Rock catchment area design charts. L. Pantelidis 1. of Thessaloniki, Thessaloniki, Greece, PH (+30) ;

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1 224 Rock catchment area design charts L. Pantelidis 1 1 Department of Civil Infrastructure Engineering, Technological Educational Institute of Thessaloniki, Thessaloniki, Greece, PH (+30) ; lyssander_p@hotmail.com ABSTRACT Studies on the effectiveness of deep ditches against rockfalls have shown that, the original Ritchie (1963) guidelines are not as conservative as previously thought. Moreover, following these guidelines, a unique ditch depth width pair of values is obtained for a given rock cutting not allowing for the chosen of the most economical solution. The above findings gave rise to the research presented herein, where, a number of design charts based on a computer simulation program (RocFall TM ) are proposed for deep rockfall ditches. Rockfall concrete walls and fences became also subject of research as there are no relevant design charts currently available. The assumptions made for the derivation of the proposed charts are: a) the number of falling rocks is one hundred, b) the rocks are detached from the slope crest, c) the initial speed of falling rocks is zero, d) the material of slope is a clean hard bedrock and e) the base of the catchment area is covered by a layer of gravel to absorb the energy of falling rocks. For the case of deep rockfall ditches it was additionally assumed that, the ditch foreslope adjacent to the roadway is vegetated. Furthermore, as a cut slope can be of any rock type and thus, charts of this category provide indicative dimensions, the RocFall TM default material settings (e.g. coefficient of restitution) were adopted. Finally, it is noted that, for the simple geometries studied using RocFall TM (slopes without outcrops and benches) the rock impact distance was always zero and therefore, the calculated catchment area width should be corrected adding the maximum impact distance of rocks obtained by Pierson et al. (2001) empirical study. 1. INTRODUCTION Ritchie studied the problem of rockfalls along highways and in 1963 proposed an empirical design table of rock ditch dimensions (minimum depth and width) required to restrict rocks from rolling up onto the pavement. This table was later adapted into a design chart (FHWA, 1989), which is still used by numerous transportation agencies to dimension catchment areas. A major limitation of the design criteria of Ritchie, however, is that, for a given slope having height H and gradient n:1 a unique rock ditch pair of values is obtained, expressed in depth width. The ditch foreslope gradient next to the roadway is also standard (1V:1.25). It is obvious that, such a rigid methodology does not allow for the most cost-effective

2 225 solution. Moreover, a pilot study conducted by Pierson et al. (1994) showed that the original Ritchie guidelines are not as conservative as previously thought. Pierson et al. (2001) carried out a comprehensive study of rock fall behavior and the dimensions of even catchment areas with gradients 1V:4H, 1V:6H and zero (flat). In the study in question slopes with height from 12.2m up to 24.4m and gradient ranging from vertical to 1V:1H were examined. The main disadvantage of this rockfall catchment area design guide, however, is that, it calls for the construction of very wide catchment areas. Therefore, this design guide is a very useful tool in highway engineering only in case where the additional catchment area width does not create construction difficulties and considerable increase in construction cost. The above findings gave rise to the research presented herein, where, design charts based on computer simulation program (RocFall TM ) have been obtained for deep rockfall ditches with a 1V:1H and 1V:1.5H foreslope adjacent to the roadway (tanβ) as well as for rockfall concrete walls or fences (Figure 1). Figure 1. i) Ritchie type ditch and ii) Flat catchment area in combination with concrete wall or fence. w is the ditch width obtained using RocFall ΤΜ and w o is the maximum impact distance of the 99% of rockfalls derived through Pierson et al. (2001) empirical study. 2. EXISTING ROCKFALL SIMULATION MODELS Since the 1980s, a number of models that simulate the behavior of rockfalls as they roll and bounce down slope faces have been proposed. Some of the more recent rockfall simulation approaches, either mathematical models or computer programs, are those of Agliardi and Crosta (2003), Azzoni and De Freitas (1995), Azzoni et al. (1995), Bozzolo, D. and Pamini (1986), Bozzolo et al. (1988), Descoeudres and Zimmerman (1987), Guzzetti et al. (2002), Hungr and Evans (1989), Jones et al. (2000), Kobayashi et al. (1990), Pfeiffer and Bowen (1989), Pfeiffer et al. (1990), Piteau (1980), Rocscience (2002), Spang (1987), Spang and Rautenstrauch (1988) and Wu (1984). Perhaps the most well known computer programs are the RocFall TM (Rocscience, 2002) and the Colorado Rockfall Simulation Program TM (Jones et al., 2000). These are statistical analysis programs that have been designed to assist with assessment of slopes at risk for rockfalls and in determining remedial measures.

