**4. Site-specific response analysis**

inconsistency can be attributed to different facts such as the available array conditions, especially length and resonance frequency of geophones which limit the

**Lithotype** *V***<sup>S</sup> range (m/s)** UCL 550–1100 BC 350–600 GL 700–1400

observable depth and the soft BC layer acting as a high-pass filter.

*A graph showing the variation of the BC shear-wave velocity with increasing UCL thickness.*

*Comparison of the observed Rayleigh-wave phase velocities (black dots) with the theoretical effective phase*

*velocities and the first three Rayleigh-wave modes for the Bahrija and Mdina sites [11].*

*The VS ranges for each lithotype obtained from all the studied sites.*

*Earthquakes - From Tectonics to Buildings*

**Table 1.**

**Figure 6.**

**Figure 7.**

**148**

Numerical site-specific response analysis was carried out using the equivalent-linear earthquake site response analysis programme SHAKE2000 [26]. The SHAKE2000 software computes the propagation of shear waves incident vertically on a package of horizontal layers, in which the wave-field in each layer is composed of upward and downward moving waves, whose amplitudes are dependent on the reflectivity/ transmission matrices. The programme requires the following three main inputs:


The *V*<sup>S</sup> profiles obtained from the ambient noise measurements (**Figures 4**, 5 and **8**) were used as input for the soil layer properties for each site. The GL layer was chosen as the bedrock reference layer given that its velocity is generally more than 800 m/s. The modulus reduction and damping curves were chosen from the set of available curves within the package itself after consulting with local geotechnical experts. The chosen curves are displayed in **Figure 9**.

As for ground motion time-history, it is recommended that a suite of records is chosen which are compatible with the national seismic hazard parameters. From the probabilistic seismic hazard analysis conducted by [28], a plausible value for the mean peak ground acceleration (PGA) on rock sites corresponding to a 475-year return period is 0.08 *g.* [28] also note that from the study of historical seismicity and seismotectonic background it is indicated that the seismic hazard of the Maltese islands is related to both moderate magnitude events (M = 5.0–6.0) at short distances (d = 10–40 km) as well as high magnitude events (M = 6.5–8.0) at distances larger than 90 km. In this chapter, the far-field scenario of high magnitude events at

utilised for this purpose. The EC8 Type 1 spectrum, anchored at a PGA of 0.08 *g* was used as a reference spectrum and the lower and upper limit were set to 90% and 130% of the reference curve respectively (as recommended in the EC8). The search was conducted for magnitudes between 6.5 and 8.0 and distances between 60 and

*Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer*

Plots of the scaled spectra of the chosen earthquakes together with the EC8 target spectra are presented in **Figure 10**. **Table 2** displays the information about

The 5% damped elastic response spectra were grouped according to the corresponding EC8 site class (based on the *V*S30) and are displayed in **Figure 11**. Considering the class A sites, it can be observed that all spectra demonstrate a higher response than the EC8 curve at periods longer than 0.5 s with Ahrax and

*The response spectra of the compatible combination of acceleration time-histories for the considered scenario.*

**Date MW Epicentral Distance**

200xa Montenegro 15/04/1979 6.9 65 Thrust 0.36 201ya Montenegro 15/04/1979 6.9 105 Thrust 1.07 302ya Campano 23/11/1990 6.9 92 Normal 5.08 1256xa Izmit 17/08/1999 7.6 92 Strike-slip 2.27 5675xa Montenegro 15/04/1979 6.9 180 Thrust 3.67 5820ya Strofades 18/11/1997 6.6 136 Oblique 0.87 5826xa Strofades 18/11/1997 6.6 90 Oblique 1.21

**(km)**

**Fault Mechanism**

**Scale Factor**

All the required parameters were inputted in SHAKE2000 and the simulations were run. The software outputs various parameters however we will be focussing mainly on response spectra, PGA values and the theoretical transfer function.

200 km [28]. Only earthquake records at stations installed on class A sites, according to the EC8, were chosen. The possibility of scaling was allowed with a

mean scaling factor not exceeding 5.

