SLOPE STABILITY BY CLASSIFICATION SSPC RMR GSI

Transcription

1 SLOPE STABILITY BY CLASSIFICATION SSPC RMR GSI ROBERT HACK ENGINEERING GEOLOGY, ESA, ITC, FACULTY OF GEO-INFORMATION SCIENCE AND EARTH OBSERVATION, UNIVERSITY OF TWENTE, THE NETHERLANDS. PHONE:+31 (0) ; TU Delft, The Netherlands, 2 October 2012

2 Causes and triggers for in-stability of a slope Slope Stability by Classification - Hack 02/10/2012 2

3 WHAT CAUSES IN-STABILITY OF A SLOPE? Wrong design (e.g. too steep, too high) Decrease in the future of ground mass properties (e.g. weathering, vegetation) Changes in future geometry (e.g. scouring, erosion, human influence road cut) Slope Stability by Classification - Hack 02/10/2012 3

4 WHAT IS REQUIRED TO ANALYSE THE STABILITY OF A SLOPE? ground mass properties present and future geometry present and future geotechnical behaviour of ground mass external influences such as earthquakes, rainfall, etcetera Slope Stability by Classification - Hack 02/10/2012 4

5 GROUND MASS PROPERTIES In virtually all slopes is a considerable variation Therefore: First divide the soil or rock mass in: homogene geotechnical units Slope Stability by Classification - Hack 02/10/2012 5

6 HOMOGENE GEOTECHNICAL UNIT? Is that possible? Slope Stability by Classification - Hack 02/10/2012 6

7 VARIATION Heterogeneity of mass causes: variation in mass properties Slope Stability by Classification - Hack 02/10/2012 7

8 GEOTECHNICAL UNIT: A geotechnical unit is a unit in which the geotechnical properties are the same. Slope Stability by Classification - Hack 02/10/2012 8

9 GEOTECHNICAL UNITS ARE BASED ON THE EXPERIENCE AND EXPERTISE OF THE INTERPRETER Slope Stability by Classification - Hack 02/10/2012 9

10 No geotechnical unit is really homogene. A certain amount of variation has to be allowed as otherwise the number of units will be unlimited Slope Stability by Classification - Hack 02/10/

11 The allowable variation of the properties within one geotechnical unit depends on: the degree of variability of the properties within a mass, the influence of the differences on engineering behaviour, and the context in which the geotechnical unit is used. Slope Stability by Classification - Hack 02/10/

12 Smaller allowed variability of the properties in a geotechnical unit results in: higher accuracy of geotechnical calculations less risk that a calculation or design is wrong Slope Stability by Classification - Hack 02/10/

13 Smaller allowed variability of the properties in a geotechnical unit: requires collecting more data and is thus more costly geotechnical calculations are more complicated and complex, and cost more time Slope Stability by Classification - Hack 02/10/

14 HENCE: the variations allowed within a geotechnical unit for a slope along a major highway is smaller the variations allowed within a geotechnical unit for a slope along a farmers road will be larger Slope Stability by Classification - Hack 02/10/

15 EXAMPLES What are the implications if the units are wrongly assumed in a design? Slope Stability by Classification - Hack 02/10/

16 ORIGINAL SITUATION Slope Stability by Classification - Hack 02/10/

17 DESIGN ERROR Slope Stability by Classification - Hack 02/10/

18 OPTIONS FOR ANALYSING SLOPE STABILITY Analytical Numerical Classification Slope Stability by Classification - Hack 02/10/

19 SLOPE STABILITY analytical: only in relatively simple cases possible for a discontinuous rock mass numerical: difficult and often cumbersome, (however, possible with discontinuous numerical rock mechanics programs such as UDEC & 3DEC) Slope Stability by Classification - Hack 02/10/

20 NUMERICAL SLOPE STABILITY(1) Extra work for deterministic numerical methods is justified if: Quantity and quality of input data is high, e.g.: representative tests of discontinuity (i.e. joint) shear strength of each discontinuity family orientations of each discontinuity etcetera, etcetera. Slope Stability by Classification - Hack 02/10/

21 NUMERICAL SLOPE STABILITY(2) High quality and quantity of data not only of the rock mass at the slope face but also in the slope! Hence: excavate the site and rebuilt (then it is exactly known) or many large-sized borehole samples required High quality and quantity of data of rock mass inside the slope rock mass are virtually never available because far too expensive to obtain Slope Stability by Classification - Hack 02/10/

