Estimating the uniaxial compressive strength of a volcanic bimrock

Transcription

1 International Journal of Rock Mechanics & Mining Sciences 43 (26) Estimating the uniaxial compressive strength of a volcanic bimrock H. Sonmez a,, C. Gokceoglu a, E.W. Medley b, E. Tuncay a, H.A. Nefeslioglu c a Department of Geological Engineering, Applied Geology Division, Hacettepe University, 632 Beytepe, Ankara, Turkey b Medley GeoConsultants, 14 Winding Way, Belmont, CA 942, USA c General Directorate of Mineral Research and Exploration, 62 Ankara, Turkey Accepted 26 September 2 Available online 8 November 2 Abstract Preparation of the standard sized cores from geological mixtures or fragmented rocks such as me langes, fault rocks, coarse pyroclastic rocks, breccias and sheared serpentinites is often extremely difficult. Therefore, determination of the mechanical parameters such as cohesion, friction angle and UCS is extraordinarily difficult for these types of rocks. This paper presents the results of studies using Ankara Agglomerate to develop an empirical approach for the determination of the UCS for a volcaniclastic mixture of strong andesite blocks within weak tuff matrix, formed from the aggregation of volcanically exploded rock debris mixed with ash fall (tuff), i.e. a bockin-matrix rock or bimrock. The uniaxial compressive strength of a volcanic bimrock can be predicted using the conceptual approach within as-yet poorly understood error limits. Therefore, the approach introduced is open to improvement depending on the number of data and cases including different type of bimrocks. r 2 Elsevier Ltd. All rights reserved. Keywords: Bimrock; Empirical equation; Ankara Agglomerate 1. Introduction The uniaxial compressive strength (UCS) is one of the important input parameters used in rock engineering designs of tunnels, foundations and slopes. NX-sized core samples are recommended by ISRM [1] for the laboratory tests performed to determine UCS values. But, it is often extremely difficult to obtain standard sized cores from geological mixtures or fragmented rocks such as melanges, fault rocks, coarse pyroclastic rocks, breccias and sheared serpentinites. Although field tests such as dilatometer and plate loading tests, are often employed for determining both modulus of elasticity and UCS at in-situ scales, empirical models are also an alternative and popular tool. This paper presents the results of studies using Ankara Agglomerate used to develop an empirical approach for the determination of the UCS for a volcaniclastic mixture of strong andesite blocks within weak tuff matrix, formed from the aggregation of volcanically exploded rock debris Corresponding author. Tel.: ; fax: address: haruns@hacettepe.edu.tr (H. Sonmez). mixed with ash fall (tuff). Volcanic agglomerates of gravel to boulder-sized blocks in weaker cemented matrix are difficult to test in the laboratory because of the often considerable strength contrasts between the blocks and the surrounding matrix. Depending on the scale of engineering interest, geological mixtures of strong blocks or rock surrounded by weaker matrix may be considered as block-in-matrix rocks, or bimrocks, which Medley [2] defined as mixtures of relatively large, competent blocks within a bonded matrix of finer and weaker texture. Geological mixtures of competent blocks of rock and weak matrix are bimrocks at the scales of engineering interest (laboratory to site scale) if there is sufficient mechanical contrast between blocks and matrix to force failure surfaces around blocks, and if the number, size distribution and volumetric proportion of blocks influences the mechanical behavior of the mixtures. Lindquist and Goodman [3] and Medley and Goodman [4] identified some of the fundamental geomechanical properties of melange bimrocks, which may be extendable to other geological mixtures, depending on the scale of interest. Lindquist and Goodman [3] showed that increases /$ - see front matter r 2 Elsevier Ltd. All rights reserved. doi:1.116/j.ijrmms

