Estimation of Modulus of Deformation Using Rock Mass Rating—A Review and Validation Using 3D Numerical Modelling
Abstract
:1. Introduction
2. Methodology
3. Statistical Analysis
4. Case Study—Tala Powerhouse Complex
4.1. Geology
4.2. 3D Numerical Modelling
4.3. Excavation Sequence and Support System
4.4. Material Properties
4.5. Comparison of Modelling Results with Instrumentation Data
5. Conclusions
- The review of various empirical models available for estimating Ed values indicates a considerable variation in the value of the deformation modulus for the Himalayan region. The empirical equations proposed by [14,20,21,29] are also in good comparison with the in situ tested value of Ed, while equations proposed by [11,23,25,27,28] overestimate, and the remaining equations underestimate Ed values.
- Based on the data obtained from 35 test locations, a predictive cubic equation (Equation (19)) could be developed, with R2, RMSE, and VAF values of 0.75, 1.70, and 74.33, respectively. These values indicate higher predictability and maximum accounted-for variance in Ed compared with other available correlations available in the literature.
- The 3D numerical modelling results show that the Ed value adopted based on the proposed Equation (19) (Model A) correlated well with that of the measured instrumentation data when compared with the value of Ed based on the in situ testing (Model B). Model B underpredicts the deformations in the powerhouse complex at all locations, indicating that the in situ tested Ed value is higher, enhancing the rock mass properties. Measured convergence matched well in Model A compared to Model B. Hence, the relation proposed in Equation (19) can be utilized to estimate the value of Ed.
- From the in situ tested data, the average ratio of Ee/ Ed for the Himalayan region is 1.5.
- The proposed equation validates rock masses from the Himalayan region, with RMR values ranging from 15 to 70.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Equation No. | Ref. | Year | Equation | Type of Equation | R2 | Limitations | Data Sets Used | RMR Range | Country of Origin | Lithology |
---|---|---|---|---|---|---|---|---|---|---|
(1) | [12] | 1978 | Linear | - | RMR > 50 | 3 Sites | 51–85 | South Africa | Shale, siltstone, dolerite, mudstone, and sandstone (hard rocks). | |
(2) | [14] | 1983 | Power | - | RMR ≤ 50 | 15 | 26–83 | - | Dolerite, sandstone, mudstone, shale, siltstone, gneiss, and granite (soft rocks). | |
(3) | [24] | 1992 | Power | 0.91 | - | 120 | - | India | ||
(4) | [25] | 1993 | Exponential | - | - | - | - | - | ||
(5) | [26] | 1996 | Exponential | - | - | - | - | Croatia | Limestone | |
(6) | [27] | 1997 | Power | - | - | - | - | - | Gneiss, granite, and sandstone. | |
(7) | [28] | 1999 | Power | - | - | 15 | 26–83 | New Zealand | Graywacke, sandstones, and mudstones. | |
(8) | [29] | 1999 | Non-linear | - | - | - | - | Various | ||
(9) | [30] | 2003 | Exponential | 0.62 | - | 115 | 20–85 | Various | Quartzdiorite, limestone, and shale. | |
(10) | [31] | 2003 | Logarithm | - | - | 57 | 38–84 | Turkey | Grey and pinky quartzdiorite. | |
(11) | [15] | 2006 | Exponential | 0.36 | - | 8 Sites | - | Korea | ||
(12) | [16] | 2008 | Linear | 0.94 | RMR ≥ 27 | 9 | 27–61 | Turkey | Graywacke | |
(13) | [17] | 2010 | Polynomial | 0.8446 | - | 42 | 10–85 | Iran | Limestone and marble | |
(14) | [18] | 2012 | Gaussian function | 0.932 | - | 43 | - | Various | Mudstone, siltstone, sandstone, shale, dolerite (hard rocks), granite, gneiss, mudstone, siltstone, sandstone, shale, and dolerite (soft rocks). | |
(15) | [19] | 2013 | Power | 0.64 | - | 420 | 7–92 | Korea | Gneiss | |
(16) | [20] | 2014 | Linear | 0.6709 | - | 52 | 30–76 | Iran | Sandy siltstone, mudstone, conglomerate, sandstone, dislocated rock mass, faulted rock mass, and shear zone. | |
(17) | [21] | 2015 | Exponential | 0.97 | - | 4 Sites | - | Turkey | Basalt, tuffites, and diabases. | |
(18) | [22] | 2013 | Power | 0.89 | - | 82 | 39–85 | Iran | Grey-green schist, phyllite, dark grey to black limestone, and limy dolomite. |
S.No. | Type of Equation | Equation | Coefficient of Regression, R2 |
---|---|---|---|
1 | Linear | 0.183RMR − 5.81 | 0.53 |
2 | Logarithmic | 5.8log(RMR) − 19.17 | 0.37 |
3 | Cubic | 0.75 | |
4 | Exponential | 0.708 |
Cavern | Support System |
---|---|
MHC–Crown | 32 mm diameter, 8 m and 6 m long rock bolts at 1.5 m × 1.5 m pattern Steel-fiber-reinforced shotcrete (SFRS) of 100 mm thickness Steel ribs of ISMB 300 at 0.6 m spacing 32 mm/26.5 mm diameter, 12 m long Dywidag rock bolts at 1.5 m spacing |
MHC–Walls | 32 mm/26.5 mm diameter, 12 m long Dywidag rock bolts at 1.5 m spacing |
THC–Crown | 32 mm diameter, 8 m and 6 m long rock bolts at 3 m × 1.5 m pattern Steel-fiber-reinforced shotcrete (SFRS) of 100 mm thickness Steel ribs of ISMB 350 at 0.6 m spacing |
THC–Walls | 32 mm/26.5 mm diameter, 8 m long Dywidag rock bolts at 1.5 m spacing |
MHC and THC Walls | Initial layer of shotcrete of 50 mm thickness Welded-wire mesh of 100 mm × 100 mm × 5 mm Final two shotcrete layers of 50 mm each |
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Bellapu, H.V.S.; Sinha, R.K.; Naik, S.R. Estimation of Modulus of Deformation Using Rock Mass Rating—A Review and Validation Using 3D Numerical Modelling. Sustainability 2023, 15, 5721. https://doi.org/10.3390/su15075721
Bellapu HVS, Sinha RK, Naik SR. Estimation of Modulus of Deformation Using Rock Mass Rating—A Review and Validation Using 3D Numerical Modelling. Sustainability. 2023; 15(7):5721. https://doi.org/10.3390/su15075721
Chicago/Turabian StyleBellapu, Hema Vijay Sekar, Rabindra Kumar Sinha, and Sripad Ramchandra Naik. 2023. "Estimation of Modulus of Deformation Using Rock Mass Rating—A Review and Validation Using 3D Numerical Modelling" Sustainability 15, no. 7: 5721. https://doi.org/10.3390/su15075721