Local site effect of soil-rock ground: 1-g shaking table test

Construction sites are not generally flat but heterogeneous. It would be of significance to explore the patterns of ground response where soil and rock strata laterally distribute near the ground surface. Shaking table test of scaled free-field model is conducted to investigate the local site effect caused by the influence of soil-rock strata. In this test, model ground with artificial soil and rock is designed to reproduce the dynamic characteristics of the prototype. Recorded earthquake waves and site-specific artificial waves are selected as the bedrock motions inputted from the shaking table, in both transverse (SH wave) and longitudinal (SV wave) directions. Four sites of the ground are classified according to the combination of the soil deposit and the rock. The standard spectral ratio (SSR) is introduced to identify the fundamental frequency and the amplification amplitude of the four sites. Correspondingly, one-dimension (1D) theoretical analysis is used to clarify the amplification effects affected by the local constitution at each local site of the ground by comparing the response spectral ratios with the 1D analysis results (Aggravation factor). Site-specific parameters, such as the peak ground acceleration, arias intensity, and acceleration response spectra, are documented with discussions. It is found that the amplifications of locations vary with thickness of soil deposit, nonlinearity of soil property under increasing seismic intensity, and scattering of high-frequency components of input motion.


Introduction
It has been long known that local site effect plays an important role in fluctuating the characteristics of the ground motion. The most famous event refers to the 1985 Mexico M w 8⋅0 earthquake (Anderson et al. 1986), which caused great damage to the structures atop the alluvial of the Mexico City sedimentary basin, while moderate damage to the 1 3 buildings located at the base rocks and the outskirts of the basin. The same phenomenon has also been observed in the 1989 Loma Prieta (Seed et al. 1990) earthquake. Apparently, this "anomalous" amplification effect at the thick sediments could not be simply explained by the one-dimensional site effect. There should be complex additional effects, such as the generation of surface waves at the soft-hard strata interface causing the enhancement of sediment amplification (Bard and Bouchon 1980a, b;Garini et al. 2020), which is also known as the "two-dimensional effect" or "basin effect". In fact, construction sites are not generally flat but laterally heterogeneous. It's common to an irregular ground condition, especially near the outcrop of ground surface where soil and rock strata distribute connectively, making a soft-hard interface.
So far, the local site effect of basin on the intensity of ground shaking and earthquake damages has been widely discussed. Early analytical research (Harmsen and Harding 1981;Aki 1993;Fishmen and Ahmad 1995) simplified the valley to idealized geometry under idealized seismic motion. Such analyses clarified the influence of parameters such as characteristics of incident waves, angle of incident, shape and geometry size of valley, and particle motion. Unfortunately, those idealized models could not be used to consider the nonlinearity effect of soil. Gelagoti et al. (2010Gelagoti et al. ( , 2012 built a celebrated numerical model to explore the two-dimensional site effects of valley. The term aggravation (AG) was used to indicate the severity of amplification of the motion contrast to what the one-dimensional theory would predict. Conclusions were derived that the surface waves generated at valley corners were responsible for AG of the seismic motion and affected by frequency content of the base motion and soil nonlinearity. Garini et al. (2020) specified the spatial variation of ground motion of four sites where the overburdened soil has a varying thickness, relying on the acceleration data observed at in-situ stations. The authors also used a two-dimensional numerical model to reveal the generation of Rayleigh waves at the edge between the hilly and lake zones, which contributed to the discrepancies in response spectra ratios between the two horizontal components. All the previous studies, with the idealized models basically developed for seismological characteristics of large-scale sites, emphasized the amplification effect of acceleration at the soft deposit, with plenty of proofs.
In the benefit of the preinstalled downhole arrays or accelerograph stations, there are extensive acceleration data recording the actual earthquake and their aftershock, facilitating the field observations of local site effect. Based on these available data, Borcherdt (1970) proposed the Standard Spectral Ratio (SSR) technique to identify the local site effect. SSR is the spectral ratio of a recording on site of interest to a corresponding one at a nearby rock site. This method has been used previously in many geological environments (Mittal et al. 2013;Milana et al. 2020;Priolo et al. 2020;Sandhu et al. 2022). Normally, it's difficult to obtain a natural reference site without contamination. Thus, another non-reference-site method was introduced by Nakamura (1989), who argued that the H/V spectral ratio allows to evaluate the reaction of local site to S-waves. The H/V method were proved to give a reliable estimate of the fundamental frequency of a site, but sometimes under-estimate the amplification amplitudes (Parolai et al. 2004). In fact, only a few specific sites have been reported the measurements of developed downhole arrays in spite of the complicated site condition rendering difficulty to a thorough study. Moreover, simultaneous strong ground motion recordings at an array of sediment sites and a reference bedrock site for multiple seismic events may be difficult to achieve, especially in regions with moderate to low seismicity (Dravinski et al. 1996). Taking all the deficiencies of research relying on the idealized models or the field observation into account, the shaking table test is an alternative method to investigate the local site effect. This paper presents seismic zonation considering the local effect of soil-rock strata, in the way of shaking table test on a free-field responses of scaled ground. With similitude relations derived considering dynamic equilibrium, the ground is produced with model soil (an artificial mixture from sand and sawdust) rest on slope of model rock (imitated with foam concrete). Uniform excitations including artificial seismic motions and adjusted amplitude real records are input from the shaking table, in both the transverse and longitudinal directions. Array of 4 accelerometers are installed on the surface of four typical locations of the site, distinguished mainly by the combination of the soil deposit and the rock. Spatial variation of the ground motion is analyzed by recorded acceleration data, with respect to recorded acceleration on the table. The amplification effects caused by the local geology are analyzed by the SSR method, considering the influence of the soil nonlinearity. The acceleration aggravation (AG) through comparing the experimental results with the theorical 1D propagation is also identified. Meanwhile, other site-specific parameters describing the ground characteristics, such as the peak ground acceleration, arias intensity, and acceleration response spectra, are discussed to clarify the inherent amplification characteristics of the site condition. This work could be used to verify numerical model, and to study further cases such as declination of the slope and mechanical variation of soil and rock.