22 NUMERICAL SLOPE STABILITY(4) Solution often used: Use a numerical program and estimate or obtain the input parameters from literature In particular dangerous because: Users (i.e. the civil engineers) expect numerical calculation to be accurate (the result becomes the "truth") Slope Stability by Classification - Hack 02/10/

23 NUMERICAL SLOPE STABILITY(5) Alternative use rock mass classification for input data or use rock mass classification without numerical calculation Slope Stability by Classification - Hack 02/10/

24 SLOPE CLASSIFICATION SYSTEMS Classification systems are empirical relations that relate rock mass properties either directly or via a rating system to an engineering application, e.g. slope, tunnel Slope Stability by Classification - Hack 02/10/

25 CLASSIFICATION SYSTEMS: For underground (tunnel): Bieniawski (RMR) Barton (Q) Laubscher (MRMR) etcetera For slopes: Selby Bieniawski (RMR) Vecchia Robertson (RMR) Romana (SMR) Haines SSPC etcetera Slope Stability by Classification - Hack 02/10/

26 ROCK MASS RATING (RMR) (BIENIAWSKI) one of the oldest still used systems (Bieniawski, 1989). developed in South Africa for underground mining but currently widely used in civil engineering as well excavation and support is determined by the RMR value and results in five different support classes. adjustment factors and refinements are possible Slope Stability by Classification - Hack 02/10/

27 RMR (2) based on a combination of five parameters Each parameter is expressed by a point rating Slope Stability by Classification - Hack 02/10/ (from De Mulder et al., 2012)

28 RMR(3) addition of the points results in the RMR rating RMR =(IRS RQD spacing condition groundwater) reduction reduction factors for: orientation, excavation damage, etc. factor(s) (from De Mulder et al., 2012) related (empirically) to rock mass cohesion, friction angle of the rock mass, and other rock mass properties Slope Stability by Classification - Hack 02/10/

29 RMR - SLOPE MASS RATING (SMR) (Romana) (modified Bieniawski) RMR rating multiplied with series of compensation factors SMR = RMR - ( F 1 * F 2 * F 3 ) + F 4 F 1 = factor F 3 SMR = Slope Mass Rating RMR = Rock Mass Rating(same as Bieniawski's RMR ) for parallelism of thestrikes of discontinuities and slope face F 2 = factor for discontinuity dip angle = factor for relation between slope face and discontinuity dip F 4 = factor for method of excavation Slope Stability by Classification - Hack 02/10/

30 RMR(5) Advantages: Simple Disadvantages: developed for tunneling in (generally) high surrounding stress environment Cohesion and friction generally considered (far) too high for low stress environment (i.e. not suitable in slopes) Slope Stability by Classification - Hack 02/10/

31 GEOLOGICAL STRENGTH INDEX (GSI) The Geological Strength Index (GSI) is derived from a matrix describing the structure and the surface condition of the rock mass Slope Stability by Classification - Hack 02/10/

32 GSI(2) structure is related to the block size and the interlocking of rock blocks surface condition is related to weathering, persistence, and condition of discontinuities. (from De Mulder et al., 2012) Slope Stability by Classification - Hack 02/10/

33 GSI(3) The GSI is one of the constituents of the Hoek-Brown failure criterion. The failure criterion does not provide excavation or support recommendations but rather determines rock mass properties, such as rock mass cohesion and rock mass angle of friction (Hoek et al., 1998, Marinos & Hoek, 2000, Marinos et al., 2005). Slope Stability by Classification - Hack 02/10/

34 SLOPE STABILITY PROBABILITY CLASSIFICATION (SSPC) three step classification system based on probabilities independent failure mechanism assessment Slope Stability by Classification - Hack 02/10/

35 SSPC - THREE STEP CLASSIFICATION SYSTEM (1) river 1 old road 2 slightly weathered fresh proposed new road cut Reference Rock Mass 3 moderately weathered 1: natural exposure made by scouring of river, moderately weathered; 2: old road, made by excavator, slightly weathered; 3: new to develop road cut, made by modern blasting, moderately weathered to fresh. Slope Stability by Classification - Hack 02/10/