2 H. Sonmez et al. / International Journal of Rock Mechanics & Mining Sciences 43 (26) 4 61 in volumetric block proportions lead to increases in the overall friction strength and decreases in cohesion strength for model melange bimrocks. The decrease in cohesion strength as volumetric block proportion increases is thought to be due to the increase in the proportion of block/matrix contacts, which in tectonically sheared melanges is generally the weakest component of the bimrock []. However, in earlier studies using Ankara Agglomerate, Sonmez et al. [6] showed that the interaction between blocks and matrix is more complex than assumed in previous literature, in that the overall strength of Ankara Agglomerate was also dependent not only on the volumetric proportion of the andesite blocks but also the high strength contrast between the blocks and the tuff matrix. Cumulative frequency finer (%) Average=1.7 Standard deviation=9.47cm Minimum=1cm Maximum=69cm Average block dimension (cm) Fig. 2. Block-size distribution of andesite blocks in Ankara Agglomerate. 2. Properties of Ankara Agglomerate Ankara Agglomerate is a volcaniclastic mixture of pink and black andesite blocks ranging from a few centimeters to about one meter in size, cemented by weak tuff matrix (Fig. 1). Measurements of blocks at some outcrops in 2- dimensions revealed that the block sizes vary between 1 and 69 cm while the mean value is 1.7 cm, as indicated in the block-size distribution graph shown as Fig. 2. The engineering properties of the constituents of the Ankara Agglomerate were determined by a series of laboratory tests performed on the tuff matrix, and the pink and black andesite blocks. The uniaxial compressive strength and unit weight tests were performed on 7 specimens in accordance with the suggested method of ISRM [1]: the results of the tests are summarized in Table 1. The average UCS for the tuff matrix is 1.6 MPa, ranging between 6.4 and 14.4 MPa. The range in UCS values for blocks was 34 MPa (minimum, pink) to 12 MPa (maximum, black). The average values of UCS for pink and black andesite blocks are and 91 MPa respectively. The UCS block /UCS matrix ratios for the constituents of the Ankara Agglomerate exhibited a significant difference, with the minimum and maximum ratios being 2.4 and 18.7, Table 1 Statistical evaluations of uniaxial compressive strength (UCS) and unit weight (g) for the constituents of the Ankara Agglomerate (After Sonmez et al. [6]) Statistical parameter g (kn/m 3 ) UCS (MPa) Black andesite Number of samples 3 33 Average Standard deviation Minimum Maximum Pink andesite Number of samples Average Standard deviation Minimum Maximum Tuff matrix Number of samples Average Standard deviation Minimum Maximum respectively. Based on the data above, Ankara Agglomerate meets one of the criteria proposed by Medley [2] for a geological mixture to be considered a bimrock, in which the UCS block /UCS matrix value should be 2 or greater. 3. Determination of volumetric block proportions Fig. 1. Outcrop of Ankara Agglomerate. To obtain accurate volumetric block proportions and block size distributions for geological mixtures at laboratory scale, it is necessary to perform sieve analysis on hard blocks separated from the weak matrix. However, in the case of volcaniclastic Ankara Agglomerate, separation of andesite blocks from tuff matrix as impossible because of the variable welding between blocks and matrix. Instead, node-counting (zero dimensions), scan-line surveys in 1-dimension, and image analyses in 2-dimensions were

3 6 ARTICLE IN PRESS H. Sonmez et al. / International Journal of Rock Mechanics & Mining Sciences 43 (26) 4 61 performed to stereologically estimate the volumetric block proportion of the bimrocks [2,7,8]. Previous studies using 1D, 2D and 3D evaluations [7] show that the shape and orientation of blocks (and the volumetric proportion itself) influence estimates of volumetric block proportions. Hence, to define the block dimensions and shapes of the blocks within the Ankara Agglomerate, the longest and shortest dimensions of many individual blocks were measured by Sonmez et al. [6] from different exposures of the Ankara Agglomerate. Due to the volcanically exploded origin of the rock, it was assumed that there was no preferred orientation of the blocks within the matrix. The ratios of the longest to the shortest dimensions of the measured blocks were generally less than 1.2, which prompted the reasonable assumption that the blocks were equi-dimensional in 2D and 3D (Fig. 2), and that the uncertainties in estimation of 3D block proportions based on 2D measurements of the Ankara Agglomerate would thus be lessened [6]. Node-counting and image classifications of grayscale and colored photographs, and were employed in previous studies [6,8 1] to evaluate the volumetric block proportions of the Ankara Agglomerate at field scale. For this purpose, scaled photographs were taken perpendicular to nearly planar agglomerate outcrop exposures (Fig. 1). The methods used for determining of the volumetric block proportion from image analyses were given in detail by Sonmez et al. [6], Gokceoglu et al. [8], Gokceoglu [9] and Sonmez et al. [1]. In the current study the data included volumetric block proportions from core samples were obtained by Sonmez et al. [6]. 