Correlation of Deformation Modulus by PMT with RMR and Rock Mass Condition

Byung-Sik Chun 1, Yong-Jea Lee1, Deok-Dong Seo2, Beyong-Seok Lim3

1 Dept. of Civil Engrg., Hangyang University, Seoul, Korea2 Construction Division, Samsung Corporation, Seongnam, Korea3 Soil Testing Engineers, Inc., LA, USA

ABSTRACT

In this paper, the applicability of available correlations that estimate the deformation modulus from Rock Mass Rating (RMR) and Pressuremeter Test (PMT) to the Korean rock mass is evaluated. The correlations between deformation modulus and other rock properties were also analyzed. It appears that the existing correlations using RMR overestimate the deformation moduli and wide variation was found between predicted moduli and the measured values. Rock Quality Designation (RQD) and unconfined compressive strength (UCS) were found to correlate to deformation modulus reasonably well, but joint spacing and joint conditions appear to correlate poorly to RQD and UCS. Groundwater could not be correlated to the modulus. The measurement depth was found to have very little contribution to deformation modulus. However, it is estimated that poor correlation result from the fact that measurement depth is coupled with not only with the deformation modulus, but with other factors including strength, joint condition, and degree of weathering. The inappropriateness of the correlations clearly demonstrate that more in depth analysis techniques such as multivariate correlations is needed to better estimate deformation modulus of rock mass from available rock properties.

1. INTRODUCTION

Many existing equations using RMR have been developed from measurement results, case studies, or back analyses related to rock mass. Most of them were derived based on foreign (no Korean) rock mass condition. Therefore, the equations have shown some limitation in applicability to domestic (Korean) rock mass. In this paper, the correlation analyses between the deformation modulus estimated by several existing major equations using RMR and PMT are compared and analyzed for the applicability to Korean rock mass. Also, the correlation analyses between the deformation modulus and the various properties of rock mass are performed. Uniaxial compressive strength (USC), RQD, joint condition, joint spacing, groundwater condition, and the measurement depth were selected as the major rock mass properties. They are usually critical factors in RMR classification.

2. THEORETICAL BACKGROUND OF RMR CLASSIFICATION AND DEFORMATION MODULUS

2.1 The Existing Equations using RMR

RMR classification have some limitations such as follows; the personal errors due to each user's judgment from the qualitative definition in RMR itself, the unreliability of the weighted points to 100

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points as a full grade in rating of each classified factors, and the gap between maximum value and minimum value within the fixed range of properties values(Kim, 1993). Especially, rock mass condition can be totally different classified from which RMR values were chosen, basic RMR values or modified RMR values based on accounting the direction of discontinuous surface. In Korea, Kim (1993) has introduced the corrected RMR value with exclusion the effect of groundwater and discontinuity surface direction in estimating of the deformation modulus and the strength parameter. On the other hand, the existing RMR classification does not account for the effect from underground stress condition and weathering of the rock mass. Therefore, the existing RMR values may implicate fundamental errors in estimating the deformation modulus of the Korean rock mass. Table 1 summarized existing equations of the deformation modulus using RMR.Table 1. Equations of Deformation Modulus based on RMR

References Required parameters Limitations Equations

Bieniawshi(1978) RMR RMR>50 Em=2RMR-100(GPa)

Serafim and Pereira (1983) Modified RMR RMR<50 Em=10(RMR-10)/40(GPa)

Kim, kyowon(1993) RMRExclude the effect of

ground water from basic RMR

Em=300×Exp(0.07RMR)×10-3(GPa)

Aydan(1997) RMR - Em=0.0097×RMR3.54×10-3(GPa)

Mohammad(1997) RMR - Em=0.562×RMR+0.183(GPa)

Gokceoglu et al. (2003) RMR - Em=0.0736×Exp(0.0755RMR)(GPa)

Nicholson & Bieniawshi(1990) Ei, RMR Need Ei(of intact rock) Em/Ei=0.0028RMR2+0.9Exp(RMR/22.82)

