NEAR-FIELD PULSE-TYPE MOTION OF SMALL EVENTS IN DEEP GOLD MINES: OBSERVATIONS, RESPONSE SPECTRA AND DRIFT SPECTRA.

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1 The 4 th October 2-7, 28, Bejng, Chna NEAR-FIELD PULSE-TYPE MOTION OF SMALL EVENTS IN DEEP GOLD MINES: OBSERVATIONS, RESPONSE SPECTRA AND DRIFT SPECTRA ABSTRACT: Artur Cchowcz Dr, Sesmology Unt, Councl for Geoscence, Pretora, South Afrca Emal: artur@geoscence.org.za Strong pulse-type motons are observed n the near source regon of large earthquakes; however, there s a lack of waveforms collected from small earthquakes at very close dstances recorded underground n mnes. The results presented n ths paper are relevant for structures of wth the heght of a few meters, placed n an underground excavaton. The strong ground moton sensor was nstalled n a deep gold mne at the surface of a sesmc actve stope. The strongest montored horzontal ground moton was caused by an event of magntude 2 at a dstance of 9 m wth PGA 3 m/s 2 and PGV.36 m/s, and the fnal dsplacement was 6.2 mm. The drft response technque based on a contnuous shear beam model s employed here to estmate the drft response subjected the near-feld earthquakes. The man features of velocty response spectra and drft spectra are smlar, whch s an ndcaton that the larger damage comes from the large velocty peaks. The strong ground motons wth PGA larger than g cause drfts of %, whch are unobserved at the earth s surface. Drft larger than several percents could cause non elastc deformaton. The dampng constant of a structure has to be ncreased sgnfcantly to decrease a value of the drft. The weak underground moton has spectral characterstcs smlar to the strong ground moton observed on the earth s surface; the drft spectrum has a maxmum value less than % n frequency range relevant to a hgh underground structure. KEYWORDS: pulse-type ground moton, drft spectrum, response spectrum. INTRODUCTION The near-feld ground motons are strongly affected by the fault geometry and rupture mechansm. The strong ground motons recorded n the near-feld are often characterzed by dstnct low frequency pulses n the acceleraton tme hstores and coherent pulses n the velocty and dsplacement tme hstores. These motons have been observed to cause structural damage. Already some structural desgn codes requre that the pulse-type accelerograms be ncorporated nto the process of modellng structure response n order that the drft demands are approprately determned. The tme hstory of ground moton n the near feld s qualtatvely qute dfferent from that of the far-feld earthquake ground moton. When nput s the far-feld ground moton, the sesmc desgn for structures s specfed n terms of a response spectrum based on a sngle-degree-of-freedom lnear system. The response spectrum s an adequate measure of demand for the far-feld ground moton that could be modelled usng modulated, broad-band random functon of tme (e.g. Boore, 983). The response spectrum generally provdes a good estmate of the global dsplacement and acceleraton demand of far-feld ground moton on structure. However, t does not provde accurate nformaton on the local shape or nternal deformaton of the response of the structure. Pulse lke ground moton wll propagate through the structure as waves, causng large, localzed deformaton that occurs before a resonant mode response can buld up (Iwan, 997). Therefore, the response spectrum alone s not a suffcent representaton of near feld ground moton features. It does not adequately represent the demand for a hgh rate of energy absorpton presented by near fault pulses.

