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DSD-NL 2018 Inverse Analysis for Workshop Anura3D MPM - Ghasemi Martinelli

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Presentatie door Pooyan Ghasemi en Mario Martinelli, Deltares, op de Geo Klantendag 2018, tijdens de Deltares Software Dagen - Editie 2018. Donderdag, 7 juni 2018, Delft.

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DSD-NL 2018 Inverse Analysis for Workshop Anura3D MPM - Ghasemi Martinelli

  1. 1. Application of Inverse analysis to the Material Point Method Pooyan Ghasemi and Mario Martinelli Geo Klantendag 2018 Workshop Anura3D Modelleren met MPM
  2. 2. dykes, dams, landslides installation, impact, SSI flowslides, erosion, liquefaction, SWI Applications
  3. 3. Applications • How can we benefit? What can we gain? • study beyond “initial” failure > progressive failures and dynamic processes • prediction of consequences > catastrophic failures • study the efficiency of remedial actions > location, type and strength of reinforcement • or defence structure • improve risk assessment
  4. 4. dykes, dams, landslides installation, impact, SSI flowslides, erosion, liquefaction, SWI Applications small deformation onset of failure
  5. 5. dykes, dams, landslides installation, impact, SSI flowslides, erosion, liquefaction, SWI Applications small deformation onset of failure Results depend on the value of the CONSTITUTIVE MODELS PARAMETERS ->> parameter calibration is crucial! <<-
  6. 6. Applications Most of the time multiple sets of data are available: • Lab tests (TX tests, …. ) • Field tests (SPT, CPT…) • Field monitoring observations CPT Real field data
  7. 7. Applications Most of the time multiple sets of data are available: • Lab tests (TX tests, …. ) • Field tests (SPT, CPT…) • Field monitoring observations CPT Real field data ?
  8. 8. Outline • What is inverse analysis • Inverse analysis in Geotechnical problem • Example 1 • Example 2 • Main case study • Remarks and conclusion
  9. 9. What is the Inverse Analysis Much research in science and engineering is devoted to constructing numerical models of physical systems. Given a complete description of the physical system, these models can be used to predict how the system affects its surroundings. This is called the direct or forward problem. When some aspects of physical system are unknown, however, it is sometimes possible to infer these characteristics from a known system response; this is the inverse problem. Inverse problem Forward problem Regular Simulation, Physical or Numerical Parameter estimation Design optimization Infer the optimal design Infer the system characteristics from experimental Data More popular in Geotechnical engineering Definition:
  10. 10. What is the Inverse Analysis We are already using inverse analysis in our mind Base on the our observation we are looking for the cause This is a difficult task if many types of dragon produce similar footprints, and becomes impossible if the footprints are even slightly smeared in mud.
  11. 11. The roles of prior Information • Numerical geotechnical models are mathematically ill- posed due to an information deficit. Sometimes, measurements barely provide sufficient information • Some models’ parameters do not have physical meaning Curve Fitting + Prior Information + (e.g. max or min value of parameter, relation between parameters) Combinations of the observations = (e.g. choose the most appropriate observation for the corresponding parameter) Inverse Analysis • In inverse Analysis method , we are trying to get closer to the solution step by step, considering only the correct parameters and the corresponding tests observations • Adding the new observations together with other remaining parameters and complete the inverse analysis -> step by step procedure • Care must be taken to ensure that the information available are used appropriately! (i.e. reasonable parameter value?, correct test to calibrate that parameter?)
  12. 12. Elementary soil behavior Triggering stage Propagation Stage • mobilized volume? • mode of collapse? • Yielding surface ? • Final run-out • final geometry What we need to do in order to calibrate a simulation of large deformation phenomenon Inverse analysis in Geotechnical problems Different Stage of Simulation and Calibration Eckersley, D. (1990). Instrumented laboratory flowslides. Geotechnique, 40(3), 489-502.
