MONITORING THE STABILITY OF SLOPES BY GPS

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1 MONITORING THE STABILITY OF SLOPES BY GPS Prof. S. Sakurai Costructio Egieerig Research Istitute Foudatio, Japa Prof. N. Shimizu Dept. of Civil Egieerig, Yamaguchi Uiversity, Japa ABSTRACT The stability of slopes is a crucial problem ot oly i ope pit mies, but also i civil egieerig situatios. The deformatioal behaviour of slopes is i geeral moitored durig/after the excavatio by carryig out field measuremets where displacemet measuremets are commoly adopted. I moitorig the slope stability it should be emphasized that the measuremet results must be properly iterpreted so as to assess whether the slopes are stable or become ustable i the future. I order to iterpret the data, back aalysis is extremely useful. I this paper a slope stability moitorig system is described. It cosists of displacemet measuremets by GPS, ad a back aalysis of measured data. The use of GPS has a great advatage, because of the fact that cotiuous displacemet measuremets with high accuracy for a large extet of cocered area ca be easily achieved. O the other had, the back aalysis ca reveal the mechaical characteristics of the groud, which make it possible to assess the stability of slopes quatitatively. 1. INTRODUCTION The Global Positioig System (GPS) ca be used to measure displacemets of slopes at ope pit mies, ladslides as well as slopes at civil egieerig situatios. The GPS has the great advatage to realize cotiuous displacemet measuremets with high accuracy, ad to make it possible to reduce the maiteace costs related to log-term moitorig, while covetioal istrumetatios by usig extesometers, icliometers, ad surveyig methods with a electroic optical distace meter or a total statio are iadequate for cotiuous moitorig with high accuracy. Furthermore, the covetioal methods result i difficulties cocerig maiteace for log-term moitorig. A ew type of GPS displacemet moitorig system has bee developed by the secod author ad his colleagues (Iwasaki et al. 23, Masuari et al. 23, Shimizu ad Matsuda 23). It ca simultaeously measure the three-dimesioal displacemets of may poits over a extesive area ad display the results o a moitor scree i real-time. The tred model, which is a data processig method, is adopted for improvig the accuracy of the measuremet results, so that the system ca provide highly accurate ad precise measuremet results comparig with covetioal GPS receivers. Practical applicatios have already show that the system is useful for moitorig the displacemets of slopes. However, a importat issue i moitorig the stability of Page 353

2 slopes is how to iterpret the measuremet results. The stability of slopes is i geeral assessed by a factor of safety, i such a way that the stregth of materials is compared with stress occurrig i a slope. For evaluatig the factor of safety the stregth parameters such as cohesio ad iteral frictio agle play the most importat role. A questio the arises how the stregth parameters ca be determied from the measured displacemet data. Sice displacemets i geeral correspod directly to the deformability parameters like Youg s Modulus, ot to the stregth parameters, a special techique must be eeded. The first author developed a back aalysis procedure for determiig the stregth parameters from the measured displacemets (Sakurai ad Nakayama 1999). I this paper, the GPS displacemet moitorig system is outlied together with a data processig method, ad the back aalysis procedure is described. 2. DISPLACEMENT MONITORING SYSTEM USING GPS 2.1. HARDWARE FOR MONITORING DISPLACEMENTS Several types of the moitorig system usig GPS has bee developed (Masuari et al. 23). Fig. 1 illustrates oe of those systems used at a limestoe quarry. Small ateas are set o the measuremet poits, ad the they are coected to receivers, respectively. The receivers trasfer the data trasmitted from the GPS satellites through a cable to a persoal computer i the cotrol office. The cable also provides power to the receivers. The computer cotrols the etire system ad aalyzes the data i order to obtai displacemets at all the measuremet poits. The measuremet results are show o the moitor scree i real time. The system has cotiuously moitored the displacemets for almost te years SOFTWARE FOR IMPROVING THE ACCURACY OF THE MEASUREMENTS The precisio of the measuremets is commoly preseted by the stadard deviatio (STD). The STD of the measuremets usig covetioal GPS receivers for a baselie legth of less tha a few kilometers is 5-1 mm ad 1-2 mm for horizotal ad vertical directios, respectively. Therefore, the precisio of the covetioal GPS is ot eough for assessig slope stability. I order to improve the precisio, a data processig method is applied to the cotiuous moitorig results. After havig tried various types of data processig methods, the tred model was foud to be the most suitable for this type of displacemet measurig. The tred model is composed of a system equatio ad a observatio equatio, as follows: y k u = where u represets the estimates for the exact values of the displacemets, ad y is the measured displacemet. The measuremet iterval is t, ad subscript deotes progressig time t (t= t). is the operator for the fiite differece ( u = u -u -1 ), = u v + w (1) (2) Page 354