Mitri et al.(1994) Ei, RMR Need Ei(of intact rock) Em/Ei=0.5×(1-cos(π×RMR/100))

2.2 Deformation characteristics based on the rock condition

From the literature review, the deformation modulus of rock mass is decreased with weathering, the porosity, and low strength of rock mass (Lee, 1998, Kim, etc. 2003). Uniaxial compressive strength (USC) has a strong correlation with the deformation modulus. The higher strength of rock get the higher deformation modulus (Deere & Miller, 1996). The stress conditions also significantly effect on the deformation modulus, which is proportional to the depth of measurement. It is well known that the deformation modulus is increased with depth (Kim etc, 2003). On the other hand, the range of the deformation modulus is highly dependant upon the measuring methods. For instances, the values of deformation modulus for field rock mass obtained from pressuremeter are double or triple smaller than the values from plate loading test (Shuri, 1981, KGS, 2000).

3. MEASUREMENT DATA OF DEFORMATION MODULUS BY PMT

In this study PMT was performed at 8 field sites which included 7 rock types as followings; granite: 30 test spots, granite gneiss: 9 test spots, andesite: 39 test spots, tuff: 55 test spots, gneiss: 63 test spots, sandstone or shale: 9 test spots. Total 205 testing data were obtained and analyzed. However, the data from sandstone and shale were disregarded in this study due to lack of the number of testing data and poor correlation with the deformation modulus. The studying areas mainly were located in Cheonla-do and some areas were in Chungcheong-do and Kyungsang-do, Korea. PMT and borehole

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jack are mostly performed to measure the deformation modulus. In this study test result mainly from PMT are analyzed.4. CORRELATION OF RMR WITH ROCK MASS PROPERTIES AND DEFORMATION MODULUS

4.1 Comparison of RMR' Correlation to Deformation Modulus in Existing Equations

Figure 1 and 2 were plotted with deformation modulus versus RMR values and with the predicted deformation modulus by existing equations using RMR values versus the measured by PMT, respectively. In Figures 1 RMR values are proportional to deformation modulus, which is well matched to previous studies. From this analysis, the deformation modulus may be expressed as an exponential function of RMR. Especially, Kim (1993) and Gokceoglu etc. (2003) has suggested exponential function that provided the best correlation in their studies. Where, the regression analysis formula in this study was derived based on the measured values as follow.

)()0485.0(3228.0 GpaRExpEm ×= (1)

From the above analysis, the deformation modulus of andesite, gneiss and granitic gneiss show relatively high correlation between both values estimated and measured. However, the correlation coefficient of the equation (1) presents low value 0.36 around which is similar values calculated by existing empirical equations, which shows again the limit of the applicability of the technique using RMR value in estimation of the deformation modulus may not be so reasonable. These consequences may come from the following several reasons. First, RMR marking assignments are more concentrated on the factors having a poor correlation to deformation modulus, such as joint condition (30 points), joint spacing (20 points), and groundwater condition (15 points). Those marking assignments need to be adjusted on the factors having a good correlation such as UCS (20 points) and RQD (15 points). Second, the personal errors exist in evaluating the qualitative conditions. Third, the effects of degree of weathering or rock types and measurement depth (confining stress) on the deformation modulus were not accounted during rating RMR. Figure 2 shows that most of the measured values are lower than the estimated values. While the estimated by Gokceoglu (2003) and Kim (1993) are matched to the measured in RMR<50, the existing equations is overestimating the deformation modulus than the measured with proportionality between and RMR and the measured. Especially, it is noted that the estimated by Mohammed (1997) are reached at the upper limit of this study.

