.059 140.525 145.385 142.404
Testing 1 Testing 2 Testing 3 Testing 4 Testing 5
0.622 0.785 0.490 0.796 0.530
Training 1 Training 2 Training 3 Training 4 Training 5 Testing 1 Testing 2 Testing 3 Testing 4 Testing 5
36
Table 9 Total rank values for developed predictive techniques Method
LMR
NLMR
Model
Total rank
1 2 3 4 5
18 20 17 16 19
1 2 3 4 5
18 19 18 17 18
37
S0263-2241(17)30471-2 http://dx.doi.org/10.1016/j.measurement.2017.07.035 MEASUR 4875
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
9 September 2015 18 January 2017 20 July 2017
Please cite this article as: E.T. Mohamad, D.J. Armaghani, A. Mahdyar, I. Komoo, K.A. Kassim, A. Abdullah, M.Z.A. Majid, Utilizing regression models to find functions for determining ripping production based on laboratory tests, Measurement (2017), doi: http://dx.doi.org/10.1016/j.measurement.2017.07.035
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Utilizing regression models to find functions for determining ripping production based on laboratory tests Edy Tonnizam Mohamad1, Danial Jahed Armaghani2*, Amir Mahdyar3, Ibrahim Komoo4, Khairul Anuar Kassim5, Arham Abdullah6, Muhd Zaimi Abd Majid7
1
Centre of Tropical Geoengineering (GEOTROPIK), Faculty of Civil Engineering, University Teknologi
Malaysia, 81310 UTM Johor Bahru, Malaysia. Email: [email protected]. 2
* Department of Civil and Environmental Engineering, Amirkabir University of Technology, 15914,
Tehran, Iran. Email: [email protected]. Tel.: +98 911 1574644 (Corresponding Author). 3
Department of Structure and Material, Faculty of Civil Engineering, Universiti Teknologi Malaysia
(UTM), 81310, Skudai, Johor, Malaysia. Email: [email protected]. 4
Chairman of South East Asia Prevention Research Institute (SEADPRI), Universiti Kebangsaan
Malaysia, 43600 Bangi, Selangor, Malaysia. Email: [email protected]. 5
Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi
Malaysia, 81310 UTM Skudai, Johor, Malaysia. Email: [email protected]. 6
Department of Structure and Material, Faculty of Civil Engineering, Universiti Teknologi Malaysia
(UTM), 81310, Skudai, Johor, Malaysia. Email: [email protected]. 7
UTM Construction Research Centre, Institute for Smart Infrastructure and Innovative Construction
(ISIIC), Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia. Email: [email protected].
1
Abstract The selection of suitable overburden loosening method has a crucial importance in several applications of geotechnical engineering. Factors such as rock properties and environmental constrains play a significant role in the selection of the needed equipment for overburden loosening. This paper presents several new models/equations for prediction of ripping production (Q) using rock material properties. To this end, three sites in Malaysia were selected and a total of 52 direct ripping tests were conducted in Johor state on sandstone and shale rock types. In addition, using the collected block samples, point load test, Brazilian test, slake-durability test, p-wave velocity test and uniaxial compressive strength test were also carried out in the laboratory. Numerous equations have been proposed to predict Q considering simple regression, linear multiple regression (LMR), and non-linear multiple regression (NLMR) models. Simple regression analysis indicated that the relationships between rock material properties and Q were meaningful and acceptable. Furthermore, both LMR and NLMR equations indicated similar performance capacity in predicting Q. Nevertheless; the use of NLMR equations resulted in prediction performance with higher accuracy in estimating Q compared to LMR equations. Keywords: Ripping production, Laboratory test, Simple regression analysis, Linear multiple regression, non-linear multiple regression.