3 ad k meas the rak k differece. Eq. (1) is a sort of probability fiite differece equatio of rak k. v ad w are the white oise with a average value of ad STD τ, ad the observatio error with STD σ, respectively. The tred model ca yield good estimates for exact displacemets from scattered data obtaied from the GPS moitorig system. It was prove that the system ca detect displacemets of 1-2 mm ad displacemet velocities of.1 mm/day through experimets ad practical applicatios (Shimizu ad Matsuda 23). Fig. 1 The GPS displacemet moitorig System Fig. 2 Parameter m as a fuctio of shear strai 3. BACK ANALYSIS OF MEASURED DISPLACEMENTS Back aalysis should be simple eough to apply for egieerig practices. Moreover, it is importat i back aalysis that the mechaical model should ot be assumed, but should be uiquely determied by back aalysis (Sakurai 1997). This meas that the covetioal umerical methods such as a elasto-plastic umerical aalysis caot be adopted, because the mechaical model should be assumed before computatio. I order to fulfill these requiremets, the first author proposed a back aalysis procedure based o FEM, i which a strai-iduced aisotropic damage parameter was itroduced (Sakurai 1999). The aisotropic damage parameter ca be determied by the back aalysis of displacemets measured by GPS. 3.1 ANISOTROPIC DAMAGE PARAMETER The aisotropic damage parameter d is defied o a slip plae as d = 1/ 2(1 + ν ) m (3) where ν : Poisso s ratio m : The ratio of shear modulus to Youg s modulus o a slip plae (Sakurai et al. 1998) Page 355

4 The parameter m for soil ad soft rock is show i Fig. 2. Sice the parameter m i a elastic state is m = 1/ 2(1 + ν ), the aisotropic damage parameter becomes d =, amely o damage occurs util a material reaches to the yieldig poit. The aisotropic damage parameter d the starts to mobilize o a slip plae, whe the material goes i plastic state. Careful ivestigatio of laboratory experimets reveals that the aisotropic damage parameter d icreases mootoically with a icrease of shear straiγ, so that it is expressed as follows; d = for γ γ 1 d = β [ 1 Exp{ α( γ γ )}] for γ > γ (4) 2(1 + ν ) where α, β : material costats : γ critical shear strai (Sakurai et al 1999) 3.2 STRESS-STRAIN RELATIONSHIP Cosiderig the above described aisotropic damage parameter, a stress-strai relatioship i a local coordiate ca be derived. For the plae strai coditio it is expressed as follows (see Fig. 3). where { σ } [ D ]{ ε } = (5) y y x slip lie Fig. 3 Local ad global coordiates y θ σ y τ xy y σ x x x x 1 ν ν c1 E D = ν 1 ν c2 (6) 2 1 ν 2ν 2 c (1 2 ) 1 c2 m ν ν [ ] where E : Youg s modulus ν : Poisso s ratio c 1,c 2 : dilatacy parameters m = 1/ 2(1 + ν ) d I global coordiate, [ D ] ca be trasformed as, [ D] [ T ][ D ][ T ] T = (7) where [ T ] : trasformatio matrix Page 356

