Adjustments to Small-Strain Damping and Soil Profile Assumptions to Improve Site Response Predictions James Kaklamanos, Assistant Professor of Civil Engineering, Merrimack College, North Andover, Massachusetts, USA Brendon A. Bradley, Professor in Earthquake Engineering, University of Canterbury, Christchurch, New Zealand Aiswarya N. Moolacattu, M.S. Student, Merrimack College Bradley M. Picard, Undergraduate Student, Merrimack College SSA 2017 Annual Meeting Denver, Colorado 18 April 2017 Abstract No. 17-232

Adjustments to Small-Strain Damping and Soil Profile Assumptions to Improve Site Response Predictions Jim Kaklamanos 1. Background and motivation 2. Physical adjustments to small-strain damping and soil profiles 3. Results 4. Conclusions

Kaklamanos and Bradley (in prep.) •

Study location: Kiban-Kyoshin network (KiK-net) of vertical seismometer arrays in Japan

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Site response studies: Linear (L), equivalent-linear (EQL), and nonlinear (NL) analyses of 5626 ground-motion records at 114 KiK-net stations

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Research goals: Analyze the uncertainty resulting from common site response modeling assumptions using a large dataset of observations, and offer recommendations for site response modeling improvements Kaklamanos, J., and B. A. Bradley (in preparation). Challenges in predicting site response using 1D analyses: Conclusions from 114 KiK-net vertical seismometer arrays.

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

Shear stress = τ Shear strain = γ

Small-strain ground motion

Large-strain ground motion

Stress-strain comparisons: 1. Linear:

𝜏𝜏 𝛾𝛾 = 𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚 𝛾𝛾 , where 𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚 = 𝜌𝜌𝑉𝑉𝑆𝑆2 .

2. Equivalent-Linear:

3. Nonlinear:

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

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

SHAKE; Frequency domain DEEPSOIL; Time domain

Bias and variability: all records Model bias (mean residual)

Total standard deviation

Key conclusion: All models are biased towards underprediction of ground motions at high frequencies (short spectral periods), where nonlinear effects are strongest.

Bias as a function of maximum shear strain Plot: Model bias for Arias Intensity (Ia) plotted against bins of maximum shear strain (γmax) Shear strain bins: Thresholds Bin size γmax < 0.002% 1625 0.002% < γmax < 0.005% 1674 0.005% < γmax < 0.01% 1047 0.01% < γmax < 0.05% 1030 0.05% < γmax < 0.1% 105 γmax > 0.1% 145

Key conclusion: The strongest bias is observed for small-strain records.

Adjustments to Small-Strain Damping and Soil Profile Assumptions to Improve Site Response Predictions Jim Kaklamanos 1. Background and motivation 2. Physical adjustments to small-strain damping and soil profiles 3. Results 4. Conclusions

Physical adjustments to model inputs • Potential explanations for the persistent underprediction of highfrequency ground motions by all site response models: 1. 2.

Poorly characterized soil properties and constitutive model parameters Breakdowns in the one-dimensional (1D) site response assumptions

• To explain this bias, we test four physical hypotheses regarding soil profiles and constitutive model parameters at ten sites that are wellmodeled by 1D site response (classified as LG by Thompson et al., 2012) • Physical adjustments: 1. 2. 3. 4.

Decrease the small-strain damping ratio Apply a depth-dependent VS gradient within layers Randomize the VS profile Increase the small-strain shear modulus

398 ground motions at 10 sites

1. Decrease the small-strain damping ratio Hypothesis: The assumed smallstrain damping in the constitutive models may be too large.

Zhang et al. (2005) damping curve

Action: In all models, the smallstrain damping ratio has been reduced by half. ′ 𝐷𝐷𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚 ∙ 𝐷𝐷𝑚𝑚𝑚𝑚𝑚𝑚

where: ′ = revised small-strain damping ratio 𝐷𝐷𝑚𝑚𝑚𝑚𝑚𝑚 𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚 ∈ [0,1] = damping reduction factor (start with 𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚 = 0.5) 𝐷𝐷𝑚𝑚𝑚𝑚𝑚𝑚 = original small-strain damping ratio

2. Apply a depth-dependent VS gradient Hypothesis: The VS profiles provided on the KiK-net website may be too coarse, and the impedance contrasts may be too sharp. Action: Within each layer, the constant value of VS is replaced with a depthdependent exponential gradient centered on the median VS for the layer.

�𝑠𝑠 𝑉𝑉𝑠𝑠 𝑧𝑧 = 𝑉𝑉

𝜎𝜎𝑣𝑣′ 𝑧𝑧 𝜎𝜎𝑣𝑣′

𝑛𝑛

where: 𝑉𝑉𝑠𝑠 𝑧𝑧 = shear-wave velocity at depth z �𝑠𝑠 = average shear-wave velocity throughout 𝑉𝑉 layer (constant) 𝜎𝜎𝑣𝑣′ 𝑧𝑧 = vertical effective stress at depth z

𝜎𝜎𝑣𝑣′ = vertical effective stress at layer midpoint 𝑛𝑛 = stress exponent (1/4 for clays, silts, and sands; 1/3 for gravels and rocks)

3. Randomize the VS profile Hypothesis: 1D site response models may not accurately represent 3D subsurface heterogeneity, and therefore adding uncertainty to the VS profiles may help better capture variability in soil properties. Action: Five randomized profiles are generated using the Toro (1995) model for VS uncertainty, and the median results of the randomized profiles are analyzed.