  13. 13. Inverse analysis in Geotechnical problem Observations : Result of Laboratory testing Calculation model testtest Model test Model Optimization algorithm Update parameters Input Parameters test BEST Fit Is min error? No Yes End and report the optimal parameters Error • Particle swarm method • Genetic algorithm • Neural Network Fuzzy Methods:
  14. 14. Inverse analysis in Geotechnical problem Soil Test toolbox element test Large deformation tests suite
  15. 15. Landslide basal surface Observation Inverse analysis in Geotechnical problem Numerical model SPH, MPM, FEM Optimization algorithm Update parameters Input Parameters Is min error? No Yes End and report the optimal parameters Observations : Physical experiments or Site inspecting Landslide basal surface Observation Simulation Landslide basal surface Observation Simulation Landslide basal surface Observation Best Fit Error Calvello M, Cuomo S, Ghasemi P (2017). The role of observations in the inverse analysis of landslide propagation. Computers and Geotechnics, 92:11-21) • Kalaman Filter • Nonlinear Regression • Modified Guass Newoton Gradient base method:
  16. 16. Elements of Inverse Analysis • There are many options for components of the procedure, for each specific problem , the best option might be varied Optimization algorithm Objective Function Examples for optimization methods : Optimization algorithm Problem Ref. • Ucode algorithm Excavation Calvello (2002) • Genetic algorithms Excavation Levasseur (2007) • PSO Constitutive model of Clay Knabe (2013) • Differential evolution (DE) Excavation Zhao (2014) • Artificial bee colony algorithm Excavation Zhao (2016) • Nelder-Mead Excavation Tian (2016) • Genetic algorithms constitutive model of rock salt Khaledi (2016) • Ensemble Kalman Filter Slope Stability Varden (2016) • hybrid methods Excavations De Santus (2015) Objective Function Observation Which Type of observation How many observation? Error Calculation Weighted Least squared Error (WSE) Robust and interpolation-free technique (Horn 2015) Calculation the area between two figures Gradient base method: • Give the Sensitivity of each Parameters • Fewer number of Iteration • Weak in the case of large number of parameters and High correlated parameters Fuzzy Method : • Robust in the Case of high correlated Parameters • Compatible for large number of parameters • Large number of Iteration is needed
  17. 17. Implementation in Anura 3D Numerical Calculation Input Parameters Output Desired Results (observation) Input.txt OutPut.txt Regression (Optimization Engine) Updated Parameters Model optimized? Anura3D INV. Interface (1st Phase of the Project) Initial Values No Yes End Start 2nd Phase of the Project Matlab and Python, Ucode Anura3D
  18. 18. Example 1: Inverse Analysis of CPT example to check the software performances • Creating the synthetic observation: MPM model while using the a set of assumed parameter value Mohr Coulomb Constitutive model: Parameters Value Porosity 0.2 Density Solid 2650 Young Modules (Kpa) 6000 Poisson Ratio 0.2 Cohesion(KPa) 1 Frictional angle 30 Dilatancy Angle 0 • Forward Model : MPM-2D Axisymmetric • Cone Diameter = 3.57 Cm GIP SIMON Project , MPM 2D Code Provided By Mario Martineli , Vahid Galavi and Faraz Sadeghi Tehrani
  19. 19. Iteration No Young Module KPa Frictional angle Weighted Error 1 4289 27.11 211.15 2 3921 34.12 20.788 3 4352 34.92 2.0565 4 4585 33.83 1.9234 5 4918 32.45 1.6839 6 5306 31.52 0.88127 7 5512 31.04 0.86326 8 6035 29.79 0.15969 9 6040 29.9 0.10034 Example1: Estimation of Mohr-Coulomb Parameters by CPT • Parameters of Interest : Frictional angle and young modules are assumed as unknown parameters • Optimization Algorithm : Modified Gauss Newton Method