3 PROPOSED ROCK CATCHMENT AREA DESIGN CHARTS 3.1 Deep ditches (Ritchie type) Catch ditches at the toe of slopes are often a cost-effective means of stopping rock falls, provided that there is adequate space at the toe of the slope (Wyllie and Mah, 2004). A set of design charts based on computer simulation program (RocFall TM ) is proposed for deep rockfall ditches with a 1V:1H and 1V:1.5H (tanβ) foreslope adjacent to the roadway and for ditch depth equal to 1.0, 1.5 and 2.0m (Figure 2 and 3). The required ditch dimensions, as defined by the depth (d) and width (w), are related to the height (H) and the gradient of cut slope (tanα). The criterion for the determination of the minimum ditch width was that no rocks are allowed to roll up onto the pavement (100% retention in ditch). Interpolation between charts can be used. According to Rocsience (2003), the roll-out distance of rocks depends mainly on the retarding capacity of the surface materials expressed mathematically by the coefficient of restitution and the slope geometry. Other factors such as the size and shape of the rock boulders, the coefficients of friction of the rock surfaces and whether or not the rock breaks into smaller pieces on impact are all of lesser significance (Hoek, 2009). As regards to the above input material parameters, it is mentioned that, the default values found in the Project Settings and Material Editor menu dialogs in RocFall TM were used. In addition, the basic assumptions made in derivation of the proposed charts are: a) the number of falling rocks is one hundred, b) the rocks are detached from the slope crest (highest point), c) both the vertical and horizontal components of initial speed of falling rocks are zero, d) the material of slope is a clean hard bedrock, e) the base of the catchment area is covered by a layer of gravel to absorb the energy of falling rocks (as commonly done in practice) and f) the material of ditch foreslope adjacent to the roadway is a soil with vegetation. As it resulted from the computer simulations, for small slope gradients (generally less than 1.75V:1H) and small ditch widths the curves of Figures 2 and 3 concave upwards due to the fact that, rock blocks strike on the foreslope surface at small angle (nearly parallel) that cause them to cover a long distance bouncing and rolling. 3.2 Rockfall concrete walls or fences Rockfall concrete walls or fences are commonly used as alternative means of stopping rock falls, provided that there is also adequate space at the toe of the slope. Applying the same methodology as for deep ditches, a set of design charts is proposed for rockfall concrete walls and fences having height equal to 1.0, 1.5 and 2.0m. The required width (w) of catchment area and height of wall or fence (d) are related to the height (H) and the gradient of slope (tanα). The criterion of 100% retention applied to deep ditches for the determination of the minimum catchment area width was also used for the case of concrete walls and fences. Furthermore, the implementation of the present analysis was also based on the default values of material parameters found in RocFall TM menu dialogs. Finally, the assumptions a to e mentioned in the previous paragraph stand for the case which is examined herein as well. Interpolation between charts can be used.

4 227 Figure 2. Proposed rock catchment area design charts: Ritchie type ditches with a 1V:1H foreslope.

5 228 Figure 3. Proposed rock catchment area design charts: Ritchie type ditches with a 1V:1.5H foreslope.

6 229 Figure 4. Proposed rock catchment area design charts: Rockfall concrete walls and fences.

