The American books I was studying had stressed primarily the theory of elasticity.

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Betty Dickerson
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1 When I began my post graduate education in geological engineering, (1957), I reflected that the engineers in charge of my first job - - design of a new freeway - - had shown little interest in the properties of the rock to be excavated except for its unit weight, its bulking factor on excavation, and its unconfined compressive strength. The American books I was studying had stressed primarily the theory of elasticity..

2 A little history from the early 1960 s U.S. mining schools start annual rock mechanics meetings. Bill Judd of the Rand Corp organizes and leads an international meeting on rock mechanics in Pasadena. He asks the profession to go beyond the usual limiting assumptions of linearity, elasticity, homogeneity, and continuity. Judd works for the creation of a National Academy of Sciences committee on rock mechanics. The new committee surveys U.S. activities and personnel in this new field. Independently, and simultaneously, an inter- society committee on rock mechanics is formed with representatives from professional societies for mining, petroleum, geology, geophysics, exploration geophysics, testing & materials, civil engineering, and engineering geology. Mining Professor Howard Hartman instructs this committee that if you want to learn about rock mechanics, just go down into the mines.

3 The Present Time: Rock mechanics modelling and analysis have now been dramatically advanced by research and development and we have ample tools to discuss the mechanical behavior of rocks that are non-linear, inelastic, heterogeneous, discontinuous, and otherwise non-ideal. Importantly, we can analyze materials that are three dimensional, that can transport liquids and gasses through pores & fractures, etc. so that we no longer have to rely on a kind of patched-up continuum mechanics based mainly on the theory of elasticity. we can compute with rock masses that are discontinuous, inelastic, time-dependent, and anisotropic. In particular, for blocky, jointed and bedded rock, we have developed theoretical and empirical methods for analysis of rock as a discontinuum.

4 In a blocky rock mass, in my opinion, Stress is a mathematical construct that may not be particularly helpful, except when discussing the behavior of an individual block. Accordingly we have learned how to work directly with forces and displacements between blocks and, if desired, to calculate the stress distribution within each of the blocks. Such an approach can be enlarged to discuss water forces and water flow between blocks, cracking within blocks, and stability of the whole system, including mechanics with water and friction forces. This type of approach can embrace block theory, DDA, DEA and other new developments in its various sub-sections.

5 Most of our problems involve friction. This immediately complicates any analysis because it becomes piecewise non-linear since: all friction forces have to be assigned a direction that opposes incipient motion ; but one generally does not know the directions in which to apply the friction forces until the analysis has already been made; and, each subsequent iteration may continue to produce a new result, with different force vectors in new directions. In any large, sophisticated model with friction forces, Iterations are required to circumvent this difficulty.

6 To make a fully satisfactory analysis in any significant rock mechanics application, we must be able to predict and identify the correct applicable modes of failure. The failure mode is dependent on the structure and arrangement of component rock materials and importantly depends on the intimate details of boundary conditions. Initial motion of the key block may be in response to shear, tension, torsion, bending, cracking, or other mechanisms. As soon as the motion has initiated, new block movement opportunities may arise, allowing continued block motion in an altogether different mode. The failure thus involves a path of incrementally adjusting or changing failure modes.

7 Geological work in the field may be able to establish a likely mode of failure based on the record of natural failures in the same or similar rock formations This should be, in my opinion, a primary contribution of the geological engineer and field geologist - - by means of geological observations and studies of case histories in the region. Some examples follow:

8 It makes little sense to proceed with an analysis that is not responsive to the most likely mode(s) of failure. In such cases, the method of analysis may call for input of inappropriate properties for the rock mass without even suspecting that the central focus of the analysis has been misdirected. Further, it will tend to create a false expectation that the geologic problem(s) are being handled.

9 Excerpt from a 1959 letter from Karl Terzaghi to Barry Cooke After you asked me to prepare discussions of your papers No 1737 and 1746, I went through the entire Symposium on Rockfill Dams and emerged rather disappointed. Many of the papers are hardly more than glorified news items. The authors tell proudly what they have accomplished, but they do not even know - - or care - - whether the fact that their structures did not fail was due to the soundness of their procedures or to sheer good luck. Thus, though getting older, they don t get wiser.