*DOI: http://dx.doi.org/10.5772/intechopen.95277*

the chosen suite of records.

**4.1 The response spectra**

**Figure 10.**

**Table 2.**

**151**

*Event information is given in Table 2 [27].*

*Details of the chosen acceleration-time histories [27].*

**Code Earthquake Name**

#### **Figure 8.**

*The best VS profiles obtained for the 12 sites not shown in Figures 4 and 5. The procedure of obtaining these profiles is the same as described in Section 3. The coloured bar represents a stratigraphical interpretation using the same colours as in Figures 4 and 5.*

**Figure 9.** *The modulus reduction (left) and damping (right) curves used for the different layers in the simulation [27].*

distances larger than 90 km will be presented considering that the worst case scenario earthquake which has hit the island was the 1693 M7.4 Sicily earthquake.

Since no real data of such earthquakes were ever recorded on the Maltese islands, the "spectrum matching" technique was used to find a suite of seven real accelerograms whose average spectra matched closely a chosen target spectrum. The REXEL code [29], which integrates the European Strong Motion Database, was *Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer DOI: http://dx.doi.org/10.5772/intechopen.95277*

utilised for this purpose. The EC8 Type 1 spectrum, anchored at a PGA of 0.08 *g* was used as a reference spectrum and the lower and upper limit were set to 90% and 130% of the reference curve respectively (as recommended in the EC8). The search was conducted for magnitudes between 6.5 and 8.0 and distances between 60 and 200 km [28]. Only earthquake records at stations installed on class A sites, according to the EC8, were chosen. The possibility of scaling was allowed with a mean scaling factor not exceeding 5.

Plots of the scaled spectra of the chosen earthquakes together with the EC8 target spectra are presented in **Figure 10**. **Table 2** displays the information about the chosen suite of records.

All the required parameters were inputted in SHAKE2000 and the simulations were run. The software outputs various parameters however we will be focussing mainly on response spectra, PGA values and the theoretical transfer function.

#### **4.1 The response spectra**

The 5% damped elastic response spectra were grouped according to the corresponding EC8 site class (based on the *V*S30) and are displayed in **Figure 11**. Considering the class A sites, it can be observed that all spectra demonstrate a higher response than the EC8 curve at periods longer than 0.5 s with Ahrax and

#### **Figure 10.**

*The response spectra of the compatible combination of acceleration time-histories for the considered scenario. Event information is given in Table 2 [27].*


#### **Table 2.**

*Details of the chosen acceleration-time histories [27].*

distances larger than 90 km will be presented considering that the worst case scenario earthquake which has hit the island was the 1693 M7.4 Sicily earthquake. Since no real data of such earthquakes were ever recorded on the Maltese islands, the "spectrum matching" technique was used to find a suite of seven real accelerograms whose average spectra matched closely a chosen target spectrum. The REXEL code [29], which integrates the European Strong Motion Database, was

*The modulus reduction (left) and damping (right) curves used for the different layers in the simulation [27].*

*The best VS profiles obtained for the 12 sites not shown in Figures 4 and 5. The procedure of obtaining these profiles is the same as described in Section 3. The coloured bar represents a stratigraphical interpretation using*

**Figure 8.**

**Figure 9.**

**150**

*the same colours as in Figures 4 and 5.*

*Earthquakes - From Tectonics to Buildings*

**Figure 11.**

*The response spectra obtained at each site compared to the EC8 recommended site spectra.*

Siggiewi showing a well-defined peak reaching up to 150% of the EC8 target spectrum for site class A. On the contrary, at shorter periods (less than 0.2 s), the majority of the sites lie below the EC8 target spectrum. The PGA (spectral acceleration at *T* = 0 s) is also lower than the EC8 target spectrum at almost all the sites. This behaviour is also similar for many of the Class B sites. As regards the class C site (Victoria 1, in Gozo), it is clear that the resulting spectrum is above the EC8 spectrum for a wide period range.

The behaviour highlighted here questions the *V*S30 criterion for site classification and its applicability in such geological settings especially in the context of the design of taller buildings that respond to higher periods of ground shaking.

