Finite Element Solutions for Geotechnical Engineering

Transcription

1 Release Note Release Date : January Product Ver. : GTSNX 2015 (v1.1) Integrated Solver Optimized for the next generation 64-bit platform Finite Element Solutions for Geotechnical Engineering

2 Enhancements 1. Pre Processing 1.1 Load Table Import / Export 1.2 Artificial Earthquake Generator 1.3 Free Field Element (Infinite Element for Dynamic Analysis) 1.4 Inelastic Hinge 2.1 SAFETY FACTOR (Mohr Coulomb Criteria) 2.2 Material : von Mises - Nonlinear 2.3 Material : Modified UBCSAND 2.4 Material : Sekiguchi-Ohta(Inviscid) 2.5 Material : Sekiguchi-Ohta(Viscid) 2.6 Material : Generalized Hoek Brown 2.7 Material : 2D Orthotropic (2D Structural Element) 2.8 Material : Enhancements in Hardening Soil 2.9 Material : Modified Ramberg-Osgood 2.10 Material : Modified Hardin-Drnevich 2.11 Option : Estimate Initial Stress 2.12 Option : Stress-Nonlinear Time History Analysis Integrated Solver Optimized for the next generation 64-bit platform Finite Element Solutions for Geotechnical Engineering

3 1. Pre Processing 1.1 Load Table Import / Export Define or modify load through excel like Load Table. Users can import load from excel and export defined load (position (node), magnitude and direction) to excel - Only one excel file can communicate with GTSNX at once Following types of loads are available : Force, Moment, Pressure, Prescribed Displacement and Element Beam Load. Useful when users have to manage (input and modify) large numbers of load sets at once. [Engineering Example : Pile-Raft Foundation] 3 / 31

4 1. Pre Processing 1.2 Dynamic Tools > Artificial Earthquake Generate artificial earthquake data from the embedded design spectral data. Following design spectral data are available in GTSNX. Read Target Design Spectral Data Compute PSD (Power Spectral Density) Function Modify PSD RSA( ) G( ) i1 G( ) i ( i ) RSA ( ) 2 Compute Acceleration z( t) I ( t) A sin( t ) n n n n Compute Response Spectrum NO Iteration i Max. Iteration YES Output Results [Process of Artificial Earthquake Generation] [Design Spectral Data] 4 / 31

5 1. Pre Processing 1.2 Dynamic Tools > Artificial Earthquake Envelope Function enables to generate transient earthquake data. There are three types of envelope functions : Trapezoidal, Compound and Exponential. GTSNX supports Trapezoidal type. Where, ω n = Frequency, A n = Amplitude, Ф n = Phase Angle, and I(t) = Envelope Function [Equation for time history function] I(t) Level Time Generate Options -Max Iterations : Maximum number of iterations to fit computed spectral data to target one. -Max. Acceleration : Maximum acceleration of artificial earthquake data -Damping Ratio : Damping ratio to calculate spectral data Rise Time [Envelope Function] Total Time Generate Acceleration : Covert from response spectrum to acceleration data -Spectrum Graph : Check results based on spectral data -Acceleration Graph : Check results based on acceleration data [Add/Modify Artificial Earthquake] 5 / 31

6 1. Pre Processing 1.3 Element > Free Field Element (Infinite Element for Dynamic Analysis) For the seismic analysis, users need to model infinite ground to eliminate the boundary effect caused by reflection wave. Since it is not possible to model infinite ground, users can apply Free Field Element at the boundary. Free Field Element enables to apply traction resulted from Free Field Analysis to the ground boundary and then, eliminate reflection wave using absorbent boundary condition. Free field Free field Main domain Seismic wave [Schematic overview of Free Field Element] [Free field effect(o), Absorb reflection(o)] Viscous boundary Viscous boundary [Free field effect(x), Absorb reflection(x)] [Free field effect(x), Absorb reflection(o)] 6 / 31