2 The 4 th October 2-7, 28, Bejng, Chna 2. DRIFT SPECTRUM A large local dsplacement demand mposed on structure by the near-feld pulse s modelled wth the drft spectrum. Iwan (997) proposed the drft spectrum as a new measure of earthquake demand sutable for pulse lke ground moton. The response of a contnuous shear beam under horzontal sesmc exctatons s proposed to model a structure vbraton exposed to a near-feld pulse ground moton. The drft spectrum s defned as the maxmum value of the shear stran u( x, t) / x of the shear beam, where u(x,t) s the dsplacement of the structure relatve to the base, x s the arbtrary heght above the base beam and t s the tme (Iwan, 997). The beam s subjected to a ground level dsplacement of the horzontal ground moton, z(t). The maxmum of the shear stran at the dmensonless heght β s gven by: D( T, ζ, β ) = max = max + + t t u( x, t) / x c N 2t / T β n n= ( ) e N 2t / T+ β n n= ( ) e e x πβζ ( nπ+ β ) ζ ( nπ+ β ) ζ v( t βt v( t nt v( t nt 2πζ + z( t βt T βt βt 2πζ + z( t nt βt T 2πζ + z( t nt βt T (2.) where c s the wave velocty n structure, ζ s the crtcal dampng n the frst mode, T s the fundamental perod, x s equal to the product of β and H, H s the heght of the shear beam, β vares from to and v(t) s the velocty of the horzontal ground moton. By analogy to the response spectrum the drft spectrum s a measure of the demand of the exctaton. Iwan s model captures the shear wave propagaton effect n a structure caused by a short duraton strong pulse, whle the response spectrum dsplacement provdes only a measure of overall dsplacement demands. When structures are subjected to a near feld ground moton, the oscllatory response may not occur before the pulse propagatng through the structure as waves cause large local deformaton. The drft spectrum can be formulated wth modal analyss by ncludng the hgher modes. Chopra and Chntanapakdee (2) show that a SDOF system wth a few modes wll match the drft spectrum developed by Iwan (997). The fundamental mode moblzed approxmately 8 percent of the total mass of the dealzed shear beam (Akkar and Gülkan, 22). In a seres of research works, Akkar and Gülkan focused on the frst mode only (Gülkan and Akkar, 23). The generalzed nterstory drft spectrum for a realstc buldng model was presented recently by Mranda and Akkar (26) usng modal analyss. Inspred by the above papers and usng Chopra s (99) notatons for model analyss, the drft spectrum for a unform underground structure s presented. Dsplacement for th mode s gven by: u ( t, x) = Γ Φ ( x) D ( t) (2.2) where Г s the model partcpaton factor of the th mode, ф (x) s the shape functon of the th mode, D (t) s the relatve dsplacement of a SDOF system, wth perod, T, and dampng rato, ζ, n the frst mode. As n ths paper only the fundamental mode s used, so the modal ndex can be dropped. The frst mode partcpaton factor for the shear beam s Г = 4/π and the shape functon can be expressed as ф (x) = sn( 2 π x /H ) (Chopra, 99). The peak ampltude of relatve dsplacement D (t) for specfc perod T and dampng rato ζ s named dsplacement response spectra, S d (T, ζ ). Therefore the maxmum dsplacement for the shear beam structure becomes u max ζ, x) 4 π x = sn( ) Sd ζ ) (2.3) π 4H

3 The 4 th October 2-7, 28, Bejng, Chna Dsplacement shape functon, ф (x), has that the largest drft n the fundamental mode occurs at the top, where x s equal to H. The heght above base, x, can be replaced wth β H. Lateral moton u(x,t) wthn the shear beam s propagated wth velocty c, consequently, H can be replaced wth Tc/4. As a result, the shear stran can be defned as later dsplacement dvded by the heght: D( T, ζ, β ) umax ζ, x) 6 = = sn( π β ) Sd ς ) (2.4) x π Tcβ The dsplacement response spectra, S d (T, ζ ), represent global dsplacement, whle drft spectrum defned wth Eqn 2.4. represents an average shear stran over heght x. 3. EXPERIMENT AND DATA DESCRIPTION In South Afrca hard rock mnng sometmes causes unstable fracturng. These mnng operatons are generally performed usng a long-wall stoppng technque. The rock around the stope appears to be one of the most heterogeneous regons n the mne, as a fractured rock zone s progressvely generated ahead of the advancng stope face. Fgure llustrates the fracture pattern whch forms ahead and behnd a typcal stope face n a deep gold mne. The shear fractures form ahead of the stope face, where the shear stresses are relatvely hgh. The concentraton of the sesmc events nduced by mnng s largest n the front of a stope face and around geologcal features such as faults and dykes. Source mechansms of sesmc events n Deep South Afrcan gold mnes have shear falure smlar to tectonc earthquakes. The double-couple model has been appled to explan the mechansms of larger, mne related sesmc events. Research s focused on the study of strong ground moton n the stope area. Several experments were conducted to montor the moton of support under sesmc loads (Cchowcz, 2, 22). The waveforms of strong ground moton are requred n order to desgn the optmal stope support n sesmcally actve areas. At a depth of 2 m several strong ground moton sensors were nstalled at the surface of underground excavatons. The montorng of the ground moton was conducted at several stes near a stope face. Durng the experment the nstrument followed the advancng of the stope face n order to be at the rght tme and place. Data provdes a new nsght nto the near-feld ground moton recorded underground. The ground moton on the surface of excavatons may be amplfed relatvely to the ground moton n sold rock, ownng to the free surface effect, surface waves and local ste effects (Cchowcz et al., 999, Cchowcz et al., 2, Mlev and Spottswood, 2). Examples of strong and weak ground moton recorded underground on the surface of excavatons are shown n Fgure 2. The strong ground moton caused by an event of magntude 2, recorded at 9 m from the sesmc source has PGA= 3 m/s 2, and PGV =.36 m/s. The velocty trace s domnated by two pulses - one up and the second down and ths s converted to one strong pulse n dsplacement. The sesmc event assocated wth a weak ground moton was not located, as t was only recorded by one staton. Ths accelerogram has a smple structure, wth a relatvely small value of PGA = 7.6 m/s 2 and the velocty trace s domnated by one pulse. 4. RESPONSE AND DRIFT SPECTRA The terms strong ground moton and weak ground moton are used to classfy the observed records. The strong ground moton s used to descrbe sesmograms characterzed by few oscllatons and a domnant pulse wth a strong component of low frequency. The near fault pulse-type ground motons can be represented by oneor more smplfed pulses. The spectrum of strong ground moton s usually broadband, so a hgh frequency sgnal s present as well. The weak ground motons have, by defnton, a smaller sgnal ampltude than strong ground moton, and for a small sesmc source has a strong component of hgh frequency.

