Modeling Dynamic Site Response Using the Overlay Concept JAMES KAKLAMANOS

Assistant Professor of Civil Engineering Merrimack College North Andover, Massachusetts with:

Luis Dorfmann, Tufts University, Medford, Mass. Laurie G. Baise, Tufts University, Medford, Mass.

3/18/2014

2014 Geo-Congress Atlanta, Georgia 25 February 2014

Modeling Dynamic Site Response Using the Overlay Concept James Kaklamanos 1. Site response background 2. Critical parameters for site response 3. The overlay concept for nonlinear site response 4. Modeling nonlinear site response at six validation sites

Modeling Dynamic Site Response Using the Overlay Concept James Kaklamanos 1. Site response background 2. Critical parameters for site response 3. The overlay concept for nonlinear site response 4. Modeling nonlinear site response at six validation sites

Site response analyses Output: Output ground motion (surface)

Soil Model:

• Linear • Equivalent-linear • Nonlinear

Input: Soil profile • S-wave velocity, VS • Density, ρ • Damping ratio, ξ • Additional parameters Input ground motion (downhole)

Site response methods Stress-strain curves at depth of 2 m for KiK-net site IWTH08

Shear stress = τ Shear strain = γ

Small-strain (linear) ground motion

Large-strain (nonlinear) ground motion

Stress-strain comparisons: 1. Linear:

𝜏𝜏 𝛾𝛾 = 𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚 𝛾𝛾 , where 𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚 = 𝜌𝜌𝑉𝑉𝑆𝑆2.

2. Equivalent-Linear: 3. Nonlinear:

𝜏𝜏 𝛾𝛾 =

𝜏𝜏 𝛾𝛾 = 𝐺𝐺 𝛾𝛾 , where 𝐺𝐺 ≤ 𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚 is determined from an appropriate modulus-reduction relationship.

𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚 𝛾𝛾 the backbone curve of a hyperbolic𝛼𝛼 , 𝛾𝛾 type nonlinear model, where 𝛾𝛾𝑟𝑟 and 𝛼𝛼 1 + 𝛾𝛾 𝑟𝑟 are model parameters.

Modeling Dynamic Site Response Using the Overlay Concept James Kaklamanos 1. Site response background 2. Critical parameters for site response 3. The overlay concept for nonlinear site response 4. Modeling nonlinear site response at six validation sites

Kaklamanos et al. (2013) • Study location: Kiban-Kyoshin network (KiK-net) of vertical seismometer arrays in Japan • Site response studies: Linear and equivalent-linear analyses of 3720 ground-motion records at 100 KiK-net stations • Objectives: o Analyze the accuracy (bias) and variability (precision) resulting from common site response modeling assumptions o Identify critical parameters that most greatly contribute to the uncertainty in site response analyses Kaklamanos, J., Bradley, B.A., Thompson, E.M., and Baise, L.G. (2013). Critical parameters affecting bias and variability in site response analyses using KiK-net downhole array data, Bulletin of the Seismological Society of America 103(3): 1733–1749.

Kaklamanos et al. (2013) Key findings: • Maximum shear strain in soil profile (γmax), observed peak ground acceleration at the surface (PGAobs), and predominant spectral period of the surface motion (Tp) are the most useful critical parameters for site response • Linear analyses fail at strains of 0.01% to 0.1%, and equivalent-linear analyses fail at strains of 0.1% to 0.4% • Nonlinearity begins to manifest itself for PGAobs ≈ 0.1g to 0.3g

Modeling Dynamic Site Response Using the Overlay Concept James Kaklamanos 1. Site response background 2. Critical parameters for site response 3. The overlay concept for nonlinear site response 4. Modeling nonlinear site response at six validation sites

Kaklamanos et al. (2014a) • The overlay concept: Number of overlays of simple models are used to capture nonlinear material behavior • Material behavior: Iwan (1967) and Mroz (1967) concept of parallel plasticity: each mechanical element consists of a linear spring (elastic component) and friction element (plastic component) 𝑛𝑛

𝜏𝜏 𝛾𝛾 = � 𝐺𝐺𝑖𝑖 𝛾𝛾 + 𝑖𝑖=1

𝑁𝑁

� 𝜏𝜏𝑌𝑌𝑖𝑖

𝑖𝑖 = 𝑛𝑛+1

𝐺𝐺𝑖𝑖 = shear modulus of element i 𝜏𝜏𝑌𝑌 𝑖𝑖 = yield stress of element i 𝑁𝑁= total number of overlay elements 𝑛𝑛 = number of elements remaining elastic up to strain level of 𝛾𝛾

Kaklamanos, J., Dorfmann, L., and Baise, L.G. (2014a). Modeling dynamic site response using the overlay concept, American Society of Civil Engineers (ASCE) 2014 Geo-Congress, Atlanta, Georgia, 23–26 February 2014.

