A block-in-matrix rock (bimrock) in the Sierra Nevada of California. Decomposed granite contains hard blocks (core-stones) surrounded by a matrix of dense sandy soil (grus). Photo: E. Medley.

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... include complex geological mixtures such as olistostromes, weathered rocks, fault rocks, and mélanges. Weathered rocks can include mixtures of decomposed soil surrounding fresher core-stones (Fig. 1). Fault rocks, composed of blocks within gouge and sheared rock (Fig. 2), exist at many scales, with blocks ranging between several tens to hundreds of meters in size to millimeter-sized fragments within gouge ( Riedmüller et al., 2001Riedmüller et al., , 2004). Mélanges, the most intractable of bimrocks, contain competent blocks of ...

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... the Franciscan mélanges measured, the range in block sizes exceeds seven orders of magnitude between sand (millimeters) and mountains (tens of kilometers), as illustrated in Fig- ure 10. Despite the considerable difference in scales, the mélanges measured from outcrops and maps shown in Figure 10 indicate individual scale-independent block-size distributions with similar appearances. ...

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... the Franciscan mélanges measured, the range in block sizes exceeds seven orders of magnitude between sand (millimeters) and mountains (tens of kilometers), as illustrated in Fig- ure 10. Despite the considerable difference in scales, the mélanges measured from outcrops and maps shown in Figure 10 indicate individual scale-independent block-size distributions with similar appearances. Consequently, blocks will always be found in Franciscan mélanges regardless of the scale of observation. ...

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... (1994a) and Medley and Lindquist (1995) showed that the largest geotechnically signifi cant block (d max ) within any given volume of Franciscan mélange is ~0.75L c (Fig. 10). Blocks greater than 0.75Lc result in such a diminished proportion of matrix in a local volume of rock mass that the volume can be considered to be massive, unmixed rock composed mostly of the block. Furthermore, for any given volume of Franciscan Ellen and Wentworth, 1995). The slopes of the log-log plots are the fractal dimension D. ...

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... be considered to be massive, unmixed rock composed mostly of the block. Furthermore, for any given volume of Franciscan Ellen and Wentworth, 1995). The slopes of the log-log plots are the fractal dimension D. The shapes of the two plots are similar despite the extreme difference in scales. After Medley (1994a). mélange, blocks <0.05L c in size (Fig. 10) constitute greater than 95% of the total number of blocks but contribute <1% to the total volume of mélange and have a negligible effect on the mechanical behavior of the mélange (Medley, 1994a). For these reasons, the threshold size between blocks and matrix at any scale is taken to be 0.05L c ...

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... weakest elements in mélanges are commonly the contacts between blocks and matrix (Fig. 11). In some bimrocks, such as welded tuffs, the contacts may be strong ( Sönmez et al., 2004). In outcrops and core, contacts may be marked by a lustrous surface on the blocks and a wafer of sheared material that weathers to a slick fi lm of clay. Matrix shears generally pass around blocks via the block-matrix contacts (Figs. 7 and 11) ...

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... blocks and matrix (Fig. 11). In some bimrocks, such as welded tuffs, the contacts may be strong ( Sönmez et al., 2004). In outcrops and core, contacts may be marked by a lustrous surface on the blocks and a wafer of sheared material that weathers to a slick fi lm of clay. Matrix shears generally pass around blocks via the block-matrix contacts (Figs. 7 and 11) with the most intense shearing commonly present adjacent to the largest blocks. Blocks within the shears are commonly entrained within and oriented subparallel to shears (Fig. 8). Because shears have a tortuous path through the rock mass, the overall orientation of entrained blocks can also abruptly change from place to place within ...

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... shown in Figure 12, Lindquist (1994a) conservatively established that <~25% volumetric block proportion the frictional strength and deformation properties of a physical model mélange was that of the matrix, a conclusion supported by the research of Irfan and Tang (1993). However, Goodman and Ahlgren (2000) and Roadifer et al. (2009) identifi ed increases to overall mélange strength at volumetric block proportions <~25%. ...

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... direct and relatively simple relationship between strength and volumetric block proportions for mélanges and other bimrocks is appealing to geopractitioners. Nevertheless, to Figure 12. This plot shows that strength of bimrocks increases with volumetric block proportion. ...

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... 5: Measure total linear block proportion L L Step 6: Assume L L is equivalent to volumetric block proportion V v and estimate uncertainty range in estimate of V v (use Fig. 14) Step 7: Establish conservative design values of volumetric block proportion, using lower bound for strength and upper bound for earthwork ...

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... 8: Measure lab strengths of specimens with different V v proportions and construct a plot of specimen strength vs. V v (such as Fig. 12 or Fig. 18) Step 9: On plot of specimen strength vs. V v identify critical volumetric block proportions and following three ...

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... 8: Measure lab strengths of specimens with different V v proportions and construct a plot of specimen strength vs. V v (such as Fig. 12 or Fig. 18) Step 9: On plot of specimen strength vs. V v identify critical volumetric block proportions and following three ...

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... models were explored with hundreds of model boreholes. The extreme variability in linear proportions, even for adjacent borings, is indicated by Figure 13. Based on thousands of randomized realizations of the model boring data, Medley ( , 2002) concluded that potentially serious errors result if volumetric block proportions, total block volumes, and block size distributions are assumed, without qualifi cation, to be equivalent to the linear block proportions measured from few borings or outcrops. ...

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... (1997) experiments showed that measured linear block proportions have to be adjusted by an uncertainty factor (actually, the coeffi cient of variation) to yield an appropriate estimate of the volumetric block proportion (Fig. 14). Uncertainty depends on both the total length of the linear measurements, such as from drilled core, and the linear block proportion itself. In Figure 14 the total length of drilled core is shown as Nd max , or multiples of the size of the largest expected block, d max , which can be estimated from fi eld exposures or else assumed to ...