1. Introduction For excavating the ground surface, three main methods, i.e., digging, ripping, and blasting are used to break or loosen the ground. 'Excavatability' is a term referring to the capability of a method in breaking up the ground into more manageable sizes. Primarily, the ground loosening mechanisms applied to surface excavation fall into two types: mechanical methods and blasting methods. The former comprises direct digging and ripping. Digging, which is done by the excavator where the ground is softer [1], refers to the cutting and displacement process that is performed using a blade or bucket. Whereas ripping refers to 2
breaking harder ground using dragging tines of a bulldozer. Ripping should be taken into account as the final mechanical method prior to blasting. Ripping is an economical and efficient way to be used in areas whose hard materials are homogeneous, with a predictable geology [2]. A number of rippability models are available in literature, which can be used for determining the rocks rippabilities. The models are classified mainly into two groups: direct and indirect models. Normally, the direct ripping runs are carried out in cases where the field consists of dozer. In the indirect models, material properties and rock mass are used to predict rippability [3, 4]. In cases where direct ripping runs are not applicable, it is recommended to make use of rock mass and material properties for the prediction of the rocks rippability; this mainly because such methods can be used easily [4]. In terms of rock material, several factors including physical properties and strength have been introduced as the most influential parameters on rippability in various studies. In the generation of a fracture mechanism during ripping, both compressive and tensile failures of rock are involved. According to Singh et al. [5, 6], effect of tensile strength on ripping production is slightly higher than compressive strength. Hardy and Goodrich [7] noted that in highly fractured rock masses with high intact strength, p-wave velocity can give a good indication of rippability. The degree and density of material compaction are the influential factors in the velocity of the seismic shock wave. A method of rock excavation based on point load strength of intact rock was developed in the study conducted by Franklin et al. [8]. Atkinson [9] proposed a model for ease of excavation in different rock types based on the velocity of longitudinal waves in the rock mass. McLean and Gribble [10] used the results of UCS and Schmidt hammer rebound number in predicting rocks’ rippability. Karpuz [11] and Basarir and Karpuz [3] proposed a rippability classification system for coal measures and marls for use in lignite mines. This was based on the seismic p-wave velocity, the point load index or uniaxial compressive strength, and the Schmidt hammer hardness. Moreover, Based on the P-wave seismic velocity for a wide variety of rocks, ripper performance charts have been proposed [12, 13]. In another study based on point load strength and the geological strength index (GSI), Tsiambaos and Saroglou [14] proposed a new classification in order to 3
ease the rock mass excavation. Summary of used rock material properties for excavation assessment by previous researchers is presented in Table 1. Although a number of models are available for prediction of excavatability, there is a lack of any world accepted model due to the limitations in applicability of any specific model to a specific geological environment. Moreover, lack of awareness or difficulties in determining input parameters in the past case studies could be another reason [14]. Therefore, there is still a need to propose a practical classification/model for predicting rock excavatability.
This study is aimed to develop several
models/equations for predicting ripping production (Q) based on results of rock material properties. To achieve this aim, sufficient direct ripping tests were conducted in various weathering zones. In addition, relevant rock material properties were determined in the laboratory.
2. Field and Laboratory Tests 2.1 Ripping Tests In order to achieve the aim of this study, 52 ripping tests were conducted on two rock types namely sandstone and shale with weathering zones in the range of slightly weathered to highly weathered. Bukit Indah, Mersing, and Desa Tebrau in Johor state of Malaysia were selected to perform the test, which their locations are shown in Figure 1. During conducting this study, the excavation works were under progress; as a result, the actual performance of ripping could be measured. During the study, these sites were being reduced down to the required platform level by using a ripping machine. To measure the penetration depth of ripper tine, the shank was painted every 10 cm with a different colour. Thus, by just observing the painted colour, the ripper depth will reflect the ease and efficiency of ripping in that run. The distance between the shank and the disturbed material boundaries was observed both during ripping and after ripping. The ripped material width was performed through measurement of the breakage that is observable from both right and left of the ripping line. To maintain consistency of 4
ripping result, the same class of ripper was used at all sites i.e. Caterpillar D9H (CAT D9). Main specifications of the CAT D9 are given in Table 2. The ripping assessment was carried out in one ripping run, with no consideration of the maneuvering time, in order to evade inconsistency of the ripper performance that may occur because of the operator performance. As a result, the ripping performance depended merely on the machine and the rock mass properties with no human factor. For the assessment of the ease of ripping, during the ripping operation, changes occurred in the shank position, depth, and loss of traction were taken into consideration.