**Figure 12** shows the resulting transfer functions for the eight chosen sites in Section 3. The fundamental frequency obtained from the 1D transfer function (peak) and the H/V peak frequency obtained for all the sites are tabulated in **Table 3**. The predominant period, which is the period at which the response spectra (**Figure 11**) is the highest, is also tabulated. The fundamental frequencies obtained are in the range 1–2 Hz except for Siggiewi, for which a value slightly higher than 2 was obtained. These are in agreement with the values obtained using the H/V method. The resulting predominant periods range between 0.15 s and 0.75 s. Both the fundamental and predominant periods obtained fall in the range of resonance frequencies of typical 2–10 storey buildings [30, 31], which are becoming increasingly common in the northern part of the islands where the clay is present. Consequently, these buildings might suffer significant damage when this scenario is

*The experimental H/V peak frequency, the fundamental frequency and the predominant period obtained for*

In order to obtain a comparative measure of the amplification characteristics of different sites from the response spectra, the amplification factors FPGA, FA and FV were calculated, as suggested by [32]. The amplification factors are defined

considered.

**Table 3.**

*each study site [27].*

as follows:

**153**

**4.2 The amplification factors**

**Site H/V peak Frequency**

*DOI: http://dx.doi.org/10.5772/intechopen.95277*

**(Hz)**

**Fundamental frequency (Hz)**

Ahrax 1.5 1.63 0.58/1.72 Bahrija 1.25 1.75 0.52/1.92 Bingemma 1.47 1.5 0.16/6.25 Comino 0.94 1.25 0.14/7.14 Dingli 1.66 1.5 0.38/2.63 Ghajnsielem 1.34 1.5 0.23/4.35 Majjistral 1.22 1.38 0.68/1.47 Manikata 1.38 1.75 0.52/1.92 Mdina 1.84 1.88 0.41/2.44 Mellieha 1.38 1.25 0.21/4.76 Mgarr 1.75 1.75 0.52/1.92 Mtahleb 1.34 1.75 0.57/1.75 Nadur 1.38 1.13 0.74/1.35 Red Tower 1.41 1.63 0.52/1.92 Selmun 1.47 1.63 0.52/1.92 Siggiewi 1.50 2.13 0.41/2.44 Victoria 1 1.47 1.5 0.57/1.75 Victoria 2 1.41 1.63 0.23/4.35 Xaghra 1.31 1.5 0.31/3.23 Xemxija 1.31 1.5 0.23/4.35

*Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer*

**Predominant period (s)/ Predominant frequency**

**Figure 12.**

*The transfer functions of the eight sites chosen in Section 3.*


*Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer DOI: http://dx.doi.org/10.5772/intechopen.95277*

#### **Table 3.**

Siggiewi showing a well-defined peak reaching up to 150% of the EC8 target spectrum for site class A. On the contrary, at shorter periods (less than 0.2 s), the majority of the sites lie below the EC8 target spectrum. The PGA (spectral acceleration at *T* = 0 s) is also lower than the EC8 target spectrum at almost all the sites. This behaviour is also similar for many of the Class B sites. As regards the class C site (Victoria 1, in Gozo), it is clear that the resulting spectrum is above the EC8

The behaviour highlighted here questions the *V*S30 criterion for site classification and its applicability in such geological settings especially in the context of the design

of taller buildings that respond to higher periods of ground shaking.

*The response spectra obtained at each site compared to the EC8 recommended site spectra.*

spectrum for a wide period range.

*Earthquakes - From Tectonics to Buildings*

*The transfer functions of the eight sites chosen in Section 3.*

**Figure 11.**

**Figure 12.**

**152**

*The experimental H/V peak frequency, the fundamental frequency and the predominant period obtained for each study site [27].*

**Figure 12** shows the resulting transfer functions for the eight chosen sites in Section 3. The fundamental frequency obtained from the 1D transfer function (peak) and the H/V peak frequency obtained for all the sites are tabulated in **Table 3**. The predominant period, which is the period at which the response spectra (**Figure 11**) is the highest, is also tabulated. The fundamental frequencies obtained are in the range 1–2 Hz except for Siggiewi, for which a value slightly higher than 2 was obtained. These are in agreement with the values obtained using the H/V method. The resulting predominant periods range between 0.15 s and 0.75 s. Both the fundamental and predominant periods obtained fall in the range of resonance frequencies of typical 2–10 storey buildings [30, 31], which are becoming increasingly common in the northern part of the islands where the clay is present. Consequently, these buildings might suffer significant damage when this scenario is considered.

