Surprises and Complications in Laboratory Assessment of Rock

SURPRISES AND COMPLICATIONS IN LABORATORY ASSESSMENT OF ROCK

Hasan Abdullah Chief Research Officer, Central Soil & Materials Research Station, New Delhi–110 016, India.E-mail: abdulahasan@rediffmail.com

ABSTRACT: The laboratory assessment of rock may entail ‘surprises’ (i.e., the responses contrary to those normally anticipated) and also has some ‘problematic’ aspects. The ‘surprises’ discussed, include: i) The bulk density being greater than the grain density; ii) The axial stress at failure decreasing with increasing confining pressure; iii) The negative value of Poisson’s ratio (computed on the basis of wave velocity). The discussed ‘problems or complications’ pertain to i) Correlation between uniaxial compressive strength and point load strength index, and ii) Computation of shear strength parameters using direct shear test. The paper is based on the data available with Central Soil & Materials Research Station (CSMRS).

1. INTRODUCTION

While assessing rock in the laboratory, one may encounter a surprise, i.e., a response, which is not in accordance with that commonly observed, and goes against the standard theories or normally employed empirical relationships. Also, at times, ‘problems or complications’ arise in case of assessment of certain parameters on the basis of laboratory testing. The surprises and complications, which have been discussed here, came to the fore during laboratory evaluation—of different rock types from different project areas—at CSMRS.

2. THE PROPERTIES AND PARAMETERS

The discussion comprises the basic material property of density (bulk vis-à-vis grain), an important engineering parameter like shear strength (computed using triaxial compression data and also based on direct shear test data), the standard theoretical relationship employed to compute deformability characteristics under dynamic loading (based on the compression and shear wave velocities and bulk density) and the empirical relationship that links point load strength index with uniaxial compressive strength.

2.1 Density (Grain and Bulk)

In classical Soil Mechanics, the ‘three-phase diagram’ is used to explain the concept of density, the computation of which is considered somewhat mundane. In Rock, although one does not explicitly use that concept; but one is generally not very alert about its inapplicability either. The concept of grain density and bulk density (in dry, and in saturated, state) is employed in case of rocks. The difference between ‘saturated bulk density’ and ‘dry bulk density’ is taken as reflective of the pores (interconnected with the surface), whereas the difference between the Grain Density and Bulk Density is taken as an indicator of the total pores. The latter understanding,

however, turns out to be fundamentally flawed, when one comes across a situation where the bulk density is higher than the grain density.

For accurate determination of bulk density, a small piece of rock is taken, and mercury displacement method is employed for the measurement of volume of rock. However, if the volume of a big sample (say, the one tested for uniaxial compressive strength or triaxial compression) is evaluated, employing water displacement, then the value of computed density differs from the first case. In the second case, the computed bulk density is generally less than the first one. Here, we shall consider the higher value, i.e., the bulk density of a small piece of rock, as comparatively that is determined more accurately. For grain density, the volume of powdered rock is determined through immersing it in kerosene. However, invariably, even high bulk density value is less than the grain density (obtained on powdering the specimen).

In case of two of the basalt rocks from P-K-C Link Project, MP, (Ajnar and T3 locations) the grain density (2855 and 2880 kg/m3) was found to be lower than the dry bulk density (2950 and 2940 kg/m3), which made us reflect if there were some un-stated assumptions in taking the difference between grain density and bulk density to be an indicator of the pores, and expecting grain density to be higher than the bulk density. These rocks belonged to ‘Very High Density’ and ‘Very Low Porosity’ class—to be precise, dry bulk density was 2940 kg/m3 and more, and the water content at saturation was 0.4% or less.

All the possible sources of error were checked, and a large number of samples were tested; but, the grain density was consistently lower than the bulk density in case of basalt from these two locations. For Mohanpura basalt from the same project, with water content of 1% and bulk density 2900 kg/m3, the grain density (3015 kg/m3) was not only higher

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Surprises and Complications in Laboratory Assessment of Rock

than the respective bulk density (2900 kg/m3), but also the bulk density of these ‘very high density and very low porosity’ varieties of basalt from Ajnar and T3 locations.

These results put a question mark over the tacit understanding that the difference between the grain density and the bulk density basically reflects the quantum of voids. There is no doubt that the voids do get eliminated on powdering the rock piece (for determination of grain density) but, simultaneously, an increase in volume (due to reduction of the size of constituent particle or breaking of bond) also seems to take place. And, in case of the two ‘very high density and very low porosity’ varieties of basalt, on powdering, the increase in volume was more than the reduction (due to removal of air voids). For data and detailed discussion, refer CSMRS’ report on P-K-C Link Project, MP (2005, unpublished).