36 THREE STEP CLASSIFICATION SYSTEM Exposure specific parameters: Method of excavation Degree of weathering Slope specific parameters: Method of excavation to be used Expected degree of weathering at end of engineering life-time of slope SLOPE GEOMETRY Orientation Height EXPOSURE ROCK MASS (ERM) Exposure rock mass parameters significant for slope stability: Material properties: strength, susceptibility to weathering Discontinuities: orientation and sets (spacing) or single Discontinuity properties: roughness, infill, karst Factor used to remove the influence of the method excavation and degree of weathering REFERENCE ROCK MASS (RRM) Reference rock mass parameters significant for slope stability: Material properties: strength, susceptibility to weathering Discontinuities: orientation and sets (spacing) or single Discontinuity properties: roughness, infill, karst Factor used to assess the influence of the method excavation and future weathering SLOPE ROCK MASS (SRM) Slope rock mass parameters significant for slope stability: Material properties: strength, susceptibility to weathering Discontinuities: orientation and sets (spacing) or single Discontinuity properties: roughness, infill, karst SLOPE STABILITY ASSESSMENT Slope Stability by Classification - Hack 02/10/

37 SSPC Excavation specific parameters for the excavation which is used to characterize the rock mass: Degree of weathering Method of excavation Slope Stability by Classification - Hack 02/10/

38 SSPC Rock mass Parameters: Intact rock strength Spacing and persistence discontinuities Shear strength along discontinuity: - Roughness - large scale - small scale - tactile roughness - Infill - Karst Susceptibility to weathering Slope Stability by Classification - Hack 02/10/

39 SSPC Slope specific parameters for the new slope to be made: Expected degree of weathering at end of lifetime of the slope Method of excavation to be used for the new slope Slope Stability by Classification - Hack 02/10/

40 SSPC Intact rock strength (IRS) By simple means test: hammer blows, crushing by hand, etcetera Slope Stability by Classification - Hack 02/10/

41 SSPC Spacing and persistence of discontinuities: Determine block size and block form by: visual assessment, followed by: quantification (measurement) of the characteristic spacing and orientation of each set Slope Stability by Classification - Hack 02/10/

42 SSPC Shear strength based on a combination of: roughness (persistence) infill presence of karst Slope Stability by Classification - Hack 02/10/

43 SSPC Roughness is a combination of: large scale roughness (Rl) small scale roughness & tactile roughness (Rs) Slope Stability by Classification - Hack 02/10/

44 SSPC Shear strength roughness large scale wavy slightly wavy i = amplitude roughness: 5 9 cm 5 9 cm i = 9-14 curved i = cm slightly curved straight i = m cm (i-angles Slope Stability and by Classification dimensions - Hack only 02/10/2012 approximate) 44

45 SSPC Shear strength roughness small scale stepped amplitude roughness > 2-3 mm undulating amplitude roughness > 2-3 mm planar 0.20 m (dimensions only approximate) Slope Stability by Classification - Hack 02/10/

46 SSPC Shear strength roughness tactile Three classes: rough smooth polished Slope Stability by Classification - Hack 02/10/

47 SSPC Infill (In): - cemented - no infill - non-softening (3 grain sizes) - softening (3 grain sizes) - gauge type (larger or smaller than roughness amplitude) - flowing material Slope Stability by Classification - Hack 02/10/

48 SSPC Karst (Ka): karst or no karst Slope Stability by Classification - Hack 02/10/

49 SSPC Shear strength - condition factor Discontinuity condition factor (TC) is a multiplication of the ratings for: small-scale roughness large-scale roughness infill karst Slope Stability by Classification - Hack 02/10/

50 SSPC CONDITION OF DISCONTINUITY wavy Roughness slightly wavy large scale (Rl) curved (visual area > 0.2 x 0.2 and < slightly curved 1 x 1 m2) straight Roughness small scale (Rs) (tactile and visual on an area of 20 x 20 cm2) rough stepped/irregular smooth stepped polished stepped rough undulating smooth undulating polished undulating rough planar smooth planar polished planar factor cemented/cemented infill no infill - surface staining Infill material (Im) non softening & sheared material, e.g. free of clay, talc, etc. coarse medium fine soft sheared material, e.g. clay, talc, etc. coarse medium fine Karst (Ka) gouge < irregularities 0.42 gouge > irregularities 0.17 flowing material 0.05 Slope Stability none by Classification - Hack 02/10/ karst 0.92

51 SLIDING CRITERION TC is related to friction along plane by: sliding angle Rl*Rs*Im*Ka Slope Stability by Classification - Hack 02/10/

