2D numerical analysis of the seismic response of a karst rock mass: importance of underground caves and geostructural details

Bruno Giovanni; Carucci Fabrizio

doi:10.2478/sgem-2019-0028

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2D numerical analysis of the seismic response of a karst rock mass: importance of underground caves and geostructural details

Studia Geotechnica et Mechanica

Volume 42 (2020): Issue 1 (April 2020)

By: Bruno Giovanni and Carucci Fabrizio

Open Access

|Mar 2020

Figures & Tables

Amplification factor (a) and spectral ratio (b) values above an underground cave inside a homogeneous and isotropic subsoil crossed by V_s waves, based on the parametric variation of the cave diameter (from [7] modified).

Geological map of the territory in which the study area is located (from [16] modified).

Electric tomography n.1: resistivity values and projection of cores drilling S1 and S2 (from Technical Department of the municipality of Turi (BA) – modified).

Location of geological surveys and section of the geological and geomechanical model.

Stratigraphy obtained from the core destruction borings.

Stratigraphies obtained from rotation drills with continuous coring, RQD trend along verticals and depth of the rock samples for geotechnical laboratory tests.

Geomechanical model section used for the LSR evaluation; the upper karst cave has a height of L= 4.00 m and a width of D= 3.00 m.

Table 1

Geomechanical classification of the altered and the compact calcareous rock mass.

	Parameters	Values	RMR'76		GSI
Rock mass Altered and karstic limestone	R₁ (compressive strength)	7	49	φ_b = 35° c_b = 0.15 MPa	49
	R₂ (RQD)	6
	R₃ (spacing of discontinuities)	15
	R₄ (joint conditions)	11
	R₅ (water conditions)	10
Rock mass Compact and not altered limestone	R₁ (compressive strength)	7	62	φ_b = 40° c_b = 0.20 MPa	62
	R₂ (RQD)	13
	R₃ (spacing of discontinuities)	15
	R₄ (joint conditions)	17
	R₅ (water conditions)	10

Table 2

Mechanical parameters of rocks and discontinuities (based on laboratory tests) of the geomechanical model.

VEGETAL SOIL AND “RED SOILS”
r (Kg/m³)	E (Pa)	v	K (Pa)	G (Pa)	φ (grade)	c (Pa)	σ_t (Pa)
1835	20 · 10⁶	0.25	13 · 10⁶	8 · 10⁶	25	50000	0

ALTERED AND KARSTIC LIMESTONE from laboratory tests							ALTERED ROCK MASS from Hoek-Brown linearized criterion

r (Kg/m³)	σ_ci (Pa)	σ_ti (Pa)	E (Pa)	v	K (Pa)	G (Pa)	φ_b (grade)	c_b (Pa)	σ_tb (Pa)	σ_cb (Pa)
2345	58 · 10⁶	7 · 10⁶	4 · 10¹⁰	0.20	22 · 10⁹	17 · 10⁹	40	0.4 · 10⁶	0.2 · 10⁶	3 · 10⁶

COMPACT AND NOT ALTERED LIMESTONE from laboratory tests							COMPACT ROCK MASS from Hoek-Brown linearized criterion

r (Kg/m³)	σ_ci (Pa)	σ_ti (Pa)	E (Pa)	v	K (Pa)	G (Pa)	φ_b (grade)	c_b (Pa)	σ_tb (Pa)	σ_cb (Pa)
2345	69 · 10⁶	8 · 10⁶	6 · 10¹⁰	0.20	33 · 10⁹	25 · 10⁹	50	1 · 10⁶	0.4 · 10⁶	8 · 10⁶

DISCONTINUITY – ALTERED AND KARSTIC LIMESTONE

jkn (Pa/m)	jks (Pa/m)	φ (grade)	c_j (Pa)	σ_ti (Pa)
1 · 10⁹	1 · 10⁸	30	0.4 · 10⁶	0

DISCONTINUITY – COMPACT AND NOT ALTERED LIMESTONE

jkn (Pa/m)	jks (Pa/m)	φj (grade)	c_j (Pa)	σ_ti (Pa)
1.2 · 10⁹	1 · 10⁸	35	0.4 · 10⁶	0

NORMAL FAULT

jkn (Pa/m)	jks (Pa/m)	φj (grade)	c_j (Pa)	σ_ti (Pa)
1.2 · 10⁹	1 · 10⁸	60	0.4 · 10⁶	0

Table 3

Relevant input data for the accelerograms search with the REXEL 3.5 software.