2.2 Monitoring of Ripping Test in Sandstone In case of sandstone in slightly weathering areas, penetration depth was greatly dependent upon joint spacing. Similar to zone III, three out of seven lines were unrippable. Note that to determine the rippability, particularly in case of the joint spacing, the discontinuities condition is of a great significance. Findings showed that more than 0.34 m of joint spacing did not allow the shank to penetrate into these materials; although, in cases where there is less than 0.29 m of joint spacing, the shank can penetrate for up to 0.7 m. This is noticeable that the ripping line width increases with an increase in the penetration depth. In case of these materials with higher strength, the discontinuity characteristic, especially the joint spacing, has a significant effect on determination of the rippability of the material. In this sense, two other important factors are the direction of ripping and the joint fill material. In case of low discontinuity spacing material, the crushing mechanism was detected. For weaker material in the zone IV, the depth of penetration was dependent, mainly on two issues: the discontinuity characteristics and joint spacing. Those discontinuities filled using iron pan minerals with more than 4 cm in thickness did not allow the ripper shank penetration, hence not monitoring any production. Lifting and crushing mechanisms were detected in this medium strength material with wide joint spacing. The penetration did not occur in the
5
zone IV that was consisted of materials with joint spacing of more than 0.55 m, and five cm-thick iron pan. 2.3 Monitoring of Ripping Test in Shale In comparison with sandstone, shale is relatively easier to rip. In general, tine penetrates further into weaker material. In areas in which joint spacing is wider, higher resistance is observed, hence expecting lower productivity. In case of low strength material that had been as low as or less than 0.5 m of joint spacing, the ploughing and lifting mechanism was observed particularly within the weathering zone IV. As observed in higher strength shale within the zone IV and lower, direction of ripping and joint spacing have a great effect since they can be used to observe if the tine is capable of penetrating or not. These are comparable to sandstone with analogous weathering zone. The tine occasionally is not able to penetrate the material initially, especially when the material is stronger; although since the developments in the machine, weight of the machine associated with the tine's penetration strength has made the ripping process more easy with the joints assisting. Generally, the range of ripper depth was between 0 and 1.2 m, while that of the ripping width was between 0 and 1.6 m. With lower weathering zone, the ripping width and depth reduced, which indicated a relationship between the ripping depth and weathering zone. The materials tested by direct ripping are briefly shown in Table 2. Results obtained from the test are presented as well as the types of material with the corresponding weathering zones.
2.4 Laboratory Tests In order to establish several models for Q prediction, more than 70 sandstone and shale block samples were taken from the mentioned sites and then transferred to the laboratory. All sample preparation and
6
laboratory test procedures in this study are according to ISRM [26]. Tests conducted were uniaxial compressive strength test, Brazilian test, p-wave velocity test, point load test and slake-durability test. Sample preparation consists of cutting and trimming of rock cores to obtain test samples of specific shape and size. A total of 52 samples were prepared for each type of test. For the UCS test, samples were cores of 54 mm diameter and height about 2.5 times their diameter. The end surfaces of the UCS samples were also lapped. This is to achieve the required surface smoothness and to ensure that both end surfaces are perpendicular to the core axis. As the failed samples along fractures or defects may not characterize the intact rock strength, these samples were extracted and not counted in the data set. Disc-shaped samples, with 54 mm diameter and thickness of about 0.5 times diameter were used for doing the Brazilian test. Moreover, aggregates/lumps (40 to 60 gr each) were prepared for the slake-durability test. P-wave tests were conducted on the same sample prepared for UCS test before that. In addition, irregular lump specimens were used for conducting point load tests. As example, several equipment for conducting pwave velocity test, slake –durability test and UCS test are shown in Figures 3 to 5, respectively. Moreover, Figures 6 to 8 display the failed samples after conducting point load test, Brazilian test and UCS test, respectively. In total, a database comprising of 52 datasets was prepared from the laboratory tests for predicting Q. As a result, the established datasets have been used to propose several models by employing several techniques and then, introduced models are compared to each other for choosing the best model among them for predicting Q. In these models, the developed datasets including point load strength index (Is(50)), Brazilian tensile strength (BTS), second-cycle slake durability index (Id2), p-wave velocity (Vp), uniaxial compressive strength (UCS) were utilized as model predictors for purposed models. Basic statistical descriptions of the measured parameters in the sites and laboratory are given in Table 3. It is worth mentioning that all observations and tests conducted in this study are in accordance with ISRM [26] suggested method.