52 SLIDING CRITERION (EXAMPLE) bedding plane description factor large scale straight 0.75 small scale & tactile rough stepped 0.95 infill fine soft sheared 0.55 karst none 1.00 sliding angle Rl*Rs* Im*Ka * 0. 95* 0. 55* degrees Slope Stability by Classification - Hack 02/10/

53 SSPC Orientation dependent stability Stability depending on relation between slope and discontinuity orientation For example: Plane and wedge sliding Toppling Slope Stability by Classification - Hack 02/10/

54 SSPC Orientation dependent stability Discontinuity related shear strength failure Plane sliding Conditions: - discontinuity must daylight - downward stress > shear strength along discontinuity plane Slope Stability by Classification - Hack 02/10/

55 SSPC Orientation dependent stability Discontinuity related shear strength failure Wedge sliding Conditions: - intersection line must daylight - downward stress > shear strength along discontinuity planes Slope Stability by Classification - Hack 02/10/

56 Orientation dependent stability Sliding if: TC * AP TC = discontinuity condition factor AP = apparent discontinuity dip in direction of slope dip Slope Stability by Classification - Hack 02/10/

57 SSPC Orientation dependent stability Sliding probability TC (condition of discontinuity) discontinuity stable with respect to sliding discontinuity unstable with respect to sliding 95 % 70 % 50 % 30 % 5 % AP (deg) Slope Stability by Classification - Hack 02/10/

58 SSPC Orientation dependent stability Discontinuity related shear strength failure Toppling Slope Stability by Classification - Hack 02/10/

59 SSPC Orientation dependent stability Toppling criterion TC * 90 AP dip discontinu ity TC = discontinuity condition factor AP = apparent discontinuity dip in direction of slope dip DIPdiscontinuity = dip of discontinuity Slope Stability by Classification - Hack 02/10/

60 SSPC Toppling probability TC (condition of discontinuity) (-) discontinuity stable with respect to toppling discontinuity unstable with respect to toppling 95 % 70 % 50 % 30 % 5 % AP + slope dip (deg) Slope Stability by Classification - Hack 02/10/

61 Orientation independent stability Slope Stability by Classification - Hack 02/10/

62 SSPC Orientation independent stability Slope instability not dependent on the orientation of discontinuities in relation with the slope orientation E.g. in situations: No discontinuities Too high stress for the soil or rock intact material strength (e.g. slope too high) So many discontinuities in so many directions that there is always a failure plane (comparable to a soil mass) Slope Stability by Classification - Hack 02/10/

63 SSPC Orientation independent stability In SSPC based on: Intact rock strength Block size and form Condition of discontinuities Slope Stability by Classification - Hack 02/10/

64 SSPC Probability orientation independent failure 10 Dashed pr obability lines indi cate that the number of sl opes used for the devel opment of the SSPC s ys tem f or t hese s ec tions of the graph is limited and the pr obability lines may not be as certai n as the pr obability lines dr awn with a conti nuous line. probability to be stable > 95 % 95 % 90 % Hmax / Hslope 1 (example) 10 % 5 % 70 % 50 % 30 % probability to be stable < 5 % mass / slope dip Slope Stability by Classification - Hack 02/10/

65 SSPCCOMPARISON BETWEEN SSPC AND OTHER CLASSIFICATION SYSTEMS number of slopes (%) visually estimated stability stable (class 1) unstable (class 2) unstable (class 3) a: SSPC b: Haines number of slopes (%) 80 visually estimated stability stable (class 1) unstable (class 2) unstable (class 3) Haines safety factor: 1.2 number of slopes (%) 0 0 < > SSPC stability probability (%) Haines' slope dip - existing slope dip (deg) unstable stable unstable stable c: SMR visually estimated stability stable (class 1) unstable (class 2) unstable (class 3) Percentages are from total number of slopes per visually estimated stability class. visually estimated stability: class 1 : stable; no signs of present or future slope failures (number of slopes: 109) class 2 : small problems; the slope presently shows signs of active small failures and has the potential for future small failures (number of slopes: 20) class 3 : large problems; The slope presently shows signs of active large failures and has the potential for future large failures (number of slopes: 55) Romana's SMR (points) 'tentative' describtion of SMR classes: completely completely unstable partially stable Slope Stability by Classification - Hack 02/10/ unstable stable stable

