Compare impact of frequency dependent $D_{min}$



In [1]:

    
import itertools

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

import pysra

%matplotlib inline



In [2]:

    
plt.rcParams['figure.dpi'] = 150

Frequency dependence of $D_{min}$ predicted by Darendeli (2001)

Calculation



In [3]:

    
plast_indices = [0, 20, 50, 100]
stresses_mean = 101.3 * np.array([0.5, 1, 2])
ocrs = [1, 2, 4]
freqs = np.logspace(-1, 2, num=31)

df = pd.DataFrame(
    itertools.product(freqs, stresses_mean, plast_indices, ocrs), 
    columns=['freq', 'stress_mean', 'plast_ind', 'ocr']
)



In [4]:

    
def calc_damp_min(row):
    return pysra.site.DarendeliSoilType(
            plas_index=row.plast_ind,
            stress_mean=row.stress_mean,
            ocr=row.ocr,
            freq=row.freq,
        )._calc_damping_min()

df['damp_min'] = df.apply(calc_damp_min, axis=1)



In [5]:

    
df.head()









    Out[5]:







  
    
      
      freq
      stress_mean
      plast_ind
      ocr
      damp_min
    
  
  
    
      0
      0.1
      50.65
      0
      1
      0.003207
    
    
      1
      0.1
      50.65
      0
      2
      0.003207
    
    
      2
      0.1
      50.65
      0
      4
      0.003207
    
    
      3
      0.1
      50.65
      20
      1
      0.004240
    
    
      4
      0.1
      50.65
      20
      2
      0.004167

Plots



In [6]:

    
centers = {'plast_ind': 20, 'stress_mean': 101.3, 'ocr': 1}



In [7]:

    
for key in centers:
    # Only select the centers
    mask = np.all([df[k].eq(v) for k, v in centers.items() if k != key], axis=0)
    selected = df[mask]
    
    fig, ax = plt.subplots()
    for name, group in selected.groupby(key):
        ax.plot(group['freq'], group['damp_min'], label=name)
    ax.set(
        xlabel='Frequency (Hz)', xscale='log',
        ylabel='Damping Min. (dec)', ylim=(0, 0.05),
    )
    ax.legend(title=key)

Site Response Calculation

Input



In [8]:

    
motion = pysra.motion.SourceTheoryRvtMotion(7.0, 30, 'wna')
motion.calc_fourier_amps()

Two profiles are created. The first is a typical profile with the minimum damping computed at 1 Hz (default value). The second profile has the minimum damping computed at each frequency of the input motion.



In [9]:

    
profiles = [
    # Frequency independent soil properties
    pysra.site.Profile([
        pysra.site.Layer(
            pysra.site.DarendeliSoilType(
                18., plas_index=30, ocr=1, stress_mean=200),
            30, 400
        ),
        pysra.site.Layer(
            pysra.site.SoilType(
                'Rock', 24., None, 0.01
            ),
            0, 1200
        ),
    ]),
    # Frequency dependent minimum damping
    pysra.site.Profile([
        pysra.site.Layer(
            pysra.site.DarendeliSoilType(
                18., plas_index=30, ocr=1, stress_mean=200, freq=motion.freqs),
            30, 400
        ),
        pysra.site.Layer(
            pysra.site.SoilType(
                'Rock', 24., None, 0.01
            ),
            0, 1200
        ),
    ])
]

profiles = [p.auto_discretize() for p in profiles]



In [10]:

    
calc_fdm = pysra.propagation.FrequencyDependentEqlCalculator(use_smooth_spectrum=False)
calc_eql = pysra.propagation.EquivalentLinearCalculator(strain_ratio=0.65)



In [11]:

    
freqs = np.logspace(-1, 2, num=500)

outputs = pysra.output.OutputCollection([
    pysra.output.AccelTransferFunctionOutput(
        # Frequency
        freqs, 
        # Location in (denominator),
        pysra.output.OutputLocation('outcrop', index=-1), 
        # Location out (numerator)
        pysra.output.OutputLocation('outcrop', index=0), 
    ),
    pysra.output.ResponseSpectrumOutput(
        # Frequency
        freqs, 
        # Location of the output
        pysra.output.OutputLocation('outcrop', index=0), 
        # Damping
        0.05
    ),
])

Run the analyses and save the output.



In [12]:

    
for name, profile in zip(['FDM - Constant $D_{min}$', 'FDM - Variable $D_{min}$'], profiles):
    calc_fdm(motion, profile, profile.location('outcrop', index=-1))
    outputs(calc_fdm, name)

calc_eql(motion, profiles[0], profiles[0].location('outcrop', index=-1))
outputs(calc_eql, 'EQL')

Plot the results



In [13]:

    
for o in outputs:
    fig, ax = plt.subplots()
    for name, refs, values in o.iter_results():
        ax.plot(refs, values, label=name)
    ax.set(xlabel=o.xlabel, xscale='log', ylabel=o.ylabel)
    ax.legend()
    fig.tight_layout();



In [ ]:

	freq	stress_mean	plast_ind	ocr	damp_min
0	0.1	50.65	0	1	0.003207
1	0.1	50.65	0	2	0.003207
2	0.1	50.65	0	4	0.003207
3	0.1	50.65	20	1	0.004240
4	0.1	50.65	20	2	0.004167