Determination of Seismic Elastic Response Spectrum Based on Imai & Tonouchi Model
1. Input Parameters:
'Imai & Tonouchi Model' requires information of the thickness, SPT-N and soil type, and soil age for soil layers in each Borehole.
I. Location of Site:
II. Importance Class of Structure:
III. PGA on rock (g):
IV. Thickness, SPT-N, and Soil Types of Soil Layers in each Borehole:
(presented in next page)
Note:
Table can be filled manually or by performing copy (CTRL+C) and paste (CTRL+V) of data from Excel spreadsheet.
D1, D2 ..D20 refer to column nos. 1-20 for inputting the thicknesses (m) of the soil layers whereas N1, N2 ..N20 refer to the input of the SPT-N (blows/300 mm) values.
Please enter group symbol of the soil types. Gravel:'GP', 'GW', 'GM', 'GC'; Sand:'SP', 'SW', 'SM', 'SC'; Silt:'ML', 'MH'; and Clay:'CL', 'CI', 'CH', correctly for each layer of soil in the 'Soil Type' column of each borehole.
Please enter the soil ages in the form of initials 'Q' for Quaternary, 'H' for Holocene, and 'P' for Plesitocene for each layer of soil correctly in the 'Soil Age' column of each borehole. If soil age is not known, specify it as 'Q'.
If all entries to a particular “thickness” column have been left blank, the program will automatically fill in a default thickness of 1.5 m.
SPT-N values that have been taken from the testing of very stiff materials have to be corrected to the penetration depth of 300 mm. For example, an SPT-N value of 50 for the penetration depth of 100 mm should be corrected to 150.
Avoid including too many borelogs from too closely spaced boreholes into one analysis as doing this would not necessarily result in obtaining an accurate estimate of the site period.
Must also avoid including borelogs taken from a very large area featuring systematic spatial variation in geology within the area. The maximum number of borelogs to be included into one analysis is capped at 20.
A borelog indicating exceptional conditions compared to other borelogs taken from the same site is a call for undertaking further investigations to determine the spatial extent of the anomalies. More borelogs need to be taken to map out the site geology to determine the subsoil profile. There is an option to employ geophones to take site natural period on a few locations to help understand the subsoil conditions better. Alternatively, take the more onerous site class for design purposes. With the construction of an important structure in onerous soil conditions, it is worth considering the option of undertaking a more detailed investigation to generate a site-specific response spectrum to override the code specified response spectrum model.
SPT-N Values and Soil Description (BG Look, 2014)
Sand
Clay
Description
SPT-N Value (blows/300 mm)
Description
SPT-N Value (blows/300 mm)
Very Loose
0-4
Very Soft
0-2
Loose
4-10
Soft
2-5
Medium
10-30
Firm
5-10
Dense
30-50
Stiff
10-20
Very Dense
>50
Very Stiff
20-40
-
-
Hard
>40
Borehole 1
Borehole 2
Borehole 3
Borehole 4
Borehole 5
Borehole 6
Borehole 7
Borehole 8
Borehole 9
Borehole 10
Borehole 11
Borehole 12
Borehole 13
Borehole 14
Borehole 15
Borehole 16
Borehole 17
Borehole 18
Borehole 19
Borehole 20
D1
N1
Soil Type
Soil Age
D2
N2
Soil Type
Soil Age
D3
N3
Soil Type
Soil Age
D4
N4
Soil Type
Soil Age
D5
N5
Soil Type
Soil Age
D6
N6
Soil Type
Soil Age
D7
N7
Soil Type
Soil Age
D8
N8
Soil Type
Soil Age
D9
N9
Soil Type
Soil Age
D10
N10
Soil Type
Soil Age
D11
N11
Soil Type
Soil Age
D12
N12
Soil Type
Soil Age
D13
N13
Soil Type
Soil Age
D14
N14
Soil Type
Soil Age
D15
N15
Soil Type
Soil Age
D16
N16
Soil Type
Soil Age
D17
N17
Soil Type
Soil Age
D18
N18
Soil Type
Soil Age
D19
N19
Soil Type
Soil Age
D20
N20
Soil Type
Soil Age
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
V. Energy Ratio (N60/Nmeasured):
Note: Energy ratio is the conversion factor for converting the measured N values to corrected N values corresponding to 60% energy efficiency. A value of 1 is suggested for the case of Malaysia (Sabatini et al., 2002).