  20. 20. Example1: Estimation of Mohr-Coulomb Parameters by CPT 3000 3500 4000 4500 5000 5500 6000 6500 1 3 5 7 9 YoungModule(KPa) Iteration No Parameters Value Desired Value 20 22 24 26 28 30 32 34 36 1 3 5 7 9 FrictionalAngle Iteration No -50 0 50 100 150 200 250 1 3 5 7 9 weightedResidualError Iteration No Iteration friction angle Young Modulus 1 10.1798 7.60181 2 11.2 6.398 3 13.7643 7.99513 4 13.08 7.5636 5 14.3756 7.272 6 15.1558 5.94192 7 14.6878 6.25564 8 16.1729 6.73256 9 15.7852 6.35672 Composite Scaled Sensitivity : the importance of different parameters to the calculation Convergence criteria: • The maximum parameter change of a given iteration is less than a user-defined tolerance • The objective function, S(b), changes less than a user-defined tolerance for three consecutive iterations
  21. 21. Example2 : The run out of a dry granular flow Small scaled flow test conducted by (DENLINGER AND IVERSON 2001) • The experiment used a small flume with a bed surface inclined 31.4° adjoined to a horizontal runout plane. • After material release, the flow accelerates gradually spreading and reaching the end of the inclined plane Denlinger, R. P., & Iverson, R. M. (2001). Flow of variably fluidized granular masses across three‐dimensional terrain: 2. Numerical predictions and experimental tests. Journal of Geophysical Research: Solid Earth, 106(B1), 553-566.) Experiment outcomes:
  22. 22. Example2 : The run out of a dry granular flow Ceccato and Simonini 2016: • only run out distance was considered as the benchmark • Parametric analysis • The best agreement with the experimental results were obtained when : basal friction angle equal to 26.6° Static friction angle equal to 40° Ceccato, F., & Simonini, P. (2016). Study of landslide run-out and impact on protection structures with the Material Point Method. In INTERPRAEVENT 2016- Conference Proceedings • MPM Model with Anura 3D 12555 Element 4 particles per element • Parameters of Interest : Soil Frictional Angle Basal frictional Coefficient Frictional contact
  23. 23. Example2 : The run out of a dry granular flow Quantitative calibration based on run out distance and also soil thickness : Benchmark : Soil thickness after propagation 𝜑 = 43 𝑡𝑎𝑛𝜑 𝑏 = 0.47 Cross Section
  24. 24. Example2 : The run out of a dry granular flow
  25. 25. Main Case Study : Liquefaction and Retrogressive failure in Cohesion less Material Scaled slope failure experiment conducted by Eckersley 1990 • Instability was induced by raising the water level • Water entered the slope from constant head tank • To avoid surface erosion , water is injected through a wire cage filled with coarse gravel • Instability starts when the water level at the rear of the model reached at 0.4 m • Glass Tank • Basal surface Plywood floor • Water proof sand paper glued to the floor in order to inhabit direct sliding along the coal / floor Interface, Angle of shearing resistance was reported in the range of 30 to 36 Eckersley, D. (1990). Instrumented laboratory flowslides. Geotechnique, 40(3), 489-502.
  26. 26. Main Case Study : Liquefaction and Retrogressive failure in Cohesion less Material: Material Properties Name = Northwich Park Coal 4 ICU triaxial tests with confining stress equal to 50 KPa Different initial void ratio : e = 0.41 , Contractive behavior e = 0.38 , contractive behavior e = 0.34 , contractive behavior e = 0.32 , Dilative behavior Specific Gravity = 1.34 𝑑10 = 0.06 − 0.3 𝑚𝑚 Minimum Density = 0.6 gr/cm3 Maximum density = 1.1 gr/cm3 Hydraulic conductivity = 0.01 cm/s2 Typical particle size distribution Effective path stress Saturated CU triaxial tests State diagram Effective critical frictional angle = 40 degree Available laboratory test Data:
  27. 27. Toe sliding duo to water seepageStage 1 Stage 2 Shallow failure along the slope surface Stage 3 Deep failure and mobilize fairly all of the domain Geometry after flow slide Main Case Study : Liquefaction and Retrogressive failure in Cohesion less Material: Over view of the experience : Failure modes Eckersley, D. (1990). Instrumented laboratory flowslides. Geotechnique, 40(3), 489-502.