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... depends on both the total length of the linear measurements, such as from drilled core, and the linear block proportion itself. In Figure 14 the total length of drilled core is shown as Nd max , or multiples of the size of the largest expected block, d max , which can be estimated from fi eld exposures or else assumed to be 0.75Lc at site scale. ...

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... the other hand, for the purpose of assessments of excavation rippability and construction preparedness in tunneling or earthwork construction, it is prudent and conservative to adjust upward the calculated estimates of volumetric block proportions. Figure 13. Plan view of an array of 100 linear block proportions ranging between 0% and 61%, measured for a physical model bimrock with an actual volumetric block proportion of 32%. ...

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... The degree to which 1-D (one dimension) chord length distributions match actual 3-D block size distributions is dependent on the orientation of blocks relative to the boring directions, volumetric block proportion, and total length of drilling. Because observed chord lengths are almost invariably smaller than the actual block diameters (Fig. 15) the frequency of larger block sizes tends to be underestimated, and the frequency of smaller sizes overestimated. Indeed, larger blocks are mischaracterized as smaller blocks to the degree that small block sizes are indicated that may not even be part of the actual 3-D block size distribution (Fig. 15). Estimates of 3-D block size ...

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... smaller than the actual block diameters (Fig. 15) the frequency of larger block sizes tends to be underestimated, and the frequency of smaller sizes overestimated. Indeed, larger blocks are mischaracterized as smaller blocks to the degree that small block sizes are indicated that may not even be part of the actual 3-D block size distribution (Fig. 15). Estimates of 3-D block size distributions from measurements of 2-D outcrop areas also yield widely erroneous estimates (Haneberg, ...

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... distributions in mélanges infl uence the construction behavior and long-term performance of dam and structure foundations, slopes (Medley and Sanz, 2004), and underground excavations ( Button et al., 2003;Moritz et al., 2004;Riedmüller and Schubert, 2002). Stress states depend on the in situ stress and lithologies; size distributions, orientations, and shapes of blocks; Figure 14. This plot provides the uncertainty in assuming that measured linear block proportions (13% to 55%) are assumed to represent volumetric block proportion. ...

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... were proposed to mitigate landslides that intermittently disrupted a main road in California. Based on borings terminated ~2 m into apparent sandstone bedrock, the investigating geopractitioner concluded that each of the landslides was composed of a shallow layer of clay and boulder colluvium sliding on the surface of underlying sandstone bedrock (Fig. 16). He recommended that the most economical repair would be removal of the failed soil down to the solid bedrock and re-grading of the failed slopes. The successful contractor bid for the designed repairs of the several landslides for a fi xed price of more than a million ...

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... landslide was actually a deep-seated earth fl ow in pervasively sheared mélange rather than a shallow soil mass sliding on top of apparent bedrock, as interpreted from exploration drilling. The interpreted bedrock was the graphical artifact of connecting straight lines between the soil-rock contacts intersected by the borings (Figs. 5 and 16). Although the geological chaos was a surprise to the geotechnical engineer, it should not have been, as publically available geological maps showed the locale of the landslide to be within Franciscan mélange, with large blocks protruding prominently from the hillside around the ...

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... linear block proportion for all the mélange explored was ~10%, which was the weighted average of block-poor mélange within the landslide (about zero percent) and block-rich mélange beneath the slide (28%). The 375 m total length of drilling was equivalent in length to 12.5d max (where d max was 30 m). Figure 14 indicates the uncertainty to be at least 0.40 for a measured linear block proportion of 10%, total drilling of 375 m equivalent to 12.5 times the length of the estimated d max of 30 m (i.e., Nd max of 12.5), and the assumption that the measured linear block proportion of 10% was equivalent to a volumetric block proportion of 10%. Hence the estimated range of volumetric block proportions ranged between 6% and 14% (10% ± 0.4 times 10%). ...

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... and 0.75 L c , for the largest block, d max . For the Scott Dam project, the block-matrix threshold was selected as 0.15 m, or 5% of the postulated 3-m-thick basal shear zone. This criterion was used to discriminate blocks from matrix when reviewing drill core and drill logs. Measurement of block chord lengths in drill logs and photographs (Fig. 17) of Scott Dam core in the assumed critical potential failure zone indicated that the linear block proportion was ~40% for the postulated critical 3-m-thick shear band of failed mélange below the ...

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... there were insuffi cient data, the estimated volumetric block proportion had to be adjusted for uncertainty. As shown in Figure 14, using the procedure described by the estimated linear block proportion was 40%, the uncertainty was 0.2, and the adjusted estimate was 32% to 48% (40% ± 0.2 times 40%). For purposes of strength estimates, it is prudent to use the lower bound, so a conservatively adjusted volumetric block proportion of 32% was selected for the volumetric block proportion of the Franciscan mélange below the dam. ...

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... testing of Scott Dam laboratory specimens with different block proportions yielded a plot of effective friction angle as a function of volumetric block proportion (Fig. 18). The overall strength of the foundation rock mass was evaluated using the adjusted estimate of rock mass volumetric block proportion and the laboratory plot of effective friction angle as a function of volumetric block proportion. For the mélange beneath Scott Dam, the friction angle was estimated to be 39° for the overall 31% ...

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... strength of the foundation rock mass was evaluated using the adjusted estimate of rock mass volumetric block proportion and the laboratory plot of effective friction angle as a function of volumetric block proportion. For the mélange beneath Scott Dam, the friction angle was estimated to be 39° for the overall 31% volumetric block proportion (Fig. ...