4.2 Correlation analysis between rock mass properties and deformation modulus

Figure 3 shows the correlation between the deformation modulus and the major properties such as UCS, RQD, joint condition, joint spacing, groundwater condition, and measurement depths. In these

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y = 0.3228e0.0485x

R2 = 0.3638

0.00

10.00

20.00

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50.00

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0 20 40 60 80 100

RMR(basic)

E(G

Pa)

Andesite Tuff GneissGranite Granite-Gneiss Regression-ARegression-T Regression-Gn Regression-GrRegression-GG Regression-Total

Figure 1. RMR' Correlation to Deformation Modulus

0.00

15.00

30.00

45.00

60.00

75.00

0 20 40 60 80 100

RMR(basic)E(G

Pa)

Andesite TuffGneiss GraniteGranite-Gneiss Kim(1993)Aydan(1997) Mohammad(1997)Gokceoglu(2003) Bieniawski(1978)This study

`

Figure 2. Comparison between the values estimated by empirical equations and measured by PMT

correlations, weathering, porosity, and elastic modulus are excluded because they are not measured and analyzed. As shown in Figure 3, the correlation between RQD and deformation modulus can be expressed as an exponential relationship, and that of deformation modulus and uniaxial compressive strength can be presented as a linear relationship respectively. However, logarithmic relationship between joint spacing and the modulus has a less correlation. In RMR classifications, the joint condition depends on joint persistence, joint roughness, filling materials, joint aperture, and weathering of joint surface. The effect of joint condition on the deformation modulus needs further research. A personnel deviation also exists in the evaluation of joint condition. On the other hand the correlation analysis between joint condition and deformation modulus is carried out with the assumption that the RMR is quantitative. The correlation coefficient, 0.24, between RMR marks of joint condition and deformation modulus showed less correlation than that of RQD and UCS. With the above same assumption groundwater condition showed almost no correlation to the deformation modulus. The exclusion of the effect of groundwater condition may be reasonable in estimating of deformation modulus of rock mass, which was already pointed out by Kim (1993). Stress condition is strongly dependent on the measurement depth. Usually, RMR does not include measurement depth.

y = 1.0704e0.0267x

R2 = 0.3013

0.00

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0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0

RQD(%)

E(G

Pa)

Andesite Tuff GneissGranite Granite-Gneiss Regression-ARegression-T Regression-Gn Regression-GrRegression-GG Regression-Total

(a) Correlation between RQDand deformation modulus

y = 0.0098x + 0.3073

R2 = 0.3134

(10.00)

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0 500 1000 1500 2000 2500 3000

qu(kg/cm2)

E(G

Pa)

Andesite Tuff GneissGranite Granite-Gneiss Regression-ARegression-T Regression-Gn Regression-GrRegression-GG Regression-Total

(b) Correlation between UCSand deformation modulus

y = 3.8947Ln(x) + 18.12

R2 = 0.2084

0.00

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50.00

60.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

The distance of discontinuity(m)

E(G

Pa)

Andesite Tuff GneissGranite Granite-Gneiss Regression-ARegression-T Regression-Gn Regression-GrRegression-GG Regression-Total

(c) Correlation between joint spacingand deformation modulus

y = 0.9776e0.0936x

R2 = 0.2366

0.00

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The condition of discontinuity(RMR points)

E(G

Pa)

Andesite Tuff GneissGranite Granite-Gneiss Regression-ARegression-T Regression-Gn Regression-GrRegression-GG Regression-Total

(d) Correlation between joint conditionand deformation modulus

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0 2 4 6 8 10 12 14 16

The condition of ground water(RMR points)

E(G

Pa)

Andesite Tuff Gneiss Granite Granite-Gneiss

(e) Correlation between groundwater

y = 0.1493x + 7.7415

R2 = 0.1485

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50.00

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0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0

depth (m)

E(G

Pa)

Andesite Tuff GneissGranite Granite-Gneiss Regression-ARegression-T Regression-Gn Regression-GrRegression-GG Regression-Total

(f) Correlation between measurement depth

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condition and deformation modulus and deformation modulus