  28. 28. Main Case Study : Liquefaction and Retrogressive failure in Cohesion less Material: Selection of of constitutive models Evaluation of constitutive models capability to simulate the material behavior through simulating an undrained consolidated Triaxial test by Anura 3D  Mohr Coulomb Strain Softening Knownorreported Parameters Density solid (gr/cm3) Porosity Intrinsic Permeability Peak Frictional angle Residual Frictional angle Peak Cohesion (Kpa) Residual cohesion Young Module Dilation angle Shape factor Value 1340 0.26 10 e-09 40 40 0.00 0 Clearly reported in case study Unknown Parameters ????????? ????????? ????????? FittingParameters Parametric Study
  29. 29. Main Case Study : Liquefaction and Retrogressive failure in Cohesion less Material: Selection of of constitutive models  Mohr Coulomb Strain Softening Fitting Parameters Parameters SET01 SET02 SET03 SET04 SET05 SET06 E KPa 1000 1000 1000 1000 1000 1000 Ψ -5 -5 -5 -15 -15 -15 𝛽 4 40 400 4 40 400 .0 20.0 40.0 60.0 80.0 100.0 120.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 DeviatoricStress(KPa) Axial Strain SET 01 SET 02 SET 03 SET 04 SET 05 SET 06 .0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 0 20 40 60 80 100 DeviatoricStress(KPa) Mean effective Stress (KPa) .0 10.0 20.0 30.0 40.0 50.0 60.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Porewaterpressure(KPa) Axial Strain SET 01 SET 02 SET 03 SET 04 SET 05 SET 06 • The model can not take into the account the effect of density (a) (b) Cuomo, Ghasemi, Martinelli, Calvello, (2017) Simulation of liquefaction and retrogressive slope failure in loose cohesionless material • one set of parameters can not predict mechanical features of all three tests at the same time pore water pressure Shear strength Effective Stress Path
  30. 30. Stress Initialization (quasi-static convergence)Removing fixities, applying liquid traction at the rear of the slope Main Case Study : Slope Model : Geometry, boundary and Initial Condition • One Particle formulation • Mixed Integration • For the Frist time Layered Soil in one particle formulation • Special Consideration for pressure smoothing in Mixed Element • Number of Element = 3,336 • Number of Particle per element = 4 Elastic material Dry Saturated Material liquid horizontal fixity Frictional Contact Liquid pressure Tracking Points and Zone: Elastic Material Zone1 Zone2 Zone3 Frictional contact Sat dry F1 F2 F3 F4 F5 Point X Y F1 0.7769 0.09424 F2 1.458 0.125 F3 1.762 0.09192 F4 0.9624 0.6130 F5 0.6833 0.6541 Liquid Fixity Linearliquidtraction
  31. 31. Slope Model : Simulation By Strain Softening Movie Time!!! • Slope Simulation MC_ Strain Softening • Progressive Collapse
  32. 32. Slope Model : Simulation By Strain Softening Parameters Values Density solid (gr/cm3) 1340 Porosity 0.26 Intrinsic Permeability 10 e-09 Peak Frictional angle 40 Residual Frictional angle 40 Peak Cohesion (Kpa) 0.00 Residual cohesion 0 Young Module 1000 Dilation angle -15 Shape factor 40 • Progressive failure • Similar to stage 1 and 2 reported in experiment • 3rd stage is missing • Excess pore water pressure was not built enough to make further collapse Time =5=0.3 Time =0.6 Final _scheme Time =1.2 Deviatoric Strain Zone 1 Zone 2 Zone 3 Time (sec) PWP(Kpa)PWP(Kpa)PWP(Kpa) (a) (b) Zone 3 Zone 2 Zone 3