7 1. Pre Processing 1.3 Element > Free Field Element (Infinite Element for Dynamic Analysis) Select free edges in 2D and free faces in 3D to define Free Field Elements [Property > Other > Free Field] Free Field -Enables to simulate infinite ground boundary Absorbent Boundary -Enables to eliminate reflection wave at the ground boundary [Create Free Field Element] Width Factor (Penalty parameter) -In order to minimize the size effect, users have to input more than This value is multiplied by model width (In case of 2D, this is plain strain thickness (unit width)) DOF (Degree of Freedom for damping) -Users can select specified DOF for damping effect 7 / 31

8 Displacement GTSNX 2015 Enhancement 1. Pre Processing 1.3 Element > Free Field Element (Model Calibration) Free field element can result in identical behavior with infinite ground model. [None] [Free field] [Ground acceleration] [Infinite ground] 4.00 Time vs displacement time None Infinite ground Free field Viscous boundary 8 / 31

9 1. Pre Processing 1.4 Element > Inelastic Hinge Inelastic hinge can be applied to the structural elements to simulate crack or local (plastic) failure. Applicable in Nonlinear Static and Time History Analysis as follows : Nonlinear, Construction Stage, Consolidation, Fully Coupled, SRM (Slope Stability) Following properties are available to define inelastic hinge : Beam, Truss, Elastic Link and Point Spring. Load Crack or local failure [Hinge Properties] Inelastic hinge [Schematic overview of Inelastic Hinge] 9 / 31

10 1. Pre Processing 1.4 Element > Inelastic Hinge (Property & Components (Single / Multi)) Refer to Online Manual (F1) in detail... Mesh >Prop./ Csys./ Func. > Hinge > Hinge Properties Mesh >Prop./ Csys./ Func. > Hinge > Hinge Components Hinge Type : Beam (Lumped / Distributed), Truss, Elastic Link, Point Spring Interaction : Single Component (None, P-M, P-M-M), Multi Component Component : Location (Lumped), No. of Sections (Distributed), Hysteresis Model, Yield Surface Parameters / Function (P-M, P-M-M, Multi Component) Hysteresis Model Type: Single Component ( ), Multi Component (Kinematic) [Hinge Properties] [Hysteresis Model Type : Single Component] [Hinge Components (Single/Multi)] [Yield Surface Parameters] [Yield Surface Function] 10 / 31

11 2.1 Safety Result (Mohr - Coulomb criteria, Material > Isotropic > General Tab) Cohesion, Friction Angle and Allowable tensile strength (optional) can be defined as the failure criteria. Stress status of material for each construction stage can be represented by Factor of Safety based on Mohr-Coulomb failure criteria. The ratio of generated stress to stress at failure for each element will be calculated automatically. Users can figure out stable, potential failure and plastic failure area directly. Check factor of safety for each element - (2D : Plain Strain Stresses > SAFETY FACTOR, 3D : Solid Stresses > SAFETY FACTOR) In case that Safety Factor is less than 1(or 1.2), it can be identical with plastic failure region. [Model Overview : Deep Excavation in 3D] [Model Overview : Tunnel Excavation in 2D] [Plastic Status : Element Stresses] [Safety Factor (region for less than 1.2)] [Engineering Examples] 11 / 31

12 2.2 Material : von Mises - Nonlinear von Mises model is often used to define the behavior of ductile materials based on the yield stress. Undrained strength of saturated soil can be appropriately presented using the von Mises yield criterion. As a material yield, hardening defines the change of yield surface with plastic straining, which is classified in to the three types : Isotropic, Kinematic and Combined. Appropriate for all types of materials, which exhibit Plastic Incompressibility. Perfect Plastic: Specify Initial Uniaxial (tensile) Yield Stress Hardening Curve : Relation between plastic strain and stress(true stress) can be resulted from uniaxial compression / tensile test or shear test. Stress Strain curve (optional) : Relation between strain and stress(true stress) Hardening Rule: Isotropic, Kinematic and Combined (Isotropic + Kinematic) - Total increment of Plastic can be expressed by Isotropic and Kinematic Hardening as follows ` h (0) (1 ) h ( e ) y c y c y p - Combined hardening factor (λc, 0~1) represents the extent of hardening. 1 for Isotropic, 0 for Kinematic, and between 0~1 for Combined hardening. 2 2 Combined hardening Initial yield surface Isotropic hardening Initial yield surface 1 1 Kinematic hardening [Yield surface for each hardening rule] 12 / 31