### **4.2 The amplification factors**

In order to obtain a comparative measure of the amplification characteristics of different sites from the response spectra, the amplification factors FPGA, FA and FV were calculated, as suggested by [32]. The amplification factors are defined as follows:

*Earthquakes - From Tectonics to Buildings*

$$F\_{PGA} = \frac{PGA\_{output}}{PGA\_{input}};$$

$$FA = \frac{SA\_{output}}{SA\_{input}};$$

$$FV = \frac{SV\_{output}}{SV\_{input}}$$

site classification. It is worth noting however that even though the Bingemma site is characterised by 52 m of UCL, the PGA is still slightly amplified. This could be due to the fact that the UCL is 'layered' into two strata with the upper layer having an average *VS* of 600 m/s. In contrast, the highest FPGA values were obtained for those sites where a thin layer of UCL limestone (less than 10 m) outcrops. This is also

*Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer*

In contrast, the amplification factor FV is greater than 1 at all sites, indicating that amplification is expected at longer periods. This is also in agreement with [33] where high FV amplification values were obtained for sites characterised by a lowvelocity layer. In general, the same relationship was obtained for FA and FV: sites with thicker UCL exhibited lower amplification values. However, other characteristics of the *V*<sup>S</sup> profiles also play an important role. For example, a higher FV value was obtained at the Majjistral site, which is characterised by a UCL thickness of 24 m, compared to sites which have a thinner UCL layer (e.g. Mdina which has a UCL thickness of 7 m). This could be interpreted as being due to the high impedance contrast (around 4) between the BC and GL layer at the Majjistral site.

To investigate possible correlations between the amplification factors and vari-

ous parameters of the *VS* profiles, the three amplification factors were plotted against: the thickness and *VS* of the UCL and BC, the impedance contrast between the BC and underlying GL layer and the *V*S30. The results are shown in **Figure 14**. The BC thickness exhibits no clear trend with any of the amplification factors. On the other hand, the FV values are seen to increase significantly with decreasing UCL thickness as well as with decreasing UCL and BC shear-wave velocities. These trends are also clear for FPGA and FA, particularly with respect to BC shear-wave velocity. A clear trend can also be observed between FV and the impedance contrast, whereby the FV increases with impedance contrast. Lastly, the three amplification factors can be seen to decrease with an increase in *V*S30. These observations highlight the role that the different properties which constitute the *VS* profile play in site amplification and the difficulty in classifying the sites in rigid groups

**4.3 The in/adequacy of** *VS30***,** *VSbedrock* **and site classification of building codes**

Many authors [34, 35] have argued that the *V*S30 is not an adequate proxy to characterize the amplification potential of a site, especially in the type of geological situation being considered here. Since the low-velocity layer is found at a depth which is usually not considered in the *V*S30 calculation, these authors have suggested

To assess the reliability of the *V*S30 and *V*Sbedrock parameters and site classification schemes as proxies for site effects, a number of different shear-wave velocity profiles, all having the same *V*S30 (670 m/s +/� 15 m/s) and *V*Sbedrock (625 m/s +/� 15 m/s) were randomly constructed. According to the *V*S30 values, these profiles classify as EC8 Class B sites. Within the profiles, the shear-wave velocity and thickness of each layer (UCL, BC, UCL) were constrained to be within the ranges of values measured in the study, shown in **Table 1**. The numerical analysis was conducted again for each of these profiles and the resulting spectra for 4 such profiles, together with the Type 1 EC8 spectra for the different site classes, are

Significant differences can be seen between the different response spectra at a

wide period range. In particular, the PGA varies from 0.68 *g* to 0.1 *g* and the maximum spectral acceleration varies from 0.2 *g* to almost 0.35 *g*. As regards the EC8 design spectra, profile 2 is the only profile whose response is comparable with the EC8 site class B design spectrum. The spectrum of profile 4 can be compared

the use of the travel-time average shear-wave velocity down to the bedrock

according to the properties of their upper 30 m of subsoil.

