Intensity Measures

SeismoGM 🔥

Solving intensity measures (IMs), response spectra, etc.

See the following two references for details on intensity measures of ground motion:

• [1] Hariri-Ardebili M A, Saouma V E. Probabilistic seismic demand model and optimal intensity measure for concrete dams[J]. Structural Safety, 2016, 59: 67-85. DOI: https://doi.org/10.1016/j.strusafe.2015.12.001
• [2] Yan Y, Xia Y, Yang J, et al. Optimal selection of scalar and vector-valued seismic intensity measures based on Gaussian Process Regression[J]. Soil Dynamics and Earthquake Engineering, 2022, 152: 106961. DOI: https://doi.org/10.1016/j.soildyn.2021.106961

In [1]:

import gmspy as gm
import matplotlib.pyplot as plt
import numpy as np

import gmspy as gm import matplotlib.pyplot as plt import numpy as np

Below is the ground motion data built into gmspy, you can also document the PEER database through loadPEER, or you can read the data from text using numpy.loadtxt.

In [2]:

ts, acc = gm.load_gm_examples("Kobe")
dt = ts[1] - ts[0]
# You can also use other acc data

ts, acc = gm.load_gm_examples("Kobe") dt = ts[1] - ts[0] # You can also use other acc data

Instantiate the class where the arg unit is used to tell the program which unit your acceleration record is in.

Default: acc:g, vel=cm, disp=cm.

In [3]:

GM = gm.SeismoGM(dt=dt, acc=acc, unit="g")
GM.plot_hist()
plt.show()

GM = gm.SeismoGM(dt=dt, acc=acc, unit="g") GM.plot_hist() plt.show()

You can also reset the units

Note

This will change the units of all time-histories, including acceleration. Subsequent IMs are computed in the latest units.

In [4]:

GM.set_units(acc="m", vel="m", disp="m")
GM.plot_hist()
plt.show()

GM.set_units(acc="m", vel="m", disp="m") GM.plot_hist() plt.show()

acc-unit: m/s2;
vel-unit；m/s;
disp-unit: m

Get IMs independent of response spectra 💫¶

In [5]:

ims = GM.get_ims(display_results=True)

ims = GM.get_ims(display_results=True)

┏━━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ IM        ┃  Value  ┃         Unit         ┃                                           Name ┃
┡━━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┩
│ PGA       │  3.382  │         m/s2         │                       Peak ground acceleration │
│ PGV       │  0.277  │         m/s          │                           Peak ground velocity │
│ PGD       │  0.097  │          m           │                       Peak ground displacement │
│ V_A       │  0.082  │          s           │                                        PGV/PGA │
│ D_V       │  0.350  │          s           │                                        PGD/PGV │
│ EDA       │  3.215  │         m/s2         │                  Effective Design Acceleration │
│ Ia        │  1.687  │         m/s          │                                Arias Intensity │
│ Ima       │  0.028  │         m/s          │                       Modified Arias Intensity │
│ MIV       │  0.433  │         m/s          │                   Maximum Incremental Velocity │
│ Arms      │  0.508  │         m/s2         │               Root-mean-square of acceleration │
│ Vrms      │  0.063  │         m/s          │                   Root-mean-square of velocity │
│ Drms      │  0.023  │          m           │               Root-mean-square of displacement │
│ Pa        │  0.737  │       (m/s2)^2       │ Housner earthquake power index of acceleration │
│ Pv        │  0.011  │       (m/s)^2        │     Housner earthquake power index of velocity │
│ Pd        │  0.001  │        (m)^2         │ Housner earthquake power index of displacement │
│ Ra        │  7.922  │     m/s2*s^(1/3)     │                  Riddell index of acceleration │
│ Rv        │  0.995  │ (m/s)^(2/3)*s^(1/3)  │                      Riddell index of velocity │
│ Rd        │  0.227  │      m*s^(1/3)       │                  Riddell index of displacement │
│ SED       │  0.163  │         m2/s         │                        Specific Energy Density │
│ If        │  0.524  │    (m/s)*s^(1/4)     │                                   Fajfar index │
│ Ic        │  2.313  │ (m/s2)^(2/3)*s^(1/2) │                       Characteristic Intensity │
│ Icm       │ 11.260  │          --          │                     Cosenza–Manfredi Intensity │
│ CAV       │ 11.614  │         m/s          │                   Cumulative Absolute Velocity │
│ CAD       │  1.622  │          m           │               Cumulative Absolute Displacement │
│ CAI       │  0.597  │         m*s          │                    Cumulative Absolute Impetus │
│ CAVstd    │  1.105  │         g*s          │       tandardized Cumulative Absolute Velocity │
│ Ip        │ 161.544 │          --          │                              Impulsivity Index │
│ Tsig_5_95 │ 12.860  │          s           │                5%-95% Arias intensity duration │
│ Tsig_5_75 │  6.510  │          s           │                5%-75% Arias intensity duration │
│ Tbd       │ 34.410  │          s           │                             Bracketed duration │
│ Tud       │ 16.435  │          s           │                               Uniform duration │
└───────────┴─────────┴──────────────────────┴────────────────────────────────────────────────┘

In [6]:

for item in ims.items():
    print(item[0], ":", float(item[1]))

for item in ims.items(): print(item[0], ":", float(item[1]))

