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Evaluating paleoseismic ground motions using dynamic back analysis of structural failures in archaeological sites. Ronnie Kamai (1) , Yossef Hatzor (1) , Shmulik Marco (2) (1) Department of Geological and Environmental Sciences, Ben Gurion University of the Negev, Beer – Sheva.
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Evaluating paleoseismic ground motions using dynamic back analysis of structural failures in archaeological sites Ronnie Kamai (1), Yossef Hatzor (1), Shmulik Marco (2) (1) Department of Geological and Environmental Sciences, Ben Gurion University of the Negev, Beer – Sheva. (2) Department of Geophysics and Planetary Sciences, Tel Aviv University.
Research objective To develop an alternative method for obtaining strong ground-motion data: by back analysis of structural failures in archaeological sites. Results will provide constraints on PGA estimates, generated by the existing seismological strong motion catalogue.
Research question – what ground motions caused these specific failure mechanism ? Avdat Mamshit Nimrod Fortress
Physical and Mechanical properties of the building stones are obtained in the Rock Mechanics Laboratory of the Negev, Ben-Gurion University Direct shear Ultrasonic waves
Results for a direct shear test on a sample from Avdat site, under three different normal stresses.
Dynamic analysis was performed with the Discontinuous Deformation Analysis method (DDA): • A numerical method of the distinct element family • Based on the second law of thermodynamics - minimization of energy in every time step • The numerical elements are real isolated blocks, having 6 degrees of freedom • No tension or penetration is allowed between blocks • The interfacial friction obeys the Coulomb-Mohr criterion • Limitations: • This research was performed with the 2-D model • Stresses and strains are constant through the blocks
gcosa*tgf gsina g a 1. Block on an incline - gravitation only Equations of Motion:
g(cosa-ksin(wt)sina)*tgf a= kgsin(wt) gsina+kgsin(wt)cosa g a 2. Block on an incline - Dynamic validation sin shape acceleration input motion Equations of Motion:
Accumulating displacement of block : Analytical vs. DDA a = f = 20 at = 0.5sin(2t)
Accumulating displacement of block: Analytical vs. DDA a < f at = 0.5sin(2t)
y 2 Responding block x 1 Ground- input motion Basement block - fixed Conditions for direction of force ( ): 3. Input motion mechanism – displacement to basement block Equations of Motion:
Input motion into Block 1: Analytical vs. DDA dt = 0.5 (1- cos (2pt))
Dynamic response of Block 2: Analytical vs. DDA Influence of m (f = 1Hz; A = 0.5m) dt = 0.5 (1- cos (2pt))
Dynamic response of Block 2: Analytical vs. DDA Influence of Amplitude (f = 1Hz; m = 0.6) dt = A (1- cos (2pt))
Dynamic response of Block 2: Analytical Vs. DDA Influence of Frequency (A = 0.02 m ; m = 0.6) dt = 0.02 (1- cos (2pwt))
Validation Conclusions • A remarkable agreement between DDA and analytical solutions of various mechanisms is shown • DDA is sensitive to interface friction and loading function parameters (Amplitude and frequency).
Case studies • Careful and accurate mapping of the structure is performed • The 2-D DDA model is built in attempt to best represent the structural situation • An Earthquake record, either a synthetic sinusoidal one, or an amplified record of Nuweiba 1995 is induced into all block centroids • A sensitivity analysis for varying Amplitudes and frequencies is performed • The dynamic displacements and stresses at pre-defined measurement points is recorded and analyzed
h Mamshit g f E • The model: • The embedding wall is very heterogenic, so material lines (red) define different • mechanical parameters for arch and wall • Dots are “fixed points”, fixating the basement block
Sensitivity analysis was performed for: Overburden (h) Amplitude of earthquake Frequency of earthquake stiffness of embedding wall The vertical displacement of the Key stone over time is the measured parameter.
h=0 Best fit to field evidence after 10sec obtained with: f =1.5 Hz, A = 0.5g and h = 0 Vkey block= -3 cm
2. Avdat Five blocks have slid westerly out of the western wall • The model: • Because of 2-D limitations, the model is of the northern wall, in order to see the westerly sliding • The model is confined on its left side because of a later structure attached to the wall to the left of the door • Red dots are “fixed” points, yellow dots are measurement points.
Preliminary results Sensitivity analysis is not completed yet, best fit up to this point: The observed blocks were displaced 4-10cm after 10sec with an earthquake of A=1g, f=3Hz for 10 sec.
Conclusions • Analysis of a structural failure in archaeological sites was performed successfully using DDA. • The new procedure can be applied to other sites in the world, provided that the displacement of a distinct element in the structure can be measured. • We find that frequency, amplitude, and duration of shaking have a strong influence on the structural response. • Specifically, for the case studies presented we find that: 1. For the site of Mamshit: • The downward displacement of the arch-keystone became possible after the collapse of the overlying layers due to the relaxation of arching stresses. • The critical frequency and amplitude for the detected failure mode in the analyzed arch is 1Hz and 0.5g, respectively. 2. For the site of Avdat: • The door opening causes an arching of the stresses, and therefore the displaced blocks are not the ones with the least vertical load. • The critical frequency and amplitude for the detected failure mode in the analyzed structure is 3Hz and 1g, respectively.