  33. 33. The model by von Wolffersdorff (1996) is now considered as a reference hypoplastic model for granular materials. It requires 8 material parameters: 𝜑𝑐 is the critical state friction angle. ℎ 𝑠 and n control the shape of limiting void ratio curves (normal compression lines and critical state line). Ec0 is critical void ratio at zero stress Ei0 is maximum void ratio at zero stress Ed0 is minimal void ratio at the state of maximum density 𝛼 controls the dependency of peak friction angle on relative Density. 𝛽 controls the dependency of soil stiffness on relative density. Reported By case Study Obtainable from State Diagram Fitting parameters Intergranular Parameters : The intergranular strain concept (Niemunis and Herle 1997) enables to model small-strain-stiffness effects in hypoplasticity. It requires 5 more material parameters: mR: parameter controlling the initial (very-small-strain) shear modulus upon 180 strain path reversal and in the initial loading mT : parameter controlling the initial shear modulus upon 90 strain path reversal R: the size of elastic range (in the strain Space) 𝛽𝑟 and 𝑥 control the rate of degradation of the stiffness with strain. Main Parameters : Fitting parameters Main Case Study : Liquefaction and Retrogressive failure in Cohesion less Material: Selection of of constitutive models • Hypoplasticity 𝜑𝑐 40 ℎ 𝑠 93KPa n 0.07 Ec0 0.93
  34. 34. i) Deviatoric stress versus axial strain ii) pore water pressure versus axial strain 𝑒𝑟𝑟𝑜𝑟 = 𝑦′ 𝑖 − 𝑦 𝑖 2 [0.01 × 𝑤𝑒𝑖𝑔ℎ𝑡 ]2 𝑛 𝑖=1𝑔𝑟𝑎𝑝ℎ𝑠 𝑛, 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑦′ 𝑖 , 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡𝑠 𝑖 𝑦 𝑖 , 𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑝𝑜𝑖𝑛𝑡𝑠 𝑖 Optimization algorithm New method called SQPSO, it is a modification of conventional Particle Swarm Optimization method adopted for the functions in which the large number of parameters are going to be estimated. (Hosseinnezhad et al 2014) Objective function: Parameters of interest: 10 Parameters 𝜑𝑐 , Ei0 , Ed0 , 𝛼 , 𝛽 , mR, mT , R, 𝛽𝑟 and 𝑥 PWP q Axial deformationAxial deformation Graph discretization (Eckersley 1986) Observation Main Case Study : Inverse analysis in order to obtain Hypo plasticity Parameters 2000 2050 2100 2150 2200 2250 0 10 20 30 40 50 60 70 80 ModelErrorFuncrion Number of Iteration
  35. 35. Test NP-02 (Initial void ratio = 0.410) Test NP-13 (Initial void ratio = 0.34) Test NP-5 (Initial void ratio = 0.38) Parameters Estimated Values 𝜑𝑐 [○] 40 ℎ 𝑠 [Kpa] 93.27195 n 0.0768 Ec0 0.93 Ei0 1.3 Ed0 0.397758 𝛼 0.349126 𝛽 0.562619 𝑚 𝑅 1.33593 𝑚 𝑇 7.05643 R 0.000142 𝛽𝑟 0.0773067 𝑥 0.951017 Main Case Study : Hypo-plasticity: Results of inverse Analysis
  36. 36. Main Case Study : Hypo-plasticity: Check the obtained Parameters Parameters Estimated Values 𝜑𝑐 [○] 40 ℎ 𝑠 [Kpa] 93.27195 n 0.0768 Ec0 0.93 Ei0 1.3 Ed0 0.397758 𝛼 0.349126 𝛽 0.562619 𝑚 𝑅 1.33593 𝑚 𝑇 1.05643 R 0.000142 𝛽𝑟 0.0773067 𝑥 0.951017 Adding Prior knowledge to the results is recalibrated 𝛼 = 0.21 0 5 10 15 20 25 30 35 40 45 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 FrictionalAngel Axial strain Alpha = 0.05 Alpha = 0.34 Alpha = 0.2 Alpha = 0.54