7
3. Estimation of Ripping Production In this section based on obtained laboratory tests, a series of analysis were conducted to Q. In this regard, initially; simple regression analysis was applied and several simple equations were proposed and then by using all laboratory results, linear and non-linear multiple regression models were developed for Q estimation. The following sections describe the mentioned analyses and their results in predicting Q.
3.1 Simple Regression To investigate the impact of the predictor or input parameters, simple regression analyses were carried out between Q and other parameters such as Is(50), Id2, BTS, UCS, and Vp. A variety of equation types, e.g., exponential, linear, power and logarithmic were conducted to achieve equations with higher capacity of performance. For the purpose of the present research, variance account for (VAF), coefficient of determination (R2), and root mean square error (RMSE) were computed in a way to control the capacity performance of all of the developed models:
(1)
VAF = [1-
(2)
RMSE =
(3)
where y′ and y stand for the predicted and measured values, respectively, ỹ denotes the mean of the y values, and N signifies the total number of data. If and only if VAF = 100, R2 = 1, and RMSE = 0, then the model is excellent. Table 4 displays the equations chosen for the prediction of Q by means of the input parameters mentioned earlier in addition to their performance indices. As it can be observed in Table 4, logarithmic, exponential, linear, logarithmic, and exponential equations provide the best results in the 8
prediction of Q by means of BTS, Is(50), Vp, Id2, and UCS, respectively. The R2 values of the developed equations were achieved as 0.504, 0.592, 0.574, 0.589, and 0.627, respectively. Figures 9-13 present the purposed relationships between Q and relevant parameters of the rock. The results revealed that these relationships are statistically meaningful but in order to get higher-performance models in practice for prediction of Q, multi-input parameters may be needed. In this regard, two modelling techniques i.e. linear multiple regression (LMR) and non-linear multiple regression (NLMR) analysis were also constructed and developed.
3.2 Linear and Non-Linear Multiple Regression Models The relationship between different variables can be extracted using regression analysis that is known as a commonly-applied statistical tool. This technique determines systematically the relationship between dependent variable (output) and independent variable (predictor) in the form of regression function [27]. According to Ceryan et al. [28], as long as inputs have acceptable correlations or determinations with output(s), the inputs are applicable as predictors to the predictive models. Multiple regression exists in two different types, namely linear and non-linear. In the following paragraphs, both types are explained. The LMR analysis determines values of parameters for a function, causing the function to best matched with a provided set of data observations. In this technique, the function is a linear (straight-line) equation. Conducting a least squares fit, LMR makes suitable solutions to engineering problems. It causes the construction of simultaneous equations by forming the regression matrix. The use of this technique results in having a number of coefficients suggested by the backslash operator [29]. In case of simple bivariate regression, in which there is a single independent variable, prediction of the dependent variable can be done by taking the independent variable into consideration using Equation (4): (4)
9
where a signifies constant, x and y stand for independent and dependent variables, respectively. This equation can be extended to a numerous-variable concept as presented in the following equation: (5) where
represent various independent variables for the prediction of y.
