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:\pril 13.2W6 <br />Gregory I.aacar / <br />2(108 (3rimstone ftd. <br />Received <br />c~dar~-d~~, c~~h,t~d~, 81x13 <br />(ono>ssv-~s1o APR 1 7 ~ <br /> ~QLg.r <br />W Jurtctlon Flald Olft <br /> <br />Mr. S[evc Shucy ~ <br />ce <br />~17A of <br />Miner~ts ~ Geology <br />Division of !vtinerals and Geology <br />r,lc <br />t2c~ 5~.;s<•-,d::whs.u~,e~;~sr^4raP~F .~t~accsti~;v~ <br />~ <br />Dear Mr. Shucy, <br />This letter is a~follow up to both my analysis of fracttues to the Rullinc sandstone <br />clitT, and lu my review of the Revey Asscxiares, Inc. gcohaznrds report. the Revey report <br />dismissed the possibility of inducing rock falls fmm vibrations generated by heavy <br />cyuipment, stating the motion was too small, but they supplied no supporting analysis. I <br />wish to explain in this letter the mcchartistn that I envision for vibration induced rexk <br />falls, and w demonstrate that the ground accelerations produced by heavy cyuipment can <br />be sufficient to produce such an event. <br />I shall begin by assuming that the blocks of sandstone in the highly jointed clitT <br />face arc held in place by cidter wedging against other blocks, nr by friction along joint <br />faces. 'Rte time of Diction is proportional to the weight per unit area of the block against <br />the joint surface. If the force normal to the joint surface decrus_ses the t'riction:tl forme also <br />dc~c;reases, and less force is reyuired along the dip slope to move the bloe:k. ~Ihr dips of <br />Iractures mcasttrcd in my analysis were approximately I(1. 20, 40, and 8U degrees. ~fhc <br />components of gravitational acceleration on a blcx k with an 80 degree joint slvpc arc <br />shown in higurc t, where g - 9.8 m/s- is the gravitational constsnt. <br />For a given ti~rcc along the joint surface there is a minimum value tiff normal <br />(perpendicular) force required to hold the. Mock on the sloping face, and this defines a <br />threshold. If the nom,ul force exceeds this value the block remains in place. while <br />anything that reduces the normal ti,rce below the threshold value will cause the block to <br />slide off'. the threshold is determined by the roughness of thejoint surfaces. A mugher <br />surface rcyuires a lower normal three to produce the same <br />friction as a smaxhcr lace. <br />Fur the example in Figure I, assume the minimttnt <br />normal acceleration rcyuircd to keep the block in place is <br />~ O.t74g 0.1658. Ihen assume a uismic wave comes along with <br />~ horizontal particle velocity of O.OS in/s, which is approximately <br />° the velocity the Revey report claims would insult fmm a dozer <br />:40 fl fmm the cliff: lltis corresponds to a particle acceleration <br />0.9958 g u(U.OS in/s x 2n x I5 Ilz = S inrs2 = 0.0138. Sinrc the <br />wavelength of seismic energy is much larger than the scale of <br />Figure 1 the cliff: the entire block will he accelerated away fmm the clifT <br />in one-half of the cycle, and the join) face will be accelerated back into the cliR-on the <br />next half-cycle, leaving a difFerential accel~ratiun betwc~n the block and the face of <br />