Kaklamanos et al. (2014a) • Implementation in finite element analysis: assign each of the finite elements identical node numbers in the finite element mesh (Nelson and Dorfmann, 1995)

Kaklamanos et al. (2014a) Advantages of the model: • Flexibility: can be easily adapted to model more complex behavior (such as cyclic hardening and softening, 2D and 3D site response, and soil-structure interaction) • Ease of implementation: can be implemented in existing finite element codes with little adjustment • Limited number of input parameters: can be applied with basic geotechnical data

Modeling Dynamic Site Response Using the Overlay Concept James Kaklamanos 1. Site response background 2. Critical parameters for site response 3. The overlay concept for nonlinear site response 4. Modeling nonlinear site response at six validation sites

Kaklamanos et al. (2014b) • Study location: Six KiK-net validation sites, found by Thompson et al. (2012) to meet the assumptions of 1D wave propagation, and therefore ideal for validating 1D site response models • Site response studies: Linear, equivalent-linear, and nonlinear analyses of 191 ground-motion records at these six sites

Kaklamanos, J., Baise, L.G., Thompson, E.M., and Dorfmann, L. (2014b). Modeling nonlinear 1D site response at six KiK-net validation sites, Soil Dynamics and Earthquake Engineering, in review.

Kaklamanos et al. (2014b) • Objective: Build upon the results of Kaklamanos et al. (2013) by performing nonlinear site response analyses at a subset of the 100 KiK-net sites, and quantifying the prediction accuracies of the site response models • 1D site response models tested: o Linear: SHAKE, DEEPSOIL, Abaqus o Equivalent-linear: Within SHAKE, the following modulusreduction and damping relationships are tested: – Zhang et al. (2005) – Darendeli (2001) o Nonlinear: – DEEPSOIL (Hashash et al., 2014) – Overlay model in finite element program Abaqus/Explicit, with N = 20 overlays (Kaklamanos et al., 2014a)

Kaklamanos et al. (2014b) Detailed comparison of a strong ground motion:

Kaklamanos et al. (2014b) Correlation coefficients between predicted and observed amplification spectra: NONLINEAR

EQUIVALENTLINEAR

LINEAR

Kaklamanos et al. (2014b) Key findings: •

Differences in accuracy are largest between the linear model and the other models; there are generally small differences between equivalent-linear and nonlinear models.

•

Linear analyses break down at strains of 0.01%–0.1%; equivalent-linear and nonlinear analyses offer significant improvements at strains beyond this level.

•

When observed and predicted amplification spectra are compared over a range of spectral periods, nonlinear models are shown to exhibit a slight improvement over equivalent-linear models for shear strains greater than 0.05%.

•

The remaining scatter in the model residuals illustrate the limitations of 1D total-stress site response models, and that other factors, such as three-dimensional (3D) effects, may need to be incorporated to fully explain the soil behavior at these sites.

References Darendeli, M. B. (2001). Development of a new family of normalized modulus reduction and material damping curves, Ph.D. Thesis, Univ. of Texas at Austin, Austin, Texas, 396 pp. Hashash, Y. M. A., D. R. Groholski, C. A. Phillips, D. Park, and M. Musgrove (2014). DEEPSOIL 5.1, User Manual and Tutorial, Univ. of Illinois at Urbana-Champaign, Champaign, Illinois, 107 pp. Iwan, W. D. (1967). On a class of models for the yielding behavior of continuous and composite systems, J. Appl. Mech. 34, 612–617. Kaklamanos, J., B. A. Bradley, E. M. Thompson, and L. G. Baise (2013). Critical parameters affecting bias and variability in site response analyses using KiK-net downhole array data, Bull. Seism. Soc. Am. 103(3):1733-1749. Kaklamanos, J., Dorfmann, L., and Baise, L.G. (2014a). Modeling dynamic site response using the overlay concept, American Society of Civil Engineers (ASCE) 2014 Geo-Congress, Atlanta, Georgia, 23–26 February 2014. Kaklamanos, J., L. G. Baise, E. M. Thompson, and L. Dorfmann (2014b). Modeling nonlinear 1D site response at six KiK-net validation sites, Soil Dynam. Earthq. Eng., in review. Mroz, Z. (1967). On the description of anisotropic workhardening, J. Mech. Phys. Solid. 15, 163– 175. Nelson, R. B., and A. Dorfmann (1995). Parallel elasto-plastic models of inelastic material behavior, J. Eng. Mech. 121, 1089–1097. Schnabel, P. B., J. Lysmer, and H. B. Seed (1972). SHAKE: A computer program for earthquake response analysis of horizontally layered sites, Report UCB/EERC-72/12, Earthquake Engineering Research Center, Univ. of California, Berkeley, 102 pp. Thompson, E. M., L. G. Baise, Y. Tanaka, and R. E. Kayen (2012). A taxonomy of site response complexity, Soil Dynam. Earthq. Eng. 41, 32-43. Zhang, J., R. D. Andrus, and C. H. Juang (2005). Normalized shear modulus and material damping ratio relationships, J. Geotech. Geoenv. Eng 131, 453–464.