𝑉𝑉𝑆𝑆𝑆𝑆 = exp ln 𝑉𝑉�𝑆𝑆𝑗𝑗 + 𝜎𝜎ln 𝑉𝑉𝑆𝑆 ∙ 𝑍𝑍𝑗𝑗

where: 𝑉𝑉𝑆𝑆𝑆𝑆 = shear-wave velocity of layer j 𝑉𝑉�𝑆𝑆𝑗𝑗 = median shear-wave velocity of layer j (from the original profile) 𝜎𝜎ln 𝑉𝑉𝑆𝑆 = assumed standard deviation of VS in natural logarithmic space 𝑍𝑍𝑗𝑗 = standard normal variable of layer j, correlated with layer j-1

4. Increase the small-strain shear modulus Hypothesis: Field measurements may underestimate the small-strain shear modulus (Gmax) because larger strains (~0.001%) may actually be incurred in the soil during testing.

Zhang et al. (2005) modulus reduction curve

Action: Increase Gmax by 10% in all analyses.

𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚 = 𝜌𝜌𝑉𝑉𝑆𝑆2

where 𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚 = small-strain shear modulus, 𝜌𝜌 = soil density, and 𝑉𝑉𝑆𝑆 = shear-wave velocity. This adjustment results in a scale factor of 1.1 to the VS profile, or an increase of approximately 5%.

Adjustments to Small-Strain Damping and Soil Profile Assumptions to Improve Site Response Predictions Jim Kaklamanos 1. Background and motivation 2. Physical adjustments to small-strain damping and soil profiles 3. Results 4. Conclusions

Results for an example ground motion Example site response observations and predictions for a moderate ground motion at IWTH08, the Mw 6.9 earthquake of 23 June 2011

Model bias for each physical hypothesis L, EQL, and NL model bias (mean residual) as a function of spectral period for the alternative physical hypotheses (all sites and ground motions)

Adjustments to Small-Strain Damping and Soil Profile Assumptions to Improve Site Response Predictions Jim Kaklamanos 1. Background and motivation 2. Physical adjustments to small-strain damping and soil profiles 3. Results 4. Conclusions

Conclusions for each physical hypothesis 1. Reduced small-strain damping: Results in significant reductions in model bias at both small and large strains, implying that greater attention should be paid the small-strain damping ratio as a critical parameter for site response prediction. 2. Depth-dependent VS gradient: Resolves the unrealistically large strain localizations that occur when constant VS is assumed over a large thickness. Noticeable reductions in model bias are observed; this adjustment should be considered in all cases where the original VS profile is coarse, and/or where the impedance contrasts may be overstated. 3. Randomized VS profile: Generally leads to more severe underpredictions at high frequencies than the original profile. This approach might work better for sites that are known to be more heterogeneous. 4. Scaled VS profile: The increased small-strain shear modulus leads to small changes in the shear-wave velocity profile, and therefore produces insignificant differences in model bias.

Key findings • Persistent site response model biases at high frequencies suggest that: (1) assumptions regarding the soil profiles and material parameters may need to be readdressed; and/or (2) many of these sites may experience a breakdown in the 1D siteresponse assumptions. • Reducing the small-strain damping ratio and applying a depthdependent VS gradient lead to significant reductions in model bias. • Increasing the small-strain shear modulus (Gmax) leads to insignificant differences in site response predictions, and randomizing the VS profile leads to more severe underpredictions than the original profile. • Rather than solely focusing on the constitutive model type (e.g. EQL vs. NL), this study suggests that greater attention should be paid to small-strain damping and soil profile assumptions, as some of these physical adjustments are more successful at reducing model bias than changing the model type.

References: 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. 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, 1733-1749. Kaklamanos, J., and B. A. Bradley (in preparation). Challenges in predicting site response using 1D analyses: Conclusions from 114 KiK-net vertical seismometer arrays. Kaklamanos, J., B. A. Bradley, A. N. Moolacattu, and B. M. Picard (in preparation). Physical hypotheses for improving 1D site response estimation assessed at 10 KiK-net vertical array sites: soil profiles and constitutive model parameters. 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. Toro, G. R. (1995). Probabilistic models of site velocity profiles for generic and site-specific groundmotion amplification studies, Technical Report No. 779574, Brookhaven National Laboratory, Upton, N.Y. 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.

Acknowledgment: This material is based upon work supported by the U.S. Geological Survey under Grant No. G16AP00002.

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