As a solution to some problems arisen in geotechnical engineering fields, the LMR technique has been employed extensively. In [27], an LMR equation is introduced for predicting the rock fragmentation that may occur due to blasting operations. The rock material's shear strength parameters (i.e., c and ϕ) were predicted by Armaghani et al. [30] by means of the LMR technique. An equation was also developed by Hajihassani et al. [31], using the LMR technique in order to estimate the ground vibrations occurred due to quarry blasting. A commonly-used approach for achieving a non-linear relationship between dependent and independent variables is the use of non-linear multiple regression (NLMR). Contrasting the conventional linear regression, NLMR is capable of predicting a model with arbitrary relationships between the input and output variables [32]. The line of the best fit is a line minimizing sum of squares of deviation of various data points from the line. Note that both linear and non-linear relationships, for instance, power and exponential, can be applied to the NLMR technique. In the context of geotechnical engineering field, NLMR establishes mathematical formulas in a way to predict the dependent variables based on identified independent variables. NLMR was also employed by Yagiz et al. [32] and Gong and Zhao [33] to predict the TBM performance. In another project, Yagiz and Gokceoglu [34] introduced an NLMR equation that could estimate the rock brittleness. However, Shirani Faradonbeh et al. [35] developed the NLMR model to predict the back-break occurring due to blasting. In this research, based on the results of laboratory study, both LMR and NLMR techniques are taken into account for developing multiple novel equations for the UCS prediction. To this end, as recommended in literature (see [32] and [36-38]), five datasets were randomly chosen for training and testing in such a way 10
that multiple regression models could be developed. The use of some data for testing is an idea for the evaluation of efficiency of the developed model. Although Swingler [39] recommended the use of only 20% of the whole datasets for testing purposes, the Looney's [40] suggestion was 25%. As a result, in the present study, 42 out of 52 datasets (i.e., 80%) were randomly selected for development of the models, and 10 other datasets (20%) were applied to testing the models. Based on the established datasets, five LMR equations have been developed to propose Q as presented in Table 5. In developing these models, Is(50), BTS, Id2, Vp and UCS were considered as model inputs and then the Q values were estimated as a function of the relevant rock properties. In Table 5, coefficient of determination values, ranging from 0.681 to 0.751 were obtained for developed LMR models. Additionally, R2 values of 0.622, 0.785, 0.490, 0.796 and 0.530 were achieved for testing of five different sets, respectively. Apart from LMR models, NLMR equations were also proposed to predict Q considering the same datasets of the LMR analyses. These equations were mainly developed using simple regression functions. Table 6 shows proposed NLMR equations for Q prediction and their performance capacities in terms of R2 of training and testing datasets. Considering training datasets of the developed NLMR equations, R2 values vary between 0.688 and 0.768, while a range of 0.504-0.830 was obtained for testing datasets. Although results indicate similar performance capacity for both LMR and NLMR models in predicting Q of various weathering zones, NLMR equations can provide higher-performance prediction compared to LMR models.
More discussions regarding the selection of the best LMR and NLMR models are
presented in the next section. It should be mentioned that SPSS 16 as a statistical software package was used for constructing the simple regression, linear and non-linear multiple regression [41].
3.3 Evaluation of the Results
11
In this section, the way to evaluate the performance of the developed models is discussed in terms of predicting Q for different weathering zones. Performing simple regression revealed the need for developing the Q predictive models with higher accuracy by means of multi-input parameters. Therefore, the LMR and NLMR models were developed. To this end, all 52 datasets were randomly divided into five datasets. Then, 5 LMR and 5 NLMR equations were developed using the constructed datasets. As mentioned before, in order to check the prediction performance of the developed models, R2, VAF and RMSE were considered and computed for training and testing datasets. Table 7 demonstrates the results obtained from R2, RMSE, and VAF of the developed LMR and NLMR models in case of five randomly chosen datasets based on training and testing. As it can be seen in Table 7, the results related to the performance indices are very similar; which makes it very difficult to select the best models. As a solution to this problem, in [36], a simple ranking method was introduced, in which a ranking value was computed and assigned separately to each training and testing dataset (see Table 7). Each of the performance indices was ordered in its own class; then, the highest rating was assigned to the best performance index. For instance, for the LMR technique, R2 values of the training datasets were 0.723, 0.687, 0.738, 0.681, and 0.751, respectively. As a result, their ratings were assigned as 3, 2, 4, 1, and 5, respectively. In case of all performance indices besides the NLMR predictive models, this procedure was iterated. Next, the ratings obtained for each of the datasets (training and testing) were separately summed up. For instance, the rating values of LMR training dataset 1 were 4 for RMSE, 3 for R2, and 3 for VAF; therefore, the performance rating was calculated as 10 (see Table 7). The concluding step to the selection of the best models is computing the total rank through summing up the rank value of each dataset (training and testing) as presented in Table 8. As it can be observed in this table, model 2 exhibits the best results in case of both NLMR and LMR methods. As it is observable by taking into consideration both training and testing datasets, the prediction performance of the selected NLMR dataset is more efficiently than that of the LMR dataset. The selected LMR and NLMR equations in predicting Q of various weathering zones are shown as follows:
12
(6)
(7) Figures 14 and 15 present the developed relationship between the predicted Q and the measured one using LMR and NLMR methods, respectively. As it can be seen in these two figures, the NLMR method with R2 values of 0.708 and 0.793 for training and testing data, respectively, is the best Q predictive model.