PGA : 3.381507
PGV : 0.27677933999999954
PGD : 0.09693236474998851
V_A : 0.08185088482738599
D_V : 0.3502153186360972
EDA : 3.21549666180272
Ia : 1.6874397912773698
Ima : 0.0279068117705535
MIV : 0.43312048806766457
Arms : 0.5076063591023476
Vrms : 0.06305087790947873
Drms : 0.02294746598091172
Pa : 0.7366588880733256
Pv : 0.011174889730021969
Pd : 0.0014749912617643029
Ra : 7.922409381417102
Rv : 0.9950298341209709
Rd : 0.22709930095021344
SED : 0.16259440009088008
If : 0.5241359052893505
Ic : 2.3128753907548854
Icm : 11.259872065686206
CAV : 11.613676410000007
CAD : 1.6223236487999961
CAI : 0.5973670751104103
CAVstd : 1.1048120000000008
Ip : 161.54431975452306
Tsig_5_95 : 12.860000000000001
Tsig_5_75 : 6.510000000000001
Tbd : 34.410000000000004
Tud : 16.434799105297873

Elastic response spectra, PSa, PSv, Sa, Sv, Sd 💫¶

In [7]:

Ts = np.arange(0.05, 4.05, 0.05)
spectra = GM.get_elas_spec(Ts=Ts, damp_ratio=0.05, plot=True)
# PSa, PSv, Sa, Sv, Sd for each column

Ts = np.arange(0.05, 4.05, 0.05) spectra = GM.get_elas_spec(Ts=Ts, damp_ratio=0.05, plot=True) # PSa, PSv, Sa, Sv, Sd for each column

In [8]:

# PSa, PSv, Sa, Sv, Sd for each column
PSa = spectra[:, 0]

# PSa, PSv, Sa, Sv, Sd for each column PSa = spectra[:, 0]

Fourier magnitude and power spectra¶

In [9]:

output = GM.get_fou_pow_spec(plot=True)

output = GM.get_fou_pow_spec(plot=True)

Constant ductility response spectra 💫¶

In [10]:

output = GM.get_const_duct_spec(
    Ts=Ts, harden_ratio=0.02, damp_ratio=0.05, mu=5, plot=True
)

output = GM.get_const_duct_spec( Ts=Ts, harden_ratio=0.02, damp_ratio=0.05, mu=5, plot=True )

Other Response Spectra Related IMs 💫¶

Spectral values at the first period of the structure¶

In [11]:

T1 = [0.5, 1.0, 1.5]
# T1 = 1.0
GM.get_elas_spec(Ts=T1)
# PSa, PSv, Sa, Sv, Sd for each column

T1 = [0.5, 1.0, 1.5] # T1 = 1.0 GM.get_elas_spec(Ts=T1) # PSa, PSv, Sa, Sv, Sd for each column

Out[11]:

array([[6.2446254 , 0.4969315 , 6.26848805, 0.45315137, 0.03954455],
       [3.44636745, 0.54850641, 3.45859766, 0.59502918, 0.08729751],
       [3.02081908, 0.72116743, 3.03136244, 0.80644359, 0.17216604]])

Cordova Intensity¶

In [12]:

GM.get_sac(T1=1.0)

GM.get_sac(T1=1.0)

Out[12]:

3.035029886358563

Vamvatsikos Intensity¶

In [13]:

GM.get_savam(T1=1, T2=0.75, T3=2)

GM.get_savam(T1=1, T2=0.75, T3=2)

Out[13]:

3.105224869186609

Multiple-Period Intensity¶

In [14]:

GM.get_samp(T1=1, T2=0.75, m1=0.2, m2=0.1)

GM.get_samp(T1=1, T2=0.75, m1=0.2, m2=0.1)

Out[14]:

3.3878000513594224

Average Spectral Acceleration, Velocity and Displacement¶

In [15]:

Tavg = np.arange(0.05, 4.05, 0.05)
GM.get_avgsavd(Tavg=Tavg)
# acceleration, velocity and displacement

Tavg = np.arange(0.05, 4.05, 0.05) GM.get_avgsavd(Tavg=Tavg) # acceleration, velocity and displacement

Out[15]:

array([1.52834295, 0.48102258, 0.0898247 ])

The peak of the response spectra¶

In [16]:

GM.get_savdp()
# acceleration, velocity and displacement

GM.get_savdp() # acceleration, velocity and displacement

Out[16]:

array([11.35077016,  1.15404101,  0.3043977 ])

Acceleration (ASI)，Velocity (VSI) and Displacement(DSI) Spectrum Intensity¶

In [17]:

GM.get_avdsi()
# acceleration, velocity and displacement

GM.get_avdsi() # acceleration, velocity and displacement

Out[17]:

array([3.09737311, 1.52456845, 0.17287519])

Housner Spectra Intensity (HSI)¶

In [18]:

GM.get_hsi()

GM.get_hsi()

Out[18]:

0.5869311558537018

Effective peak acceleration (EPA), velocity (EPV) and displacement (EPD)¶

In [19]:

GM.get_epavd()

GM.get_epavd()

Out[19]:

array([3.05773882, 0.29902056, 0.04619255])