4. Properties of the database used for regression analysis Recognizing the problems that occur because of the differences in between in-situ and laboratory samples, block samples with relatively small andesite blocks were collected from outcrops of Ankara Agglomerate. UCS tests were performed on the core samples in accordance with the procedure suggested by ISRM [1]. Fig. 3 shows a typical laboratory set-up for testing of a core sample. A total of 27 core samples were obtained by Gokceoglu et al. [8], Gokceoglu [9] and Sonmez et al. [1]. The database was established between 1997 and 24, which is admittedly a long period, but was due to the difficulties encountered in obtaining high quality core samples from the Ankara Agglomerate. A histogram of UCS values of the Ankara Agglomerate is illustrated in Fig. 4. The UCS values vary between.7 and. MPa and are dependent on the volumetric block proportion of the andesite blocks [6,8 1]. Statistical assessments of unit weight, UCS and the percentage of the constituents of the Ankara agglomerate core samples are given in Table 2. In addition, specimens of 1 cm diameter were tested to check the performance and evaluate the size effect of the empirical equation generated from the study discussed here [8 1]. Fig. 3. The experimental setup used for uniaxial compressive strength tests.. Conceptual approach for volcanic bimrocks Lindquist and Goodman [3] and Lindquist [11] determined that the overall mechanical properties of melange bimrocks are simply and directly related to the volumetric proportion of blocks in the bimrock. Between a range in volumetric block proportion of about 2 percent and 7 percent, the presence of blocks contributes strength to the bimrock, additive to that of the matrix. Below about 2 percent, the frictional strength of a bimrock is the same as the matrix strength, and above 7 percent, there is no further increase in strength (Fig. ). Given some matrix strength, the increase in friction angle can be as much as 1 degrees to 2 degrees greater [11]. In general, the contact between blocks and matrix in sheared bimrocks such as melanges and fault rocks is weaker than the matrix, and observed failure surfaces generally negotiate around blocks. However, for failed specimens of Ankara Agglomerate with high block proportions, failure paths were observed to cross from matrix into and through andesite particles (Fig. 6).

4 H. Sonmez et al. / International Journal of Rock Mechanics & Mining Sciences 43 (26) Therefore, there is some justification for proposing that both the volumetric block proportion and the block/matrix strength contrast contribute to overall strength. For the empirical approach investigated in this study, it is assumed that the overall UCS of Ankara Agglomerate increases directly with both increasing volumetric block proportion and increasing block/matrix contrast. Since black andesite is stronger than pink andesite; the likely effect of black andesite on the overall strength of bimrock was considered higher than for pink andesite. Although the sum of the volumetric proportions of black and pink andesite blocks is equal to the total block proportion, a weighted calculation incorporated the UCS difference between the two different block types to produce an equivalent block proportion (EBP) of the bimrock including two or more different type of blocks: EBP ¼ Xn UCS i VBP i, (1) UCS i max block where VBP i is the volumetric block proportion of ith element, UCS i is the uniaxial compressive strength of the 3 Std.Dev=1.2 MPa Mean=24.9 MPa N = 27 ith element, n is the number of different types of blocks, and UCS max_block is the uniaxial compressive strength of the strongest block. The