2. Results: Soil Characteristics and Elastic Response Spectrum
I. Soil Profile with SPT-N Value:
Figure 1: SPT-N Profile
Table 1: Thickness (m) and SPT-N (blows/300mm) Values of Soil Layers of Different Boreholes Note: D1, D2, ..D20 and N1, N2, ..N20 columns in the table are thickness and SPT-N values of soil layers of the respective boreholes.
(This page is left blank because there are no inputs defined for borehole numbers 11-20.)
II. Average Shear Wave Velocity (Vs) and Natural Time Period (Ts) of Soil:
The following equations given by 'Imai & Tonouchi Model' are used to calculate shear wave velocity of each soil layer 'i'.
For gravel (GP, GW, GM, GC)
$$ {Holocene: SWV_i = 72.5 \times N_{60_i}^{0.35}}\tag{1a}$$
$$ {Plesitocene: SWV_i = 132.4 \times N_{60_i}^{0.25}}\tag{1b}$$
For sand (SP, SW, SM, SC)
$$ {Holocene: SWV_i = 85.0 \times N_{60_i}^{0.29}}\tag{1c}$$
$$ {Plesitocene: SWV_i = 106.6 \times N_{60_i}^{0.29}}\tag{1d}$$
For silt and clay (ML, MH, CL, CI, CH)
$$ {Holocene: SWV_i = 103.8 \times N_{60_i}^{0.27}}\tag{1e}$$
$$ {Plesitocene: SWV_i = 124.4 \times N_{60_i}^{0.26}}\tag{1f}$$
$$ {V_s = \frac{H_s}{ \sum^n_{i=1} \dfrac{d_i}{SWV_{i}} }}\tag{2}$$
$$ {T_s = \frac{4 \times H_s}{V_s}}\tag{3}$$
Where:
Hs = total depth of soil,
n = number of soil layers,
di = thickness of soil layer 'i',
N60i = corrected SPT-N value (corresponding to 60% energy efficiency) of soil layer 'i'
Table 2: Average Shear Wave Velocity and Site Period of Soil of each Boreholes
Borehole No.
Average Shear Wave Velocity (m/sec)
Site Period (sec)
Table 3: Site Characteristics and Ground Type
III. Seismic Elastic Response Spectrum:
a. Response Spectral Acceleration (RSA) and Acceleration Displacement Response Spectrum (ADRS) Diagram:
Figure 2: RSA Diagram
Figure 3: ADRS Diagram
RSA is Response Spectral Acceleration.
ADRS diagram is Acceleration-Displacement Response Spectrum diagram.
β is the lower bound factor used in Eurocode 8 to stipulate a minimum level of response spectral accelerations in the long period range. The recommended value is 0.2.
Table 4: Response Spectral Acceleration (RSA) and Response Spectral Displacement (RSD) of soil
T (sec)
RSA-soil_without β (g)
RSD-soil_without β (mm)
RSA-soil_with β (g)
RSD-soil_with β (mm)
3. References:
Department of Standards Malaysia (2017). MS EN 1998-1:2015 Malaysia National Annex to Eurocode 8: Design of structures for earthquake resitance – Part 1: General rules, seismic actions and rules for buildings.
European Commitee for Standardization (2004). EN 1998-1:2004 Eurocode 8: Design of structures for earthquake resistance - Part 1 : General rules, seismic actions and rules for buildings.
Look, B. G. (2014). Handbook of geotechnical investigation and design tables. CRC Press.
Sabatini, P.J., Bachus, R. C., Mayne, P. W., Schneider, James A., Zettler, T. E. (2002). Geotechnical Engineering Circular No. 5: Evaluation of Soil and Rock Properties, Report no: FHWA IF-02-034. Federal Highway Administration, Washington, DC United States.
Wair, B. R., DeJong, J. T., & Shantz, T. (2012). Guidelines for estimation of shear wave velocity profiles. Pacific Earthquake Engineering Research Center.
Disclaimer
The authors assume no responsibility for any injury, damage, liability, negligence and/or otherwise to any individual or property from the use or application of any of the methods, products, instructions, or ideas contained in the material herein.