13 Shear Stress Stress Ratio GTSNX 2015 Enhancement 2.3 Material : Modified UBCSAND An effective stress model for predicting liquefaction behavior of sand under seismic loading. GTSNX Liquefaction Model is extended to a full 3D implementation of the modified UBCSAND model using implicit method. In elastic region, Nonlinear elastic behavior can be simulated, elastic modulus changes according to the effective pressure applied. In plastic region, the behavior is defined by three types of yield functions : shear (shear hardening), compression (cap hardening), and pressure cut-off. In case of shear hardening, soil densification effect can be taken into account by cyclic loading. Elastic: Shear modulus is updated according to the effective pressure(p ) based on the following equation. - Allowable tensile stress (Pt) is calculated using cohesion and friction angle automatically. - Poisson s ratio is constant and bulk modulus of elasticity will be determined by following relation. G p' p KG pref p ref e e t Plastic/Shear : Depending on the difference between mobilized friction angle(ф m ) and constant volume friction angle(ф cv ), shear induces plastic expansion or dilation is predicted. - The Plastic shear strain increment is related to the change in shear stress ratio assuming a hyperbolic relationship and can be expressed as follows. np1 2 p G p p' sin m sinm s KG 1 Rf s sin m sinm sin p' p sin cv ref p ` ne s K e p p G 3(1 2 ) e Constant volume cv p G / p' Dilative Contractive sin m S Mean Stress Maximum Plastic Shear Strain Beaty, M. and Byrne, PM., An effective stress model for predicting liquefaction behaviour of sand, Geotechnical Special Publication 75(1), 1998, pp Puebla, H., Byrne, PM., and Phillips, R., Analysis of CANLEX liquefaction embankments: protype and centrifuge models, Canadian Geotechnical Journal, 34, 1997, pp [Reference for UBCSAND model] 13 / 31

14 2.3 Material : Modified UBCSAND Parameter Description Reference Pref e K G ne Reference Pressure Elastic (Power Law) Elastic shear modulus number Elastic shear modulus exponent Plastic / Shear In-situ horizontal stress at midlevel of soil layer Dimensionless Dimensionless p cv Peak Friction Angle Failure parameter as in MC model Constant Volume Friction Angle - C Cohesion Failure parameter as in MC model p K G np ` Plastic shear modulus number Plastic shear modulus exponent Dimensionless Dimensionless R f Failure ratio (qf / qa) 0.7~0.98 (< 1), decreases with increasing relative density F post Post Liquefaction Calibration Factor Residual shear modulus F dens Soil Densification Calibration Factor Cyclic Behavior Advanced parameters Pcut Plastic/Pressure Cutoff (Tensile Strength) - p K B mp Cap Bulk Modulus Number - Plastic Cap Modulus Exponent - OCR Over Consolidation Ratio Normal stress / Pre-overburden pressure 14 / 31

15 2.3 Material : Modified UBCSAND (Model Calibration) Monotonic and cyclic drained Direct Simple Shear (DSS) test (skeleton response). Constant volume DSS test (undrained test) Single Element test and Calibration using Standard Penetration Test (SPT) - ((N 1 ) 60 : Equivalent SPT blow count for clean sand. ` e KG N p e KG KG N p cv N N / N cv N1 /10.0 max 0.0, N R 1.1 N f 0 0 cv ne 0.5 np [Parameters and Equations for Calibration] 15 / 31

16 Shear stress [kpa] Shear stress [kpa] GTSNX 2015 Enhancement 2.3 Material : Modified UBCSAND (Model Calibration) 25 Test Analysis 25 Test Analysis Shear strain [%] [Undrained DSS (Monotonic)] 15 Vertical Stress [kpa] ` Test 15 Analysis Soil densification Vertical Stress [kpa] -15 [Undrained DSS (Cyclic)] Vertical Stress [kpa] 16 / 31