4. Conclusions In this paper, several field and laboratory, tests were conducted in order to develop the predictive equations for estimating ripping production. 52 ripping tests were performed in three sites on weak rock types, i.e. sandstone and shale in various weathering zones ranging from slightly weathered to highly weathered using Caterpillar D9H machine (CAT D9).
For evaluation and prediction of ripping
production, several block samples were taken from the sites and various laboratory tests i.e., Brazilian, point load, slake-durability test, uniaxial compressive strength, and p-wave velocity were also conducted. By performing simple regression analysis, it was found that predictors and the Q have acceptable and meaningful relationships. Since each mentioned predictor has good relationship with the Q, multiple regression i.e. linear and non-linear models were also generated to achieve the best accurate results. In this regard, all datasets were divided to five randomly selected datasets and then 5 LMR, and 5 NLMR equations were developed to estimate ripping production. Considering model performance indices and using simple ranking method, the best LMR and NLMR equations were chosen among all constructed models. The obtained performance indices results of NLMR model are slightly higher than LMR model. The R2 equal to 0.708 and 0.793 for training and testing datasets, respectively suggests the superiority of the NLMR technique in predicting Q, while this value was obtained as 0.687 and 0.785 for LMR model. 13
It should be noted that the proposed equations in this study are designed for ripping production of shale and sandstone rock types; therefore, the use of the proposed equations for estimating Q of the other rock types is not recommended.
Acknowledgement The authors would like to extend their appreciation to the Government of Malaysia and Universiti Teknologi Malaysia for the FRGS grant No. 4F406 and for providing the required facilities that made this research possible.
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[38] Jahed Armaghani D, Mohamad ET, Hajihassani M, Abad SANK, Marto A, Moghaddam MR (2015b) Evaluation and prediction of flyrock resulting from blasting operations using empirical and computational methods. Eng. Comput doi: 10.1007/s00366-015-0402-5 [39] Swingler K (1996) Applying Neural Networks: A Practical Guide. Academic Press, New York [40] Looney CG (1996) Advances in feed-forward neural networks: demystifying knowledge acquiring black boxes. IEEE Transactions on Knowledge and Data Engineering 8 (2):211–226 [41] SPSS Inc. (2007). SPSS for Windows (Version 16.0). Chicago: SPSS Inc List of Tables: Table 1 Summary of the used rock material properties for excavation assessment Table 2 Specification of Caterpillar D9 Table 3 Monitored ripping tests at Bukit Indah site in different weathering zones Table 4 Summary of the measured parameters and their details Table 5 Selected equations to predict Q Table 6 Proposed LMR equations for 5 randomly selected datasets to predict Q Table 7 Proposed NLMR equations for 5 randomly selected datasets to predict Q Table 8 Results of performance indices for each model and their rank values Table 9 Total rank values for developed predictive techniques
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List of Figures: Figure 1. Location of studied areas Figure 2. Ripping process at Bukit Indah site by a CAT D9 ripper Figure 3. Equipment for conducting p-wave velocity tests Figure 4. Equipment for conducting slake –durability tests Figure 5. Equipment for conducting UCS tests Figure 6. Failure due to conducting point load test Figure 7. Failure due to conducting Brazilian test Figure 8. Failure due to conducting UCS test Figure 9. Relationship between point load strength index and ripping production Figure 10. Relationship between Brazilian tensile strength and ripping production Figure 11. Relationship between slake durability index and ripping production Figure 12. Relationship between p-wave velocity and ripping production Figure 13. Relationship between uniaxial compressive strength and ripping production Figure 14. Measured and predicted values of Q by LMR equation for training and testing datasets Figure 15. Measured and predicted values of Q by NLMR equation for training and testing datasets
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20
21
22
23
24
25
26
27
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Table 1 Summary of the used rock material properties for excavation assessment Property Reference Vp X X
UCS
Is(50)
Rn
TS
A
Caterpillar [16] Atkinson [12] X X Franklin [11] X Bailey [18] Weaver [19] X X Church [15] X Kirsten [20] X Muftuoglu [21] X X Abdullatif et al. [22] X X Smith [23] Anon [24] X Singh et al. [9] X X X X (PL Bozdag [25] X T) Karpuz [14] X X X MacGregor et al. [26] X X Pettifer and Fookes [27] X Kramadibrata [28] X X X Hadjigeorgiou and Poulin [1] X Basarir and Karpuz [3] X X X X X X X Basarir et al. [4] 11 10 9 3 1 2 Popularity (No.) Remarks: Vp: p-wave velocity, UCS: uniaxial compressive strength, Is(50): point load strength index, Rn: Schmidt hammer rebound number, TS: tensile strength, A: abrasiveness.