66 EXAMPLES Slope Stability by Classification - Hack 02/10/

67 POORLY BLASTED SLOPE Slope Stability by Classification - Hack 02/10/

68 POORLY BLASTED SLOPE New cut (in 1990): Visual assessed: extremely poor; instable. (SSPC stability < 8% for slope height 13.8 m high, dip 70, rock mass weathering: 'moderately' and 'dislodged blocks' due to blasting). Forecast in 1996: SSPC final stability: slope dip 45. In 2002: Slope dip about 55 (visually assessed unstable). In 2005: Slope dip about 52 Slope Stability by Classification - Hack 02/10/

69 SABA - DUTCH ANTILLES - LANDSLIDE IN HARBOUR Slope Stability by Classification - Hack 02/10/

70 SABA - GEOTECHNICAL UNITS Slope Stability by Classification - Hack 02/10/

71 SABA Pyroclastic deposits Calculated SSPC Laboratory / field Rock mass friction (measured) Rock mass cohesion 39kPa 40kPa (measured) Calculated maximum possible height on the slope 13m 15m (observed) Slope Stability by Classification - Hack 02/10/

72 FAILING SLOPE IN MANILA, PHILIPPINES Slope Stability by Classification - Hack 02/10/

73 FAILING SLOPE IN MANILA (2) volcanic tuff layers with near horizontal weathering horizons (about every 2-3 m) slope height is about 5 m SSPC non-orientation dependent stability about 50% for 7 m slope height unfavourable stress configuration due to corner Slope Stability by Classification - Hack 02/10/

74 BHUTAN Widening existing road in Bhutan (Himalayas) Slope Stability by Classification - Hack 02/10/

75 BHUTAN Method of excavation Slope Stability by Classification - Hack 02/10/

76 BHUTAN Slope Stability by Classification - Hack 02/10/

77 BHUTAN Above road level: Various units Joint systems (sub-) vertical Present slope about 21 m high, about 90 or overhanging (!) Present situation above road highly unstable (visual assessment) Below road level: Inaccessible seems stable Slope Stability by Classification - Hack 02/10/

78 BHUTAN Above road level: Following SSPC system about m for a 75 slope (depending on unit) (orientation independent stability 85%) Below road level: Inaccessible different unit? and not disturbed by excavation method Slope Stability by Classification - Hack 02/10/

79 FUTURE DEGRADATION OF SOIL OR ROCK DUE TO WEATHERING, RAVELLING, ETC. Forecasting future geotechnical properties of soil or rock mass Slope Stability by Classification - Hack 02/10/

80 FUTURE DEGRADATION Slope Stability by Classification - Hack 02/10/

81 FUTURE DEGRADATION Reduction in slope angle due to weathering, erosion and ravelling (after Huisman) z [m] y [m] Excavated 1999 May 2001 May 2002 Slope Stability by Classification - Hack 02/10/

82 FUTURE DEGRADATION Main processes involved in degradation: Loss of structure due to stress release Weathering (In-situ change by inside or outside influences) Erosion (Material transport with no chemical or structural changes) Slope Stability by Classification - Hack 02/10/

83 bedding planes CINDARTO SLOPE: VARIATION IN CLAY CONTENT IN INTACT ROCK CAUSES DIFFERENTIAL WEATHERING April 1990 Slightly higher clay content Slope Stability Slope Stability by Classification by - - Hack 02/10/

84 CINDARTO SLOPE VARIATION IN CLAY CONTENT IN INTACT ROCK CAUSES DIFFERENTIAL WEATHERING mass slid April 1992 Slope Stability Slope Stability by Classification by - - Hack 02/10/

85 SIGNIFICANCE IN ENGINEERING When rock masses degrade in time, slopes and other works that are stable at present may become unstable Slope Stability by Classification - Hack 02/10/

86 Slope Stability by Classification - Hack 02/10/

87 Slope Stability by Classification - Hack 02/10/

88 IMPACT OF WEATHERING From: De Mulder, E.J.F., Hack, H.R.G.K., Van Ree, C.C.D.F., Sustainable Development and Management of the Shallow Subsurface. The Geological Society, London. ISBN: p Slope Stability by Classification - Hack 02/10/

89 The susceptibility to weathering is a concept that is frequently addressed by the weathering rate of a rock material or mass. Weathering rates may be expected to decrease with time, as the state of the rock mass becomes more and more in equilibrium with its surroundings. Slope Stability by Classification - Hack 02/10/

90 app log 1 WE t WE R t init WE WE(t) = degree of weathering at time t WE init = (initial) degree of weathering at time t = 0 R app WE = weathering intensity rate WE as function of time, initial weathering and the weathering intensity rate Slope Stability by Classification - Hack 02/10/