17 2.4 Material : Sekiguchi - Ohta (Overview) Critical state theory model which is similar to Modified Cam Clay model Nonlinear stress-strain behavior in elastic region Stress induced anisotropy - Ko dependent term in yield function : Always have to apply Ko condition for initial stress of ground (Ko Anisotropy is not applicable ) Time dependent behavior, Creep (Viscid type only) - time variable in yield function which is similar to SSC (Soft Soil Creep) model, but based on different elasto-visco plastic theory f SO p p ln v 0 1e0 p0 1e0 M f CC p q p ln v 0 1e0 p0 1e0 M p f MCC 2 p q p ln ln 1 v 0 1e p 1e M M p 3 sij scij sij scij 2 p pc p pc K0 1 3 sij sij q 2 p p p q C.S.L K0 -line p c p ` C.S.L [Sekiguchi-Ohta (Inviscid)] [Cam Clay] [Yield Function : If K0=1, Original Cam Clay model is equal to Sekiguchi-Ohta model] Soft Soil Creep Sekiguchi-Ohta(viscid) Always plastic state Plastic state after yielding [Modified Cam Clay] 1) These equations have a common term as their first term. 2) Second term in each equation represents the contribution of dilatancy, the volume change caused by the change in the ratio of shear stress to hydrostatic stress. 17 / 31

18 2.4 Material : Sekiguchi - Ohta (Inviscid) Representative cohesive soil model that can consider the elasto-plastic behavior, but time-independent one. The same background with Modified Cam Clay model, but can simulate irreversible dilatancy considering initial stress (Ko) of normally consolidated state. Para meter Description Non-Linear Reference value λ Slope of normal consolidation line Cc / / (1 + e 0 ) κ Slope of over-consolidation line Cs / / (1 + e 0 ) (Cc / 5 for a rough estimation) V k isotropic normal consolidation line overconsolidation line critical state line q critical state line M M ` Slope of critical state line 6 x sinф / (3-sinФ ) (Ф : Effective internal friction angle) KOnc Ko for normal consolidation 1-sinφ (< 1) OCR / Pc Cap yield surface Over Consolidation Ratio / Pre-overburden pressure When entering both parameters, Pc has the priority of usage ln(1) ln P P T allow Allowable Tensile Stress * Note * Note : Allowable Tensile Stress This model fundamentally do not allow tensile stress in the failure criteria (stress-strain relationship). However, various conditions can generate tensile stress, such as the heaving of neighboring ground due to embankment load during consolidation or uplift due to excavation. To overcome the material model limits and increase the applicability, analysis on tensile stress within the 'allowable tensile stress' range can be conducted. The size of the allowable tensile stress is not specified, and requires repeated analysis to input a larger value than the tensile stress created from the overburden load (embankment) or failure behavior. However, when directly entering the pc (pre-consolidation load), the allowable tensile stress cannot surpass the pc value. When defining using the OCR, the pc value is automatically calculated internally by considering the size of the input allowable tensile stress. 18 / 31

19 2.5 Material : Sekiguchi - Ohta (Viscid) Representative cohesive soil model that can consider the elasto-visco plastic behavior, and time-dependent one like soft soil creep model Parameter Description Reference value Non-Linear λ Slope of normal consolidation line Cc / / (1 + e 0 ) κ M Slope of over-consolidation line Slope of critical state line Cs / / (1 + e 0 ) (Cc / 5 for a rough estimation) 6 x sinф / (3-sinФ ) (Ф : Effective internal friction angle) * Note : Time Dependent log time ` KOnc Ko for normal consolidation 1-sinφ (< 1) OCR / Pc Cap yield surface Over Consolidation Ratio / Pre-overburden pressure When entering both parameters, Pc has the priority of usage T allow Allowable Tensile Stress * Note strain Primary Secondary 0 t 0 Time Dependent α Coefficient of secondary consolidation Cc / 20 for a rough estimation 0 Initial volumetric strain rate * Note t 0 Time when primary consolidation ends * Note 19 / 31