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Table 2. Specification of Caterpillar D9 Specification
Value
Flywheel power
410hp/ 306kW
Operating Weight
47900 kg 4.24 m2
Ground contact area Maximum penetration force (shank vertical)
153.8 kN
Pry out force
320.5 kN
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Table 3 Monitored ripping tests at Bukit Indah site in different weathering zones Material type Sandstone
Shale
Weathering zone II III IV II III IV
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No. of ripping test 3 4 7 2 4 9
Table 4 Summary of the measured parameters and their details Parameter
Unit
Symbol
Category
Min
Max
Mean
Point load strength index
MPa
Is(50)
Predictor
0.15
3.93
1.39
Brazilian tensile strength
MPa
BTS
Predictor
0.83
4.12
2.35
%
Id2
Predictor
31.3
97.5
69.8
P-wave velocity
m/s
Vp
Predictor
1455
2994
2266
Uniaxial compressive strength
MPa
UCS
Predictor
8.35
67.5
24.4
Q
Output
45.9
1136.1
517.5
Second-cycle slake durability index
Ripping production
3
(m /h)
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Table 5 Selected equations to predict Q Predictor
Equation Type
Is(50) BTS Id2 Vp UCS
Exponential Logarithmic Logarithmic Linear Exponential
Developed Equation
33
R2
RMSE
VAF
0.592 0.504 0.589 0.574 0.627
190.738 190.436 173.278 176.419 191.057
51.683 50.374 58.914 57.411 51.336
Table 6 Proposed LMR equations for 5 randomly selected datasets to predict Q
R2 Training
R2 Testing
1
0.723
0.622
2
0.687
0.785
3
0.738
0.490
4
0.681
0.796
5
0.751
0.530
Dataset No.
Proposed Equation
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Table 7 Proposed NLMR equations for 5 randomly selected datasets to predict Q
R2 Training
R2 Testing
1
0.754
0.574
2
0.708
0.793
3
0.760
0.504
4
0.688
0.830
5
0.768
0.576
Dataset No.
Proposed Equation
35
Table 8 Results of performance indices for each model and their rank values Method
LMR
NLMR
72.302 68.699 73.817 68.055 75.056
Rating for R2 3 2 4 1 5
Rating for RMSE 4 2 5 1 3
Rating for VAF 3 2 4 1 5
Rank value 10 6 13 3 13
174.457 140.391 185.027 150.198 167.683
62.053 78.501 36.227 78.487 35.477
3 4 1 5 2
2 5 1 4 3
3 5 2 4 1
8 14 4 13 6
0.754 0.708 0.760 0.688 0.768
133.475 143.193 134.639 143.926 137.496
75.401 70.723 75.964 68.692 76.745
3 2 4 1 5
5 2 4 1 3
3 2 4 1 5
11 6 12 3 13
0.574 0.793 0.504 0.830 0.576
186.516 132.337 180.873 133.964 188.885
57.279 79.279 38.177 82.512 36.535
2 4 1 5 3
2 5 3 4 1
3 4 2 5 1
7 13 6 14 5
Model
R2
RMSE
VAF
Training 1 Training 2 Training 3 Training 4 Training 5
0.723 0.687 0.738 0.681 0.751
141.631 144.059 140.525 145.385 142.404
Testing 1 Testing 2 Testing 3 Testing 4 Testing 5
0.622 0.785 0.490 0.796 0.530
Training 1 Training 2 Training 3 Training 4 Training 5 Testing 1 Testing 2 Testing 3 Testing 4 Testing 5
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Table 9 Total rank values for developed predictive techniques Method
LMR
NLMR
Model
Total rank
1 2 3 4 5
18 20 17 16 19
1 2 3 4 5
18 19 18 17 18
37