(*V*Sbedrock) as an alternative.

presented in **Figure 15**.

**155**

similar for the amplification factor FA.

*DOI: http://dx.doi.org/10.5772/intechopen.95277*

where the input values are obtained from the mean spectrum in **Figure 10** while the output values are obtained from the mean output spectra shown in **Figure 11**. *SA* and *SV* are obtained as follows:

$$\text{SA} = \frac{\int\_{0.STA}^{1.STA} \mathcal{S}\_a \, dT}{TA}$$

where *TA* is the period at which the spectral acceleration (*Sa*) is maximum (also called the predominant period in Section 4.1 above); and

$$SV = \frac{\int\_{0.8TV}^{1.2TV} \mathbf{S}\_v \, dT}{\mathbf{0}.4TV}$$

with *TV* representing the period at which the velocity response spectrum (*Sv*) is maximum.

It can be noted that TA is generally smaller than TV, and that the integral in SA is generally determined over a range that includes shorter periods. In fact [33] deduce that FA is more relevant at shorter periods (< 0.5 s) while FV may be related to the behaviour at longer periods, and thus more relevant in the case of taller buildings. The values of FPGA, FA and FV are mapped in **Figure 13**.

The FPGA and FA values are in the majority of the cases both larger than 1 which implies that amplification is expected. However in a few cases values less than 1 were obtained, indicating that these sites are capable of deamplifying the input ground motion. FPGA values are less than 1 at sites which are characterised by a UCL thickness greater than 48 m and are thus classified as class A according to the EC8

**Figure 13.** *Maps showing the three amplification factors at the studied sites: (a) FPGA; (b) FA and (c) FV [27].*

### *Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer DOI: http://dx.doi.org/10.5772/intechopen.95277*

site classification. It is worth noting however that even though the Bingemma site is characterised by 52 m of UCL, the PGA is still slightly amplified. This could be due to the fact that the UCL is 'layered' into two strata with the upper layer having an average *VS* of 600 m/s. In contrast, the highest FPGA values were obtained for those sites where a thin layer of UCL limestone (less than 10 m) outcrops. This is also similar for the amplification factor FA.

In contrast, the amplification factor FV is greater than 1 at all sites, indicating that amplification is expected at longer periods. This is also in agreement with [33] where high FV amplification values were obtained for sites characterised by a lowvelocity layer. In general, the same relationship was obtained for FA and FV: sites with thicker UCL exhibited lower amplification values. However, other characteristics of the *V*<sup>S</sup> profiles also play an important role. For example, a higher FV value was obtained at the Majjistral site, which is characterised by a UCL thickness of 24 m, compared to sites which have a thinner UCL layer (e.g. Mdina which has a UCL thickness of 7 m). This could be interpreted as being due to the high impedance contrast (around 4) between the BC and GL layer at the Majjistral site.

To investigate possible correlations between the amplification factors and various parameters of the *VS* profiles, the three amplification factors were plotted against: the thickness and *VS* of the UCL and BC, the impedance contrast between the BC and underlying GL layer and the *V*S30. The results are shown in **Figure 14**. The BC thickness exhibits no clear trend with any of the amplification factors. On the other hand, the FV values are seen to increase significantly with decreasing UCL thickness as well as with decreasing UCL and BC shear-wave velocities. These trends are also clear for FPGA and FA, particularly with respect to BC shear-wave velocity. A clear trend can also be observed between FV and the impedance contrast, whereby the FV increases with impedance contrast. Lastly, the three amplification factors can be seen to decrease with an increase in *V*S30. These observations highlight the role that the different properties which constitute the *VS* profile play in site amplification and the difficulty in classifying the sites in rigid groups according to the properties of their upper 30 m of subsoil.