  37. 37. Main Case Study : Hypo-plasticity: Check the obtained Parameters Comparing the results without and with modification: f1 f3 f4 f2 Point 3 Point 2 Point 4 Point 2 f1 f3 f4 f2 Point 1 f1 f3f4 f2 f1 f3 f4 f2 2nd Stage(time = 0.6 sec) 1st Stage (time = 0.3 sec) 3rd Stage(time = 1.3 sec) Final Shape (Time =1.7) (b) 2nd Stage (time = 0.6 sec) Final Shape (Time =1.4) 1st Stage (time = 0.3) 3rd Stage (time =1.1 Sec) (a) Deviatoric Strain Without modification With modification TEST results
  38. 38. Slope Model : Simulation By Hypo plasticity Movie • Slope simulation with Hypo plasticity • Retrogressive failure:
  39. 39. Slope Model : Simulation By Hypo plasticity Movie • Slope simulation with Hypo plasticity • Static Liquefaction :
  40. 40. -2 -1 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 PoreWaterPressure(KPa) Time (sec) -2 -1 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 PoreWaterPressure(KPa) Time (sec) -2 -1 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 PoreWaterPressure(KPa) Time (sec) Porewaterpressure(KPa) Zone1 Mean effective stress Zone2 Zone3 Stage 1 Stage 2 Stage 3 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 MeanEffectiveStress(KPa) Time (sec) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 MeanEffectiveStress(KPa) Time (sec) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 MeanEffectiveStress(KPa) Time (sec) Stage 1 Stage 2 Stage 3 Zone3 Zone2 Zone1 Meaneffectivestress(KPa) Overall Time (sec) Stage 1 Stage 2 Stage 3 Overall Time (sec) Zone3 Zone2 Zone1 f1 f3 f4 f2 Point 3 Point 2 Point 4 Point 2 f1 f3 f4 f2 Point 1 f1 f3f4 f2 e initial = 0.60 Deviatoric Strain Solid 1st Stage 2nd Stage 3rd Stage 2nd Stage(time = 0.8 sec) 1st Stage (time = 0.4 sec) 3rd Stage(time = 1.1 sec) Slope Model : Simulation By Hypoplasticity • Geometric Validation • Soil Response in Fixed Coordinate
  41. 41. Remarks Most advantage of Anura 3D: Capable to simulate all of the stage of phenomenon . appropriate for both of inverse modeling scale; to calibrate small and large deformation parameters Advanced numerical method are being developed, the validation of their capability is extremely needed • Large deformation phenomenon usually involves complex mechanism • Simulation of complex system usually involves complex constitutive model • Many advanced constitutive models are already implemented in Geotechnical Codes but the difficulties in choosing their parameters undermines their capability and applications • Inverse Analysis feature could simplify the usage of advanced model Strain Softening Mohr-coulomb Modified Cam clay Hypoplasticity Mohr-coulomb • Inverse Analysis could easily estimates Numerical Parameters which doesn't have physical meaning : Shape factor Contact coefficient And ……… Modified hypoplasticity Norsand • Using the inappropriate constitutive model could lead to wrong prediction of the phenomenon
  42. 42. Thank you Pooyan Ghasemi and Mario Martinelli Deltares
  43. 43. Appendix Comparing the results without and with modification: f1 f3 f4 f2 Point 3 Point 2 Point 4 Point 2 f1 f3 f4 f2 Point 1 f1 f3f4 f2 f1 f3 f4 f2 2nd Stage(time = 0.6 sec) 1st Stage (time = 0.3 sec) 3rd Stage(time = 1.3 sec) Final Shape (Time =1.7) (b) 2nd Stage (time = 0.6 sec) Final Shape (Time =1.4) 1st Stage (time = 0.3) 3rd Stage (time =1.1 Sec) (a) Deviatoric Strain Without modification With modification

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