2.2 Shear Strength Parameters (on the basis of Triaxial Test)

The Suggested Methods published by the International Society for Rock Mechanics (ISRM) recommend that in order to determine the shear strength parameters (i.e., cohesion and angle of internal friction) of a given rock type (without any preferred plane of failure), a set of 5 (or 9 as per ASTM) cylindrical rock specimens, at different confining pressures (spread over the range of interest), be tested under triaxial compression. The ‘Mohr-Coulomb Failure Envelope’ or the ‘Hoek and Brown Failure Criterion’ is commonly employed for the determination of shear strength of rock, on the basis of the triaxial tests’ data. However, the assessment of shear strength becomes problematic, when both these methods become inapplicable.

Figure 1 presents the triaxial test data of granitic gneiss (different notations representing samples from different drillholes) of a project site, where samples of a given rock type, even from a single drillhole, do not show any definite trend of increase in axial stress (at failure) with increasing confining pressure of the tested specimens.

Fig. 1: Strength Envelop for Granitic Gneiss

Only when around 50 samples were tested, thereby revealing the rock’s natural response, it could be inferred that because of the presence of micro-cracks in this granitic gneiss rock (with high uniaxial compressive strength), the samples failed at a relatively lower axial stress when these cracks were largely aligned along the natural failure plane; and, also, the effect of increase in confining pressure did not result in appreciable increase of the failure axial stress. In other words, the uniaxial compressive strength was the dominant factor, and the increase in strength due to confinement was relatively quite small. For a detailed discussion, refer to Abdullah & Dhawan (2004).

2.3 Dynamic Deformability Characteristics (Employing Wave Velocity Data)

The assumptions of continuity, homogeneity, isotropy, and linear elasticity (acronym CHILE) are invoked to scientifically deal with the rock in a practical way—although, these assumptions are seldom, if ever, valid. Through the monitoring of strain (axial and diametric) under uniaxial compression, employing static loading, the ‘realistic’ results can be obtained for the deformability characteristics (tangent modulus and Poisson’s ratio).

At times, for the very same rock samples that give satisfactory results for the static elastic parameters, the computation of these parameters (in dynamic state), using wave velocities and bulk density, employing the following classical relationships, leads to absurd results—especially with regard to Poisson’s ratio. That is so because the Poisson’s ratio is the ratio of two very small quantities, thereby inappropriateness of the assumption leads to unacceptable results.

(1)

(2)

To cite a specific instance, the case of quartz mica gneiss samples from Tala HE Project is briefly discussed ahead. For several of these rock core samples, the evaluated Poisson’s ratio (dynamic)—employing wave velocities (set-up shown in Figure 2) and bulk density—was unacceptable. The extreme values for Poisson’s ratio were –9 and +48! For some samples, the Poisson’s ratio was negative in dry state but greater than +1 in saturated state!

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Fig. 2: Wave Velocity through Specimen

Significantly, for all these rock samples, the evaluated Poisson’s ratio (under static loading condition) was in the acceptable range. Also, the modulus value (dynamic) was within reasonable limits for most of these samples. That means, the assumptions of DIANE go awry particularly in case of the estimation of Poisson’s Ratio (dynamic). The referred wave velocity data is discussed by Abdullah & Dhawan (2007) and the report on Tala HE Project (CSMRS 1999). For a detailed discussion on wave velocity, refer to Abdullah et al. (1999, 2002).

2.4 Point Load Strength Index and Uniaxial Compressive Strength

The point load strength index (Is(50)) and Uniaxial Compressive Strength (UCS) are correlated, and the ‘averaged’ multi-plication coefficient of Is(50) to evaluate UCS is given as 22 in standard international literature. But, the only justification for this ‘empiricism’ is the limited data that was employed to correlate these two parameters long ago. However, it is well known and even ISRM Suggested Methods (1985) mentions that the above-mentioned multiplier could vary from 15 to 50. And, in our work, spread over a few years, and involving over 1000 samples of different rock types, this ‘multiplier’ was evaluated to be as low as 8, and was also not unique even for a given rock type (Abdullah et al. 1999).

There are several complexities involved in correlating UCS and Is(50). The nature of the two tests is different. The point load test is essentially a tensile test and reflects (at the most) the strength of the plane of failure, whereas in UCS, the whole sample resists the applied compressive force, and the sample fails in shear.

The difference in the nature of the two tests, one being compressive and the other tensile, and the difference in the resisting areas/volumes, are the main reasons for the variation of the ‘constant’ multiplier. In many cases, the saturation also changes the ‘constant’ multiplier because, on saturation, the percentage reduction in UCS is less than the corresponding reduction in Is(50).

For anisotropic rocks, if Is(50) (along weak plane) is estimated employing diametric tests, the value thus obtained, greatly differs from the Is(50) obtained under axial loading. That is so, because in case of diametric loading along weak plane, the force is required only to initiate the failure, and the complete area of the specimen does not come into play in the resistance of the failure load.