UCS of the Ankara Agglomerate specimens, denoted by UCS N, were normalized by dividing by the average UCS of the matrix tuff. Fig. 7 illustrates the graphed distributions of EBP vs. UCS N data. Two exponential-type equations were obtained by regression analyses of the data (Fig. 7): one being a bestfit line with a coefficient of correlation of.482; and the other a regression forced to a y-value of unity, which is more representative for high values of EBP, but with a decreased correlation of coefficient (.42). The two Incremental friction angle (deg) Scott Dam melange Physical models weathered Scott Dam melange Irfan ve Tang [12] conservative trend, Lindquist [11] Volumetric block proportion (%) Frequency 2 1 Fig.. Relationship between incremental friction angle (increase in friction is added to the friction strength of matrix) and volumetric block portion (After Medley [7])) [11,12] Uniaxial compressive strength, UCS (MPa) Fig. 4. Histogram of the UCS values of Ankara Agglomerate. Fig. 6. Cross-section through failed NX-size core specimen perpendicular to failure surface, showing failure surface penetrating matrix and block. Table 2 Statistical evaluations of uniaxial compressive strength (UCS) and unit weight (g) for Ankara Agglomerate (After Sonmez et al. [6]) Statistical parameter g (kn/m 3 ) UCS (MPa) Proportion of constituents Black andesite (%) Pink andesite (%) Tuff matrix (%) Number of samples Average Standard deviation Minimum Maximum

5 8 ARTICLE IN PRESS H. Sonmez et al. / International Journal of Rock Mechanics & Mining Sciences 43 (26) 4 61 regression equations are: UCS N ¼ 1:3361 expð1:12 EBPÞ; r ¼ :482, (2) UCS N ¼ expð1:6874 EBPÞ; r ¼ :42, (3) where UCS N is the normalized uniaxial compressive strength of the Ankara agglomerate, and EBP is equivalent block proportion varying between.4 and.8. Cross-checks between estimated and observed uniaxial compressive strengths were also performed using Eqs. (2) and (3), as illustrated in Fig. 8, where the data are compared with 1:1 line representing perfect estimation. The data generated using the Eq. (3) estimates actual UCS data better than the data generated by Eq. (2), although both data sets exhibit considerable scatter. Based on the apparent better fit with Eq. (3), a generalized relationship was written (and illustrated as Fig. 9): UCS N ¼ expðc EBPÞ, (4) where the C constant controls the curvature of the equation and amount of increase in normalized UCS depending on the strength contrast between blocks and matrix. We suggest that the form of Eq. (4) may be more universally applicable, and that different kinds of bimrock will have different strength contrasts. Variations in the C value were investigated using the Ankara Agglomerate database of UCS values. As can be seen from Table 1, average strengths of black and pink andesite are different from each other. Therefore, if the weighted UCS values of andesite blocks are considered, the block/matrix strength contrast of each core sample changes depending on the type and amount of andesite blocks. The strength contrast of each core was thus calculated by using the by weighted average method incorporating block proportions and UCS values of black and pink andesites. The strength contrasts of whole core samples varied between 4.8 and 8.6. The data were classified into three classes ranges of 4 6, 6 8 and 48, and are illustrated in Fig. 1. Although one rock type with a relatively narrow agglomerate tuff matrix Normalized uniaxial compressive strength, UCS = UCS N UCS UCS = e N r= EBP Equivalent block portion, EBP UCS = e N r= EBP Strength range of tuff matrix Fig. 7. Relationships between (EBP) equivalent block portion and normalized UCS of the Ankara Agglomerate. Normalized uniaxial compressive strength, UCS N Not Applicable for low matrix content (less than 2 %) Equivalent block proportion, EBP Increase in strength contrast SC=2 Strength range of matrix Fig. 9. Schematic illustration of approach proposed in this study. SC= Observed uniaxial compressive strength (MPa) y=1.7 r=.9 1: (a) Predicted uniaxial compressive strength (MPa) 1:1 2:1 Observed uniaxial compressive strength (MPa) y=1. r=.8 1: (b) Predicted uniaxial compressive strength (MPa) 1:1 2:1 Fig. 8. The cross-checks between predicted and observed uniaxial compressive strength considering (a) Eq. (2) and (b) Eq. (3).