Figure 3. Correlation between major rock mass properties and deformation modulusEven though the measurement depth showed a positive relation with the modulus, the poor correlation was observed in this study. It can be explained as follows. Firstly, the deformation modulus of rock is less sensitive to overburden stresses compared to that of soil. Secondly, the measurement depth could not be representative of actual depth of rock mass unless all measurement depth was obtained on the same thickness of overburden soil. Thirdly, the measurement depth is coupled with not only with the deformation modulus, but with other factors including strength, joint condition, and degree of weathering. Even though it is apparent that the deformation characteristics should be influenced by the measurement depth, it is necessary to introduce the more exquisite analysis techniques instead of the simple regression analysis used in this study to properly quantify the effect of the measurement depth.

5. CONCLUSIONS AND SUGGESTIONS

(1) Most of the existing equations of RMR overestimate the deformation modulus of rock mass due to no reasonable consideration of the influence of the properties of rock mass in Korean rock conditions. Regression analyses showed that an exponential relationship exist in the correlation between the measured deformation modulus and RMR values.

(2) Analyses are performed to determine the correlation between the deformation modulus and uniaxial compressive strength, RQD, joint condition, joint spacing, groundwater condition, and measurement depth. From the analyses, RQD and UCS have high correlation, but joint spacing, measurement depth and joint condition result in poor correlations with the modulus. Groundwater condition was found to have no correlation with the deformation modulus.

(3) To get more reliable correlation between measurement depth and the deformation modulus, it is necessary to introduce a more exquisite analysis technique since it is influenced by various inter-dependent variables. Further study is warranted to determine more accurate correlation.

REFERENCES

A. Kayabasi, C. Gokceoglu and M. Ercanoglu, 2003. “Estimating the deformation modulus of rock masses:a comparative study”, International Journal of Rock Mechanics and Mining Sciences 40, pp. 55-63.

Bieniawski Z.T., “Engineering Classification of jointed rock masses”, Trans S Afr. Inst. Civ. Eng. 1973;15(12):335-44.

Bieniawski Z.T., 1976, “Rock mass classification in rock engineering”, Proc., of symposium on Exploration for Rock Engineering, Vol. 1, pp. 97-106.

Bieniawski Z,T., 1978, “Determining rock mass deformability: experience from case histories”, Intnl. J. Rock Mechanics and Mining Sciences, Vol. 15, pp. 237-247.

Bieniawski Z.T. (1989), Engineering Rock Mass Classification. pp. 51-64.C. Gokceoglu, H. Sonmez and A. Kayabasi, 2003. “Predicting the deformation moduli of rock

masses”, International Journal of Rock Mechanics and Mining Sciences 40, pp. 701-710.H. S. Chung, 2004. Rock mechanics for the Civil engineer. SAERON Publications, pp. 33-44, 201-

209, 303-321.

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H. S. Shin, 1988. Rock engineering for the civil engineer (V). Journal of the Korean Geotechnical Society, Vol. 14, No 5. pp. 248-258.

H. Sonmez, C. Gokceoglu and R. Ulusay, 2004. “Indirect determination of the modulus of deformation of rock masses based on the GSI system”, International Journal of Rock Mechanics and Mining Sciences 41, Issue 5, pp. 849-857.

K. W. Kim, 1993. “Revaluation of geotechnical classifications of rock masses”, Proceedings of the Korean Geotechnical Society Conference, pp. 33-40.

Lianyang and H.H. Einstein, 2004. “Using RQD to estimate the deformation modulus of rock masses”, International Journal of Rock Mechanics and Mining Sciences 41, pp. 337-341.

Mitri HS, Edrissi R and Henning J. 1994. “Finite element modelling of cable bolted stopes in hard rock ground mines”. Presented at the SME Annual Meeting. Albuquerque: New Mexico. pp. 94-116.

Zekai Sen and Bahaaeldin H. Sadagah. 2003. “Modified rock mass classification system by continuous rating”. Engineering Geology 67, pp. 269-280.

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