The minimum value of Is(50) is obtained when the diametric test (Fig. 3) is performed with the sample’s weakness plane along the loading plane (formed by the two conical end points of the loading frame). And, if the axial test is performed (with weakness plane across the loading plane), the maximum Is(50) is obtained. And, in our study, this ratio of maximum to minimum point load strength index (Anisotropy Index), was as high as 3. Whereas, for most rocks, the minimum UCS is obtained when the loading direction makes an angle of around 30° with the weakness plane, and the value of UCS increases as the angle (between plane of loading and weakness plane) varies from 30° (to 0° and 90°, both).

Fig. 3: Point Load Strength Index Test (Diametric)

2.5 Shear Strength Parameters (on the basis of Direct Shear Test)

The direct shear strength test, particularly when performed with the help of portable direct shear test apparatus (Fig. 4), has serious limitations—some of which are discussed ahead. Therefore, the shear strength, computed on the basis of the data generated through this apparatus, is not quite reliable.

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Fig. 4: Direct Shear Test Apparatus (Portable)

The small area of the tested specimen (around 2100 mm2) brings to fore the far reaching consequences of the divergence between theory and practical situation, thereby putting a serious question mark over the computed parameters. Here, the involved assumptions make the data inherently inaccurate.

For instance, it is presumed that the applied normal force and shear force act at the failure plane—but, practically, the testing arrangement does not ensure the same. And, this aspect gets highlighted when the strength of the failure surface is not very low because, in such a situation, on increasing the applied shear force, the bottom half of the sample gets lifted up.

The applied shear force also has to pull the upper half of the assembly along with the upper half of he casting and the specimen. The intervening medium (in which the sample is cast) also absorbs some of the force. And, all these aspects are not duly accounted for, thereby giving rise to fundamentally flawed results of shear strength parameters from the direct shear test.

One more complication arises because of the inclination of the joint, i.e., the shear plane. Theoretically, it is all well to resolve the force components, and compute the strength; but, in practice, it results in large errors, especially when the involved samples are small. Then, there are issues of unevenness, and the sample not being perfectly aligned with the direction of the pull/push.

In case of the samples with open joints, to ensure proper placement of the test sample becomes very difficult. To keep the gouge material in place has its own problems, especially because of the saturation of the sample, and also the water excreted by the casting material (plaster of Paris/cement mortar).

The foregoing factors put a question mark over the validity and appropriateness of the generated test data. For a detailed discussion on the direct shear test in respect of rock from Omkareshwar HE Project, MP, refer CSMRS’ report (2005).

3. CONCLUSIONS

The data, generated in the process of offering geotechnical consultancy for different projects, or as self-sponsored research at CSMRS, forms the basis for the foregoing discussions. And, it prods one to be conscious with regard to the appropriateness of assumptions and/or theories (‘scientific’

or empirical) for the assessment of any property or parameter for a given rock. And, the fundamental reason for most of these surprises and complications is that we fail to appreciate (i) the full importance of the assumptions involved in theoretical formulations, and (ii) the restricted applicability of the empirical correlations. And, for proper assessment, the rock needs to be evaluated holistically.

ACKNOWLEDGEMENTS

The CSMRS’ Rock Mechanics laboratory personnel’s contribution, and also that of Dr. A.K. Dhawan, former Director, CSMRS, is gratefully acknowledged.

REFERENCES

Abdullah, H. and Dhawan, A.K. (2004). “Some Implications of Empiricism and Assumptions in Laboratory Testing”, Proc. SINOROCK 2004 Symposium, Paper 1A 19 (7 pages).

Abdullah, H. and Dhawan, A.K. (2007). “Assessment of Rock from Tala Hydroelectric Project”, Proc. International Workshop on Experiences Gained in Design and Construction of Tala Hydroelectric Project, Bhutan, New Delhi, 122–128.

Abdullah, H., Bandyopadhyay, A. and Dhawan, A.K. (2002). “Waves Velocities and Rock Cores”, Proc. INDOROCK, New Delhi (India), 60–69.

Abdullah, H., Dhawan, A.K. and Bandyopadhyay, A. (1999). “Point Load Strength Index and Uniaxial Compresssive Strength”, Proc. Int. Conf. on Rock Engineering Techniques for Site Characterisation, Bangalore (India), 333–340.

Abdullah, H., Dhawan, A.K. and Bandyopadhyay, A. (1999). “Use of Waves Velocities in Laboratory Investigation of Rock”, Proc. Indian Geotechnical Conference, Calcutta (India), 20–23.

CSMRS (1999). “Report on Laboratory Investigations of Rock from De-Silting Chamber of Tala Hydroelectric Project, Bhutan, Report No. RM-II/6/1999 (unpublished)”, Central Soil & Materials Research Station, New Delhi, India.

CSMRS (2005). “Report on Laboratory Investigations of Rock from Omkareshwar HE Project”, MP, Report No. 7/RM-II/CSMRS/E/12/2005 (unpublished), Central Soil & Materials Research Station, New Delhi, India.

ISRM (1985). “Suggested Method for Determining Point Load Strength”, International Journal of Rock Mechanics, Mining Sciences & Geomechanics Abstracts, Vol. 22, No. 2, 51–60.

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