7 230 As it resulted from the computer simulations, for small slope gradients and catchment area widths the curves of Figure 4 concave upwards due to the fact that, the rockfall trajectories are interrupted by the wall or fence before gaining their maximum height during the first bounce. Therefore, a wall or fence as short as 2.0m (or less) is adequate to stop the falling blocks even in case of high cuttings. 3.3 Impact distance of falling rocks (w o ) It is noted that, the maximum impact distance of rocks taken from Pierson et al. (2001) design guide of even catchment areas (Figure 5) should be summed to the calculated catchment area width. Impact distance is defined as the measured distance from the base of the rock cut slope to the point where a falling rock first strikes the ground. This is done due to the fact that, for the simple geometries studied using RocFall TM (slopes without benches and outcrops) the impact distance was always equal to zero. Figure 5. Maximum impact distance of the 99% of rockfalls (after Pierson et al., 2001). The curves have been slightly refined. 4. RELIABILITY OF THE PROPOSED CHARTS The validity of the proposed charts depends mainly on the reliability of RocFall TM codes used to simulate rockfall trajectories and, as previously mentioned, on the chosen values of coefficient of restitution. A recent research carried out by Alejano et al. (2007) concluded that the computer simulations performed using RocFall TM approximate sufficiently well the trend in the curves obtained empirically by Pierson et al. (2001), provided that the input material parameters are well calibrated. It is important to be noted that, the design charts developed by Pierson et al. (2001) and Ritchie (1963) refer to specific rock types. The first, indeed, are considered conservative as the rock type at the test site is a hard durable basalt that rebounds well after impact and rolls well (Pierson et al., 2001). Consequently, as a

8 231 cut slope can be of any rock type, charts of this category provide indicative ditch dimensions. On this basis, regarding the proposed charts (Figures 2, 3 and 4) the RocFall TM default material settings were used as the best available data. The reliability of the proposed charts is also shown through the following example. Pierson et al. (1994), as part of a pilot study rolled 275 rocks from a 24.4 meter high 4V:1H slope into a Ritchie catchment area to determine its effectiveness. The tested ditch was 7.3 meters wide, 2.0 meters deep with a flat bottom and 1V:1H foreslope. Although the Ritchie shaped ditch used for testing was wider, deeper and contained a steeper foreslope than a standard Ritchie ditch, 8% of the rocks were still able to escape the catchment area (92% were retained). Pierson et al. (2001) also demonstrated that, had the catchment area been designed to a standard Ritchie width of 6.1 meters, the ditch would have been capable of retaining around 85% of falling blocks. Evans (1989) drew a similar conclusion based on real tests with mine benches. On the other hand, according to the proposed methodology the required width and depth of a flat bottom ditch with a 1V:1H foreslope for the retention of the 99% of falling blocks are 11.2 and 2.0 meters respectively. The width of 11.2 meters derives from the third chart of Figure 2 (w=4.5m) and Figure 5 (w o =6.7m, maximum impact distance of the 99% of rocks). Using the same comparison chart with Pierson (1994, 2001), it is inferred that the calculated ditch is capable of retaining the 98.5% of rockfalls. The last shows the agreement with the 99% used (Figure 5). 5. CONCLUSIONS A number of catchment area designs charts have been proposed by simulating rockfalls in computer. The effectiveness of deep ditches as well as concrete walls and fences were studied. The fact that for a given rock cut slope, different catchment areas with the same rockfall retention effectiveness expressed in depth width can be obtained, allows for the investigation of the optimum technical economic solution. The methodology proposed herein is an innovative procedure, where computer simulation is combined with published field data. More specifically, the maximum impact distance of rocks taken from Pierson et al. (2001) empirical study of even catchment areas is summed to the calculated catchment area width. The last is done due to the fact that, contrary to what stands in practice, for the simple geometries studied using RocFall TM (slopes without benches and outcrops) the impact distance was always zero. Finally, it is noted that, comparison of the results obtained by the proposed methodology with respective actual field data provided by Pierson et al. (2001) showed full agreement. REFERENCES Agliardi, F., and Crosta, G.B. (2003). High resolution three-dimensional numerical modeling of rockfalls. Int. J. Rock Mech. Min. Sci., Elsevier, 40(4), Alejano, L.R., Pons, B., Bastante, F.G., Alonso, E., and Stockhausen, H.W. (2007). Slope geometry design as a means for controlling rockfalls in quarries. Int. J. Rock Mech. Min. Sci., Elsevier, 44(6),