6 H. Sonmez et al. / International Journal of Rock Mechanics & Mining Sciences 43 (26) Normalized uniaxial compressive strength, UCS N 6 Strength conrtast ratio (SC) between 8 and 9 between 6 and 8 between 4 and Observed uniaxial compressive strength (MPa) :2 y=1.3 r=.62 1:1 2:1 Equivalent block proportion, EBP Fig. 1. The distribution of classified data based on strength contrast ratio. Table 3 The variation of the constant C for different strength contrasts (SC) Predicted uniaxial compressive strength (MPa) Fig. 11. The cross-check between predicted UCS (incorporating strength contrasts), and observed UCS of Ankara Agglomerate. Strength contrast (SC) C constant strength contrast was considered, the data showed that for specimens of Ankara Agglomerate with the same equivalent block proportion (EBP), smaller block/matrix strength contrasts are correlated with generally lower normalized strength than with higher strength contrast. On the basis of this finding, each strength class was reevaluated using Eq. (4), and C, constants obtained by trial and error, summarized in Table 3. The relation between C and strength contrast was also obtained as a logarithmic equation (Eq. ()). The cross check between estimated and observed UCS, taking into account strength contrasts, is illustrated in Fig. 11. The correlation of coefficient (r ¼ :62) is slightly higher than that of the non-classified regression that yielded Eq. (3). C ¼ :8 ln ðscþ; ðr :99Þ, () SC ¼ UCS block UCS matrix, (6) UCS block ¼ P n i¼1 VBP block i UCS blocki P n i¼1 VBP block i, (7) where SC is the strength contrast between blocks and matrix. Based on this limited study, it is suggested that the UCS of a bimrock may be estimated using relations of the form of Eqs. (1) and (4 7), with input parameters of volumetric block proportion and the strengths of blocks and matrix. Uniaxial compresive strength (MPa) (19.6 %) Observed UCS values Predicted UCS values (3.2 %) However it is cautioned that estimates of volumetric block proportion are subject to considerable uncertainty, particularly where the blocks are less uniformly shaped than those in the Ankara Agglomerate. Furthermore, since the relationships introduced in this paper were constructed using data obtained from a few specimens of one volcanic bimrock, the relation given by Eq. () should be tested and refined test data from different bimrocks with a variety of strength contrasts. 6. Testing the proposed approach The predictive performance of the proposed approach was tested with five additional data obtained from the 1 mm diameter core samples of Ankara Agglomerate (Fig. 12). The percentages of the black and pink andesite (-2.2 %) Sample No Fig. 12. Comparison between predicted and observed UCS for 1 mm diameter Ankara Agglomerate core samples. (-27.8 %) (8. %)

7 6 ARTICLE IN PRESS H. Sonmez et al. / International Journal of Rock Mechanics & Mining Sciences 43 (26) 4 61 Table 4 Performance check of the conceptual approach using 1 mm diameter core samples of Ankara Agglomerate Sample no Proportion of black andesite (%) Proportion of pink andesite (%) Proportion of Tuff matrix (%) Equivalent block proportion (EBP) Observed UCS (MPa) Estimated UCS (MPa) Percentage error (%) Fig mm diameter Ankara Agglomerate core samples. Inset shows the two faces of a failed andesite block. content of the samples (Table 4) were obtained by Sonmez et al. [1] using image analysis techniques. The UCS values of the constituents were taken from Table 1. The predicted UCS values of the core samples were determined by the conceptual approach using Eqs. (1) and (4 7). Since the proposed conceptual approach was developed from data obtained by laboratory studies on NX-size samples, the observed UCS values were corrected using the Hoek and Brown empirical correction equation given in Eq. (8) which considers mm diameter as a reference diameter close to NX size (as recommended by ISRM [1]). UCS ¼ UCS d. (8) :18 ð=dþ The comparison between observed and predicted UCS values is illustrated in Fig. 12 and summarized in Table 4. While three of the five results were predicted with errors less than 1%, the other two results had errors of about 2% and 3%. One reason for the variance in results may be that, despite assumed strength contrasts between tuff matrix and andesite blocks, some of the blocks in were observed to have failed (Fig. 13). 7. Conclusions It can be concluded that the uniaxial compressive strength of a volcanic bimrock can be predicted using the conceptual approach within as-yet poorly understood error limits.