Target Spectrum	a_g (g)	Geographic Coordinates ED50		Site class	Topographic category	Nominal Life	Functional Type	Limit State	M	R (km)

		Lat. N	Long. E
Italian Building Code 2008	0.074	17.0222	40.9185	A	T1	50 years	III	SLV	6–7	0–100

Table 4

Main data of the seismic events extracted from the database for the X-acceleration (above) and the Z-acceleration (below).

Waveform ID	Earthquake ID	Station ID	Earthquake Name	Date	Mw	Fault Mechanism	Epicentral Distance (km)	EC8 Site class
286	146	ST92	Campano Lucano	11/23/1980	6.9	normal	78	A

Waveform ID	Earthquake ID	Station ID	Earthquake Name	Date	Mw	Fault Mechanism	Epicentral Distance (km)	EC8 Site class
172	81	ST48	Basso Tirreno	04/15/1978	6	oblique	58	A

Acceleration–period spectrums of the combinations no 8 and accelerogram/velocity time–history of the two earthquakes chosen (red circled) for the LSR analysis: X-component (a) and Z-component (b).

Trend of displacements in the Y-direction (left) and plastic zones (right) in the geomechanical model with two overlapping underground caves: in static (above) and dynamic (below) conditions.

LSR amplification/deamplification, as X-accelerations FA, in each of the control points at the ground level of case study model.

Table 5

FA, calculated in the absence and presence of karst caves, as ratio of the maximum X-acceleration and ratio of the Fourier’s amplitudes spectrum in three ranges of frequency.

Output Point ID	$\frac{A_{Xmax . Top}}{A_{Xmax . Bottom}}$		$\frac{\int_{0.2 Hz}^{2.0 Hz} Fourier Ampl . Top (f)}{\int_{0.2 Hz}^{2.0 Hz} Fourier Ampl . Bottom (f)}$		$\frac{\int_{2.0 Hz}^{3.8 Hz} Fourier Ampl . Top (f)}{\int_{2.0 Hz}^{3.8 Hz} Fourier Ampl . Bottom (f)}$		$\frac{\int_{3.8 Hz}^{5.6 Hz} Fourier Ampl . Top (f)}{\int_{3.8 Hz}^{5.6 Hz} Fourier Ampl . Bottom (f)}$

	Without caves	With caves	Without caves	With caves	Without caves	With caves	Without caves	With caves
1	0.060	0.033	0.067	0.039	0.072	0.033	0.065	0.032
2	0.084	0.221	0.120	0.043	0.122	0.097	0.118	0.070
3	0.012	0.129	0.161	0.090	0.176	0.048	0.171	0.040
4	0.730	0.036	0.161	0.090	0.176	0.048	0.171	0.040
5	0.048	0.009	0.098	0.071	0.123	0.040	0.119	0.053
6	0.169	0.057	0.079	0.035	0.113	0.021	0.142	0.024
7	0.093	0.024	0.079	0.035	0.113	0.021	0.142	0.024
8	1.672	0.899	0.259	0.272	0.274	0.172	0.236	0.342
9	0.120	0.019	0.093	0.058	0.143	0.052	0.084	0.113

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DOI: https://doi.org/10.2478/sgem-2019-0028 | Journal eISSN: 2083-831X (formerly 0137-124X) | Journal ISSN: 0137-6365

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Language: English

Page range: 61 - 73

Submitted on: Apr 12, 2019

Accepted on: Aug 21, 2019

Published on: Mar 19, 2020

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Keywords:

2D local seismic response analysis,

rock mass,

karstic underground caves

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2020 Bruno Giovanni, Carucci Fabrizio, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 42 (2020): Issue 1 (April 2020)

2D numerical analysis of the seismic response of a karst rock mass: importance of underground caves and geostructural details

Figures & Tables

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Table 1

Table 2

Table 3

Table 4

Figure 8

Figure 9

Figure 10

Table 5

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