5 3.3 FINITE ELEMENT ANALYSIS The relatioship betwee the icremets of exteral forces ad displacemets is expressed as, [ K ]{ δ } = { P} (8) where [ K ] : Stiffess matrix { δ} : Icremet of displacemets. Some of them are measured values. T { P} = [ B] [ D][ C]{ σ }dv + (9) [ B ] T { σ }dv where [ C] = m m m i (1) Fig.4 Relatioship betwee icremets of parameter m ad shear strai Eq. (9) idicates that there are two ways for the cause of displacemets i slopes. Oe is due to the reductio of stresses caused by excavatio. The other is due to the reductio of stregth of materials. That is, the parameter m decreases with o excavatio. This may be caused by weatherig. I Eq. (1) m ad mi express the values of m at preset ad past at the measurig iterval t, respectively, as show i Fig BACK ANALYSIS PROCEDURE OF DETERMINING THE STRENGTH PARAMETERS (COHESION AND INTERNAL FRICTION ANGLE) (1) The parameter m ad Youg s Modulus E ca be obtaied by the back aalysis. I this back aalysis, total displacemets are ot eeded, but oly the icremets of measured displacemets for the time iterval t are good eough. (2) Shear modulus G ca be calculated by the defiitio of m as follows; G = me (11) Page 357

6 (3) The critical shear strai γ is the estimated by cosiderig the relatioship betwee the critical shear strai ad shear modulus G. (Sakurai et al. 1999). (4) Shear stregth τ c ca be determied by the defiitio of critical shear strai as follows; τ c = γ G (12) (5) Cohesio c is the determied by the followig equatio assumig the iteral frictio agleφ. 1 siφ c = τ c (13) cosφ (6) The factor of safety ca be calculated by a covetioal limit equilibrium method. 4. CONCLUSIONS (1) GPS is a powerful tool for moitorig the stability of slopes i large extet of area. Both the hardware ad software of GPS moitorig system have bee developed for moitorig displacemets ad improvig the accuracy of the measuremets (2) The measuremet results must be iterpreted properly for assessig the stability of slopes. For this purpose the strai-iduced aisotropic damage parameter is proposed ad itroduced ito back aalysis procedure based o FEM. (3) I this back aalysis procedure, oly the icremets of measured displacemets for the time iterval t are sufficiet. This meas that we ca start the measuremets at aytime after the fracture like ope cracks occurs i slopes. (4) Accordig to the back aalysis procedure, the stregth parameters (cohesio ad iteral frictio agle) ca be determied from the measured displacemets. A factor of safety of slopes ca the be evaluated by usig a covetioal limit equilibrium method. REFERENCES IWASAKI,T. TAKECHI, K. TAKEISHI, A. MASUNARI, T. TAKECHI, Y. SHIMIZU, N. Web-based displacemet moitorig system usig GPS for the maiteace of roadside slopes, It. Sympo. Field Measuremets i Geomechaics, FMGM3, 23. pp MASUNARI, T. TANAKA, K. OKUBO, N. OIKAWA, H. TAKECHI, K. IWASAKI, T. SHIMIZU, N. GPS cotiuous displacemet moitorig system. It. Sympo. Field Measuremets i Geomechaics, FMGM3, 23. pp SAKURAI, S. Moitorig the stability of cut slopes, Proc. 2 d Plaig ad Equipmet Selectio, Calgary, 199. pp It. Sympo. Mie SAKURAI, S. Lessos leared from field measuremets i tuelig, Tuellig ad Udergroud Space Techology, Vol.12, No.4, pp Page 358

7 SAKURAI, S. AKAYURI, C.F.J. Deformatioal aalysis of geomaterials cosiderig strai-iduced damage, Proc. 4 th Europea Coferece o Numerical Methods i Geotechical Egieerig NUMGE 98, pp SAKURAI, S. Iterpretatio of the results of displacemet measuremets i geotechical egieerig projects, Proc. 5 th Iteratioal Symposium o Field Measuremets i Geomechaics FMGM99/Sigapore, pp SAKURAI, S. NAKAYAMA, T. A back aalysis i assessig the stability of slopes by meas of surface measuremets, Proc. Iteratioal Symposium o Slope Stability Egieerig IS-Shikoku 99, Vol.1, pp SHIMIZU, N. MATSUDA, H. Displacemet moitorig usig GPS ad its iterpretatio method for the assessmet of slope stability. It. Sympo. Field Measuremets i Geomechaics, FMGM3, 23. pp Page 359

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MATHEMATICAL MODELLING OF ARCH FORMATION IN GRANULAR MATERIALS

6 th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE MATHEMATICAL MODELLING OF ARCH FORMATION IN GRANULAR MATERIALS Istva eppler SZIE Faculty of Mechaics, H-2103 Gödöllő Páter. 1., Hugary Abstract: The mathematical