9 232 Azzoni, A., and De Freitas, M.H. (1995). Experimental gained parameters, decisive for Rock fall analysis. Rock Mech. And Rock Eng., Springer, 28(2), Azzoni, A., La Barbera, G., and Zaninetti, A. (1995). Analysis and prediction of rockfalls using a mathematical model. Int. J. Rock Mech. Min. Sci. And Geomech. Abstr., Elsevier, 32(7), Bozzolo, D., and Pamini, R. (1986). Simulation of rockfalls down a valley site. Acta Mech., Springer, 63, Bozzolo, D., Pamini, R., and Hutter, K. (1988). Rockfall analysis - a mathematical model and its test with field data. Proc., 5 th Int. Symp. on Landslides, A. A. Balkema, Rotterbam, Lausanne, Switzerland, 1, Descoeudres, F., and Zimmermann, T. (1987). Three-dimensional dynamic calculation of rockfalls. Proc., 6 th Int. cong. of Rock Mechanics, Balkema, Rotterbam, Montreal, Canada, Evans, C. L. (1989). The design of catch bench geometry in surface mines to control rockfall. MS thesis, Univ. of Arizona. FHWA (Federal Highway Administrations) (1989) Rock slopes: Design, Excavation, Stabilization. Pub.No. FHWA-TS , FHWA, Georgetown, Virginia. Guzzetti, F., Crosta, G.B., Detti, R., and Agliardi, F. (2002). STONE: a computer program for the three-dimensional simulation of rockfalls. Comput. Geosci., Elsevier, 28(9), Hoek, E. (2007). Practical Rock Engineering. Rocscience, (May 26, 2009). Hungr, O., and Evans, S. G. (1989). Engineering aspects of rockfall hazard in Canada. Geological Survey of Canada, _e.php?id=130673>(may 26, 2009) Jones, C. L., Higgins, J. D., and Andrew, R. D (2000). Colorado Rockfall Simulation Program Version 4.0, Colorado Department of Transportation, Colorado Geological Survey, Colorado School of Mines, Denver. Kobayashi, Y., Harp, E.L., and Kagawa, T. (1990) Simulation of rockfalls triggered by earthquakes. Rock Mech. Rock Eng., 23(1), Pfeiffer, T., and Bowen, T. (1989). Computer simulation of rockfalls. Bull. Ass. Eng. Geol., 26(1), Pfeiffer, T. J., Higgins, J. D., Turner, A. K. (1990). Computer aided rockfall analysis. Proc., 6 th Int. IAEG Cong., Amsterdam, Netherlands, A.A. Balkema Publishers, Brookfield, VT., Pierson L.A., Davis S.A, and Pfeiffer T.J. (1994) The nature of rockfalls as the basis for a new fallout area design criteria for 0.25:1 slopes, Oregon Department of Transportation and Federal Highway Administration, Salem. Pierson, L.A., Gullixson C.F., and Chassie R.G. (2001) Rockfall Catchment Area Design Guide. Final Report SPR-3(032), Oregon Department of Transportation and Federal Highway Administration, Salem. Piteau D. R. and Associated Ltd. (1980). Slope stability analysis for rockfall problems: The computer rockfall model for simulating rockfall distribution. Rock Slope Engineering, Department of transportation, Washington DC,

10 233 Ritchie, A. M. (1963). Evaluation of rockfall and its control. Highway Research Board, Highway Res. Rec., 17, Rocscience inc. (2002). RocFall - Risk Analysis of Falling Rocks On Steep Slopes - User s Guide. Rocscience, RocFall%20Tutorial.pdf>(May 26, 2009) Rocscience inc. (2003) Advanced Tutorial: Determining Input Parameters for a RocFall Analysis., Rocsience, RF_adv_tutor_1_tutorial.pdf>(May 26, 2009) Spang, R. M. (1987). Protection against rockfall stepchild in the design of rock slopes. Proc. 6 th Int. Cong. on Rock Mechanics, A. A. Balkema, Rotterdam, Montreal, Canada, Spang, R.M. and Rautenstrauch, R.W. (1988). Empirical and mathematical approaches to rockfall prediction and their practical applications. Proc.5 th Int. Symp. on Landslides, A. A. Balkema, Rotterbam, Lausanne, Switzerland, 2, Wu, S.S. (1985). Rockfall evaluation by computer simulation TRR, TRB, 1031, 1-5. Wyllie D. C., and Mah C. W. (2004). Rock Slope Engineering: Civil and Mining (4th edition), Spon Press, London.

Simulation and Statistical Analysis of Motion Behavior of a Single Rockfall

International Journal of Civil and Environmental Engineering 6 22 Simulation and Statistical Analysis of Motion Behavior of a Single Rockfall Iau-Teh Wang, Chin-Yu Lee Abstract The impact force of a rockfall