20 2.5 Material : Sekiguchi - Ohta (Review of soil parameters) Sekiguchi Ohta model requires some material properties, which can be obtained by triaxial tests. Following empirical relations can be used to estimate the additional soil parameters : Karibe Method Plastic index Input Parameters Compression index Drainage distance I p Unit: cm e Remarks sin log I p 2 log cv 0.025I p cm / min Tv 0 2 H T 90% v 90% c v I p C c H 0.434C c Paramet er Description Non-Linear Reference value λ Slope of normal consolidation line Cc / / (1 + e 0 ) κ M Slope of over-consolidation line Slope of critical state line Cs / / (1 + e 0 ) (Cc / 5 for a rough estimation) 6 x sinф / (3-sinФ ) (Ф : Effective internal friction angle) KOnc Ko for normal consolidation 1-sinφ (< 1) OCR / Pc Cap yield surface Over Consolidation Ratio / Pre-overburden pressure When entering both parameters, Pc has the priority of usage T allow Allowable Tensile Stress * Note Time Dependent α Coefficient of secondary consolidation Cc / 20 for a rough estimation 0 Initial volumetric strain rate * Note t 0 Time when primary consolidation ends * Note 20 / 31

21 (Sxx-Szz)/p0 (Sxx-Szz)/p0 GTSNX 2015 Enhancement 2.5 Material : Sekiguchi - Ohta (Model Calibration) Undrained triaxial compression and extension - Effect of strain rate %/min 0.1%/min 0.01%/min 0.001%/min %/min M 1.12 e0 1.5 nc K dispalcement strain : 20% 0.40 Plastic pressure Triaxial- Compression t 1 : 2.0e1 min. t 2 : 2.0e2 min p/p0 t 3 : 2.0e3 min. 1%/min 1.20 Triaxial- Extension dispalcement t 4 : 2.0e4 min. t 5 : 2.0e5 min. 0.1%/min 0.01%/min 0.001%/min %/min Plastic Undrained strength : max xx 2 zz Undrained strength depends on the rate of shearing in different ways on the compressional and extensional sides of shearing Axial strain Sekiguchi, H. and Ohta, H., "Induced anisotropy and time dependency in clays", 9th ICSMFE, Tokyo, Constitutive equations of Soils, 1977, / 31

22 2.6 Material : Generalized Hoek-Brown Representative model to simulate general rock behavior (stiffer and stronger than other types of soil). Hoek-Brown model is isotropic linear elastic behavior. Generalized Hoek-Brown is to link the empirical criterion to geological observations by means of one of the available rock mass classification schemes. All geological index was subsequently extended for weak rock masses. Applicable for Strength Reduction Method (slope stability analysis) m b GSI 100 mi exp D GSI 100 s exp 9 3D 1 1 a e e 2 6 GSI /15 20/3 3 ` 1 m b fhb 1 3 ci 1 s ci a t [Yield Function] [Failure surface in principle stress plane] 22 / 31

23 2.6 Material : Generalized Hoek-Brown (Review of model parameters, Geological Index (Hoek,1999)) [Uniaxial Compressive Strength] ` [Geological Strength Index (GSI)] [Guidelines for estimating Disturbance Factor (D), (0 ~ 1) [Intact Rock Parameter] 23 / 31

24 2.6 Material : Generalized Hoek-Brown (Model Calibration) The Shear Strength Reduction Method for the Generalized Hoek-Brown Criterion Hammah, R.E., Yacoub, T.E. and Corkum, B.C. Rocscience Inc., Toronto, ON, Canada Curran, J.H. Lassonde Institute, University of Toronto, Toronto, ON, Canada [Reference - F.S. : 1.15] [GTSNX - F.S. : 1.19] 24 / 31

25 2.7 Material : 2D Orthotropic Applicable to 2D element type such as Shell, Plane Stress and 2D Geogrid. Users can define different values of stiffness along each direction which is defined by the following parameters : E1, E2, V12, G12, G23, and G31. Useful to define geometrically orthotropic with significant different stiffness in horizontal and vertical direction. E1 21E T 12E2 E T G G G ` [Stress-strain relation in 2D] [Engineering Examples] 25 / 31