10 Obsequent scarps (uphill facing normal faults) typically occur at the top of a toppling failure.

16 A process of failure in discontinuous rock can initiate in many ways, including the following: Sliding of an initial, planar key block, releasing blocks behind it; Forward rotation of a key-block (toppling); Cracking of a non-convex block to create removable sub-blocks; Surface erosion that enlarges the space pyramid to expose new key-blocks; Torsion of a potential key-block about an axis through a block corner; and more..

17 3. Rock strength is generally understood to vary with the shear and normal displacements on discontinuities. However this conclusion is insufficient in general, since these displacements depend not only on translations of blocks but on their general motions in space. A more complete analysis could require that additional potential inter-block modes of neighboring blocks be considered, as described by Dr. Markus Poetsch. Dr. Poetsch showed that each of two contiguous blocks can transfer energy between them involving block surfaces and block edges in 16 different modes of sliding and /or rotation. He has shown how to analyze and characterize all these potential modes. (Markus Poetsch, (2011)The analysis of rotational and sliding modes of failure for slopes, foundations and underground structures in blocky, hard rock, Technische Universitaet Graz, Institute fuer Felsmechanik und Tunnelbau, Heft 42.

19 From The analysis of rotational and sliding modes of failure for slopes, foundations, and underground structures in blocky, hard rock- by Markus Poetsch, TUGraz,, Austria 2011

20 Rotational modes of a block on a plane surface analyzed by Markus Poetsch in The analysis of rotational and sliding modes of failure for slopes, foundations, and underground structures in blocky hard rock (2011) Tech Univ. of Graz, Austria

22 Cohesion along joints is sometimes conveniently ignored. This is a common, presumably conservative, approach because one cannot easily evaluate cohesion by normal methods of investigation used in engineering practice. Further, the French dam engineer, Pierre Londe argued that introducing cohesion makes the problem of calculating the safety of rock blocks scale-dependent; whereas problems of calculating blocks with cohesionless connections (without rotations) have been treated as scaleindependent.

23 Londe s Analysis (Londe, Vigier, Vormeringer-1969)

24 Pierre Londe s Stability analysis for the critical foundation wedge of Malpasset Dam.

25 Considering only sliding modes, Pierre Londe maintained that inter-block sliding, as opposed to rotation, is always the most critical mode - a finding that greatly simplifies engineering analysis. However this is not true when allowing rotational modes - - if friction is large. (Pierre Londe wrote that he finally agreed with this statement, in a letter written to me shortly before his death).

27 CONCERNING COHESION At PG&E s Helms Underground Pumped Storage Project, Calif., I studied the sliding possibility of various potential rock blocks. Without cohesion, some of these blocks were found to reach a Factor of Safety below 1.0 with water pressures of the order of 0.1 bar. The water pressures in the rock mass in the vicinity of potential key blocks was 2 to 5 Bars. Yet no block failures have occurred. CONCLUSION -- The joints can be said to have cohesion. The amount of cohesion can be bounded by back-calculation of any real keyblock failures.

29 As noted previously, when rock masses start to move, new modes are likely to develop. Some examples follow.

30 Base Friction model of a large opening into block-jointed rock.

42 Toppled wedge block

49 Belden Tunnel 1 portal and upstream slope of siphon

50 Belden Tunnel

54 Open jointed welded tuff exposed in R. Abutment of Teton Dam after failure

56 Teton Dam, completed 1975, 305 high; failed 1976; TETON DAM

57 MALPASSET DAM, FRANCE

60 Pierre Londe s Stability analysis for the critical foundation wedge of Malpasset Dam.

61 The bases of the three nested rock wedges in volcanic rock of Horse Mesa Dam Foundation Arizona - analysed using Block Theory

64 Rock Slide in Powerhouse Excavation during construction for the MorrowPoint Dam

66 The difference between science and engineering is that Science seeks Truth, but never finds it; Engineering seeks what works, but never knows why.

67 The French version of this (according to Tom Doe of Golder Assoc.) is as follows: Three engineering schools are asked to build a bridge. E cole Technologique s bridge is clunky and over-designed, but it works.

68 E cole Superieure s bridge is more elegant, but it falls down, and they have no idea why.

69 E cole Polytechnique s bridge is very elegant. It also falls down, but they know why.

Seismic Analysis of Concrete Dams Workshop Field investigations and foundation material properties USSD Annual Conference April 6-7, 2017

Seismic Analysis of Concrete Dams Workshop Field investigations and foundation material properties Foundation deformation modulus For analysis purposes, approach used at Reclamation is to reduce the laboratory