8 H. Sonmez et al. / International Journal of Rock Mechanics & Mining Sciences 43 (26) Following results and conclusions can be drawn from the study described above: (a) The results of the tests performed on core specimens of Ankara Agglomerate showed that the UCS depends on both the volumetric block proportion and the strength contrast between blocks and matrix. (b) The UCS of volcanic bimrocks such as Ankara Agglomerate, can be predicted using a quantitative conceptual approach. The equations proposed herein accommodate more than one type of block. However, the proposed equations cannot be used to reliably predict the UCS of a bimrock having volumetric block proportions greater than 8%. (c) The empirical approach introduced in this study was developed from data obtained from Ankara Agglomerate, a volcanic bimrock, for which the strength contrast between blocks and matrix is high compared to other types of bimrocks where there is no welding between blocks and matrix. For other bimrocks, the mechanical contrast between blocks and matrix will differ depending on the origin of bimrock. Accordingly, the conceptual approach proposed in this paper should only be considered for bimrocks where the strength between blocks and matrix is approximately equal to that of matrix alone. (d) The approach introduced is open to improvement depending on the number of data and cases including different type of bimrocks. (e) The strength contrast between blocks and matrix contributes significantly to the overall strength of volcanic bimrocks. (f) The predictive performance of the conceptual approach, as checked using core specimens of Ankara Agglomerate with large diameter, indicates that the approach has promise. (g) Strength anisotropy of bimrocks due to blocks shape and orientations was not considered in the proposed approach, but is an important factor given that sheared and foliated bimrocks such as fault rocks and me langes have anisotropic behavior. Considerable additional study is necessary to investigate whether correction factors could be introduced to the approach. Acknowledgement This research was supported by TUBITAK (The Scientific and Technical Research Council of Turkey) (Project no: 12Y33). References [1] ISRM (International Society for Rock Mechanics). In: Brown E.T., editor. ISRM suggested method: rock characterization, testing and monitoring, London: Pergamon Press; 1981, 211pp. [2] Medley E. The engineering characterization of melanges and similar block-in-matrix rocks (bimrocks). PhD thesis, Department of Civil Engineering, University of California, 1994, 17pp. [3] Lindquist ES, Goodman RE. The strength and deformation properties of a physical model mélange. In: Nelson PP, Laubach SE, editors. Proceedings of the first North American rock mechanics conference (NARMS), 1994, Austin, TX. Rotterdam: AA Balkema. [4] Medley E, Goodman RE. Estimating the block volumetric portion of mélanges and similar block-in-matrix rocks (bimrocks). In: Nelson PP, Laubach SE, editors. Proceedings of the first North American rock mechanics conference (NARMS), 1994, Austin, TX. Rotterdam: AA Balkema. [] Medley E. Observations on tortuous failure surfaces in Bimrocks. Felsbau Rock Soil Eng 24;:3 43. [6] Sonmez H, Gokceoglu C, Tuncay E, Medley E, Nefeslioglu HA. Relationships between volumetric block proportions and overall UCS of a volcanic Bimrock. Felsbau Rock Soil Eng 24;:34 7. [7] Medley E. Orderly characterization of chaotic Franciscan Melanges. Felsbau Rock Soil Eng 21;19(4):2 33. [8] Gokceoglu C. A fuzzy triangular chart to predict the uniaxial compressive strength of the Ankara Agglomerates from their petrographic composition. Eng Geol 22;66:39 1. [9] Gokceoglu C, Kasapoglu KE, Sonmez H. Prediction of uniaxial compressive strength of Ankara Agglomerates from their petrographical composition. In: Moore D, Hungr O, editors. Proceedings of the eighth international congress of IAEG and the environment, Vancouver, Canada. Rotterdam: AA Balkema; p [1] Sonmez H, Tuncay E, Gokceoglu C, Nefeslioglu HA. Matriks ic-inde blok ic-eren kayac-ların deformasyon modu lu nu n saptanabilmesine yönelik fotoanaliz destekli yaklas-ımların aras-tırılması. TUBITAK, Report No: 12Y33, 131pp (in Turkish). [11] Lindquist ES. The strength and deformation properties of melange. PhD thesis, University of California, pp. [12] Irfan TY, Tang KY. Effect of the coarse fraction on the shear strength of colluvium in Hong Kong. Hong Kong Geotech Eng Office 1993 TN 4/92.