91 WEATHERING RATES Material: Gypsum layers Gypsum cemented siltstone layers Middle Muschelkalk near Vandellos (Spain) Slope Stability Slope Stability by Classification by - - Hack 02/10/

92 SSPC system with applying weathering intensity rate: - original slope cut about 50º (1998) - in 15 years decrease to 35º Slope Stability by Classification - Hack 02/10/

93 KOTA KINABALU, MALAYSIA 10 years old Slope Stability by Classification (after- Tating, Hack Hack, 02/10/2012 & Jetten, 2011) 93 93

94 KOTA KINABALU Side road (dip 45, 5 years old) sandstone: slightly weathered SSPC stability: Sandstone: stable (92%) Shale: unstable (< 5%) Slope Stability by Classification - Hack 02/10/

95 KOTA KINABALU Main road (dip 30, 10 years old): sandstone: moderately weathered SSPC stability: Sandstone: stable (95%) Shale: ravelling (<5%) 10 years old Slope Stability by Classification - Hack 02/10/

96 KOTA KINABALU time [years] dip [degre es] unit RM friction RM cohesion [degrees] [kpa] shale SSPC visual SSPC probability slightly in stable moderately in stable sandstone slightly stable moderately stable Slope Stability by Classification - Hack 02/10/

97 SSPC system in combination with degradation forecasts gives: reasonable design for slope stability with minimum of work and in a short time (likely a reasonable tool to forecast susceptibility to weathering) Slope Stability by Classification - Hack 02/10/

98 REFERENCES De Mulder, E.J.F., Hack, H.R.G.K., Van Ree, C.C.D.F., Sustainable Development and Management of the Shallow Subsurface. The Geological Society, London. ISBN: p Hack, H.R.G.K., An evaluation of slope stability classification; Keynote lecture. In: Dinis Da Gama, C., Ribeira E Sousa, L. (Eds) ISRM EUROCK 2002, Funchal, Madeira, Portugal. Sociedade Portuguesa de Geotecnia, Av. do Brasil, 101, Lisboa, Portugal, pp Hack, H.R.G.K., Price, D.G., Rengers, N., A new approach to rock slope stability : a probability classification SSPC. Bulletin of Engineering Geology and the Environment. 62 (2). DOI: /s pp Hack, H.R.G.K., Price, D., Rengers, N., Una nueva aproximación a la clasificación probabilística de estabilidad de taludes (SSPC). In: Proyectos, U.D., Minas, E.T.S.I. (Eds), Ingeniería del terreno : ingeoter 5 : capítulo 6. Universidad Politécnica de Madrid, Madrid. ISBN: p (in Spanish) Hoek, E., Marinos, P., Benissi, M., Applicability of the geological strength index (GSI) classification for very weak and sheared rock masses. The case of the Athens Schist Formation. Bulletin of Engineering Geology and the Environment. 57 (2). DOI: /s pp Huisman, M., Hack, H.R.G.K., Nieuwenhuis, J.D., Predicting Rock Mass Decay in Engineering Lifetimes: The Influence of Slope Aspect and Climate. Environmental & Engineering Geoscience. 12 (1). DOI: / pp Marinos, P., Hoek, E., GSI: A geologically friendly tool for rock mass strength estimation. In: Drinan, J., Geom Australian (Eds) GeoEng International Conference on Geotechnical & Geological engineering, Melbourne, November Technomic Publishing Co, Lancaster, PA, USA, pp Marinos, V., Marinos, P. & Hoek, E The geological strength index: applications and limitations. Bull. of Engineering Geology and the Environment 64/1, doi: /s , Price, D.G., De Freitas, M.H., Hack, H.R.G.K., Higginbottom, I.E., Knill, J.L., Maurenbrecher, M., Engineering geology : principles and practice. De Freitas, M.H. (Ed.). Springer-Verlag, Berlin, Heidelberg. ISBN: p White, A.F., Blum, A.E., Schulz, M.S., Vivit, D.V., Stonestrom, D.A., Larsen, M., Murphy, S.F., Eberl, D., Chemical Weathering in a Tropical Watershed, Luquillo Mountains, Puerto Rico: I. Long-Term Versus Short-Term Weathering Fluxes. Geochimica et Cosmochimica Acta. 62 (2). DOI: /s (97) pp Slope Stability by Classification - Hack 02/10/