4 The 4 th October 2-7, 28, Bejng, Chna Fgure Cross secton of an underground stope and surroundng hard rock (fgure courtesy of S. Spottswoode, used wth permsson). The varous zones shown above assocated wth the underground mnng envronment are descrbed as follows: Zone I s the excavaton where mnng takes place, Zone II s the vrgn rock, Zone III s the hghly fractured zone ahead of the stope face that could extend to 2 m, Zone IV s the hangngwall, Zone V s the sesmogenc regon n the stope. m/s 2 m/s - m x -3 PGA = 3 m/s 2 PGV =.36 m/s PGD =.62 m Tme [s] Fgure 2 (Left) An example of a strong ground moton. Sesmc event wth magntude 2 s located 9 m from strong ground moton sensor. Horzontal component of the accelerogram s converted to velocty and dsplacement wth PGA = 3 m/s 2, PGV =.36 m/s and PGD =.62 m. (Rght) An example of a weak ground moton wth PGA = 7.64m//s 2, PGV =. m/s and PGD =.37 m. m/s 2 m/s m - x -3-4 x - 2 PGA = 7.64 m/s 2 PGV =.9 m/s PGD = 3.72e- m Tme [s] The strong ground moton of the acceleraton response spectrum, the velocty response spectrum, the dsplacement response spectrum and the drft spectrum are shown n Fgure 3. The spectra are calculated wth dampng constant equal to %. The acceleraton response spectrum has dstnct peaks below.2 sec, and these hgh frequency peaks do not affect structure underground. The heghts of the underground structure can vary from to 6 m, so the perods from.3 to.6 sec for shear wave velocty c = m/s are of nterest for engneerng applcatons. The wave speed n the renforced, concrete structure typcally vares from to 2 m/s (Iwan, 997). The shape of the velocty response spectrum s domnated by one broad pulse wth a maxmum around.4 sec (2 Hz). The values of the dsplacement spectrum steadly ncrease wth the ncrease

5 The 4 th October 2-7, 28, Bejng, Chna of the perod. The drft spectrum was obtaned for fve dfferent elevatons above base of the structure:.2h,.4h,.6h,.8h and.h. The drft spectrum has a maxmum at the base of the structure and has smlar features as velocty response spectrum. In perods rangng from.3 to.6 sec the drft spectrum vared from. to.2 (see Fgure 3). The largest drft s observed at the bottom of the structure and at the hgh frequences. Drft spectrum predcts demands mposed by a strong pulse-type moton to an extent not antcpated by the dsplacement response spectra. It s unlkely, that a structure exposed to a large drft wll be deformed elastcally. Therefore, the drft spectrum obtaned for the strong ground moton should be corrected for ductlty by ntroducng nelastc to elastc dsplacement factors (Gülkan and Akkar, 23), or by modfyng the natural vbraton perod. However, a modfcaton of vscous dampng of the equvalent lnear system s the most common practce and s acheved by addng an extra term responsble for the ductlty of a structure. The ncrease n the dampng could be as large as 4% (Chopra and Goel, 2). An example of the analyss of weak ground moton s shown n Fgure 4. Typcally weak ground moton s observed n a far feld. In ths case, the weak ground moton s caused by a small event, so the spectra are domnated by hgh frequency peaks. Ther shapes are smlar to those of strong ground moton; however, all peaks have shfted towards hgher frequences, as was expected. The drft spectrum n the perods of engneerng nterest s lower than % and ths value s smlar to drft observed at the surface caused by natural earthquakes. 3 7 Acceleraton Spectrum [g] 2 2 ζ = Velocty Spectrum [m/s] ζ = Dsplacement Spectrum [m] ζ = Drft Spectrum ζ = Fgure 3 Acceleraton, velocty, dsplacement and drft spectrum of strong ground moton. The assocated waveforms are dsplayed on the left sde of Fgure 2.