26 2.8 Hardening Soil (Enhancement in Modified Mohr Coulomb model: Review of model parameters) Improvement of Convergence in algorithms : Implicit Backward Euler Method Additional (advanced) parameter to define allowable tensile strength. Parameter Description Reference value (kn, m) Soil stiffness and failure E50ref Secant stiffness in standard drained triaxial test Ei x (2 Rf) /2 (Ei = Initial stiffness) Eoedref Tangent stiffness for primary oedometer loading E50ref Eurref Unload / reloading stiffness 3 x E50ref m Power for stress-level dependency of stiffness 0.5 m 1 (0.5 for hard soil, 1 for soft soil) C (C inc ) Effective cohesion (Increment of cohesion) Failure parameter as in MC model φ Effective friction angle Failure parameter as in MC model ψ Ultimate dilatancy angle 0 ψ φ Advanced parameters (Recommend to use Reference value) Rf Failure Ratio (qf / qa) 0.9 (< 1) Pref Reference pressure 100 KNC Ko for normal consolidation 1-sinφ (< 1) Dilatancy cut-off Porosity Initial void ratio - Porosity(Max) Maximum void ratio Porosity < Porosity(Max) Cap yield surface OCR / Pc Over Consolidation Ratio / Pre-overburden pressure When entering both parameters, Pc has the priority of usage α Cap Shape Factor (scale factor of preconsolidation stress) from KNC (Auto) β Cap Hardening Parameter from Eoedref (Auto) Tensile Strength Tallow Allowable Tensile Strength * Note (Refer to Sekiguchi-Ohta model) 26 / 31

27 Force GTSNX 2015 Enhancement 2.9 Material : Modified Ramberg-Osgood One of Hysteresis models for inelastic hinge, an extension was made to 2D and 3D solid elements. Can be applied to simulate crack or local (plastic) failure. Applicable in Nonlinear Static and Time History Analysis as follows : Nonlinear, Construction Stage, Consolidation, Fully Coupled, SRM (Slope Stability) Parameter Description Reference G o Initial Shear Modulus r Reference Strain G o 2 h 2 max, 2 hmax rgo h max Shear Only Maximum Damping 0.05 (for soil), Check : Consider shear modulus for each direction separately (Gxy, Gyz, Gzx) Uncheck : Consider equivalent shear modulus (Geq) Skeleton Curve G o 1, 1 u 1.5E+02 GTS NX Civil m m 1.0E+02 Dyna2E G o k c 5.0E E Hysteresis Curve -5.0E E E+02 [Modified Ramberg-Osgood model] [Load] [System] [Results] [Verification Example] Deform 27 / 31

28 Force GTSNX 2015 Enhancement 2.10 Material : Modified Hardin-Drnevich One of Hysteresis models for inelastic hinge, an extension was made to 2D and 3D solid elements. Can be applied to simulate crack or local (plastic) failure. Applicable in Nonlinear Static and Time History Analysis as follows : Nonlinear, Construction Stage, Consolidation, Fully Coupled, SRM (Slope Stability) Hysteresis curves are formulated on the basis of the Masing s rule. Parameter Description Reference G o r Shear Only Initial Shear Modulus Reference Strain Go 1 Check : Consider shear modulus for each direction separately (Gxy, Gyz, Gzx) Uncheck : Consider equivalent shear modulus (Geq) r Skeleton Curve G o 1, 1 u 1.0E+02 GTS NX G o m m 8.0E E+01 Civil Dyna2E 4.0E+01 k 2.0E+01 c 0.0E E+01 Hysteresis Curve -4.0E E E E+02 Deform [Modified Hardin-Drnevich model] [Load] [System] [Results] [Verification Example] 28 / 31

29 2.11 Analysis Option : Estimate Initial Stress of Activated Elements * Note : Initial Stress for Activated Elements during construction In order to calculate the initial stress of ground, GTSNX perform Linear Analysis even if nonlinear material is assigned to the elements. In this case, it can result in, sometimes, overestimating the soil behavior (large displacement). Initial Stress Options can eliminate this problem especially for newly activated elements which are to simulate a fill-up ground such as backfill and embankment. ` [Without Initial Stress Option : Horizontal Displacement : 84mm] [Engineering Example : Excavation and Backfill] [With Initial Stress Option : Horizontal Displacement : 30mm] 29 / 31

30 2.12 Construction Stage > Stress - Nonlinear Time History Analysis * Note : Perform nonlinear dynamic analysis based on initial stress of ground resulted from construction stage analysis Users can perform nonlinear dynamic analysis considering stress status of ground resulted from not only self weight but also construction stage (the history of stress). Nonlinear time history stage must be set at the final stage. ` [Stage Set : Stress-Nonlinear Time History] [Define construction stage] 30 / 31