6 The 4 th October 2-7, 28, Bejng, Chna.6.8 Acceleraton Spectrum [g] ζ = Velocty Spectrum [m/s] ζ =.2.2 x -3. Dsplacement Spectrum [m] ζ = Drft Spectrum ζ = Fgure 4 Acceleraton, velocty, dsplacement and drft spectrum of the weak ground moton. The assocated waveforms are dsplayed on the rght sde of Fgure 2.. CONCLUSIONS Structures exposed to pulse-type ground moton must be specfed n terms of drft spectrum. The drft response technque based on a contnuous shear beam model s employed to estmate the drft response. Data collected from surface of underground excavatons show that the drft spectra have features smlar to velocty response spectra. The drft spectrum predcts demands mposed by a strong pulse-type moton to an extent not antcpated by the dsplacement response spectra. The strong ground moton characterzed by ntensty larger than g, causes a drft of %, whch s unobserved at the earth s surface. Ths value of drft wll cause nelastc deformaton of underground structures of heght varyng from to 6 m and a dampng constant n the range from to %. In order to avod analyss of the nelastc system the dampng constant of structures has to be ncreased sgnfcantly to decrease the value of the drft. The equvalent vscous dampng s ncreased by addng an addtonal term responsble for the ductlty of a structure and t could be as large as 4%. The weak underground moton has spectral characterstcs smlar to strong ground moton observed on the earth s surface wth drft lower than %. REFERENCES Akkar, S. and Gülkan, P. (22). A crtcal examnaton of near-feld accelerograms from the Sea of Marmara

7 The 4 th October 2-7, 28, Bejng, Chna regon earthquakes. Bulletn of the Sesmologcal Socety of Amerca, 92:, Boore, D. M. (983). Stochastc smulaton of hgh frequency ground motons based on sesmologcal models of the radated spectra. Bulletn of the Sesmologcal Socety of Amerca, 73:6, Cchowcz, A. (2). The meanngful use of peak partcle velocty at excavaton for the optmsaton of the rockburst support crtera for tunnels and stopes. Safety n Mnes Research Advsory Commttee, GAP 79b. Cchowcz, A. (22). Interacton between stope support and ground moton n the hangngwall and footwall. Safety n Mnes Research Advsory Commttee, GAP84-REP-4, Cchowcz, A., Mlev, A.M. and Durrhem, R.J. (999).Transfer functon for a sesmc sgnal recorded n sold and fractured rock. The South Afrcan Insttute of Mnng and Metallurgy 99:4,-6. Cchowcz, A., Mlev, A.M. and Durrhem, R.J. (2). Rock mass behavour under sesmc loadng n deep mne envronment. The South Afrcan Insttute of Mnng and Metallurgy :2,2-28. Chopra, A.K. (99). Dynamcs of structures, theory and applcatons to earthquake engneerng, Prentce Hall, New Jersey. Chopra, A.K. and Chntanapakdee, C. (2). Drft spectrum vs. modal analyss of structural response to near-fault ground motons. Earthquake Spectra 7:2,22,-234. Chopra, A.K. and Goel, R. K. (2). Evaluaton of NSP to estmate sesmc deformaton: SDF systems. Journal of Structural Engneerng, Aprl, Gülkan, P. and Akkar, S. (23). Demand and capacty requrement mplcatons from near-fault ground motons. Ffth Natonal Conference on Earthquake Engneerng, Istanbul, Turkey. Iwan, W.D. (997). Drft spectrum: Measure of demand for earthquake ground moton. Journal of Structural Engneerng, 23:4, Mranda, E. and Akkar, S.D. (26). Generalzed nterstory drft spectrum. Journal of Structural Engneerng June, DOI:.6/(ASCE) (26)32;6(84). Mlev, A.M. and Spottswood, S.M. (2). Strong ground moton and ste response n deep South Afrcan mnes. Journal of the South Afrcan Insttute of Mnng and Metallurgy,, -.