Prototype site condition
The present study is based on an actual engineering site in Nanjing, China (Fig. 1). The study region of interest is located at the South Yellow Sea seismic zone. There have been many destructive earthquakes near the site in history. Since the 1970s, there have been three 5.0 < M < 6.0 earthquakes and one earthquake of M > 6.0. The largest earthquake reached a magnitude of 7, recorded as the Yellow Sea earthquake in 1846. Besides the active period of frequent earthquakes, what makes the situation complicated is the complex underlain geological condition. The geometry of the study area and soil profile are shown in Fig. 2a, b. This profile presents apparent lateral heterogeneity of sediment layers caused by the undulation of the underlain bedrock. This particular geological structure includes factors such as the valleylike shape and the shallow overburden condition, which have attracted extensive attention from the seismologists, and then are proven to have a great amplification effect on the ground motion. As summarized in Table 1, the soft sediment layers consist mainly of silt, fine sand, and medium-coarse sand. The shear wave velocities vary from 184 to 1037 m/s from the top layer to bedrock (Fig. 2c), provided by the borehole located on the thickest sediments location. The properties listed in the table are obtained by geotechnical and geological exploration in situ and laboratory tests.

Test facilities and scaling relations
Shaking table test is conducted on the multi-functional shake table system of Tongji University. The size of the shaking table is 10 m long and 6 m wide. Load capacity of the shaking table is 140 ton. Maximum acceleration output is 1.5 g. Operation frequency ranges from 0.1 to 50 Hz. The table has three degrees of freedom in horizontal plane, namely, transverse, longitudinal and rotational. The model system is depicted in Fig. 3. A rigid model container is manufactured and installed on the shaking table by high-strength bolts.  The external dimensions of the container are 10.1 m long, 6.1 m wide and 2 m tall, providing an internal operation space of 9.5 m long, 5.5 m wide and 2 m tall. The main structure of the container is composed of 15 layered frames made of H-steel beam. Steel plates are fixed on the side walls to ensure the lateral stiffness of model container. Inside the container, there are prefabricated model rock (Fig. 3b) and artificial model soil. The model rock is bolted on the table through a rigid concrete slab, and then the model soil is filled into the model container layer by layer. To mitigate boundary effect, energy absorption material is stuck to the inside of lateral wall. It is necessary to ensure that the simulated depth range should include all sedimentary layers above bedrock. Thus, the rigid shaking tables could be considered as the bedrock. Given that the maximum thickness of sediments layers is 50 m and the model container is 2 m high, the geometry similitude ratio can be predetermined as S l = 1/25. The other scaling relations are derived through dimensional analysis (Fuglsang and Ovesen 2020) and dynamic equilibrium (Fung 1977). Firstly, based on the hyperbolic model proposed by Konder (1963), the nonlinear stress-strain response of soil could be expressed by Eq. 1: where 1 and 3 are major and third-principle stress; is strain; and a and b are constants. Hence, the similitude ratio of strain could be derived as 1. Secondly, combine the dynamic equilibrium equation and the stress-strain relationship based on Hooke's law, and it can be written as where and G are the Lame's constants; and , u and t are density, displacement and time, respectively. Equation 2 gives the relationships of similitude ratios of abovementioned physical variables where S G , S l , S and S a are similitude ratios of shear modulus, geometry, density and acceleration, respectively.
(1) In this present study, the similitude ratios of geometry, density and modulus are determined as the fundamental similitude relationship, considering the limitation of test space and selection of experimental materials. They are 1/25, 1/2.3 and 1/58.8, respectively. The similitude ratios of other physical parameters are deduced by dimensional analysis theory (Meymand 1998) and Buckingham π theorem. Table 2 shows the major similitude relations adopted in this test.

Ground model
The prototype ground condition is multi-layered and lateral heterogeneous, causing great difficulties in the simulation of ground model. Simulating the detailed ground condition does not fall within the scope of this present study, and next work concentrates on the rationally simplifying of prototype strata. Regarding the prototype soil deposit as a single model soil layer, the weighted average method is adopted to calculate the average weight and equivalent shear wave velocity of the soil profile. The process of weighted average can be expressed as where i , V i and h i are the density, shear wave velocity and thickness of the particular i layer, respectively; and i corresponds to the soil number listed in Table 1. Finally, an idealized single-layer profile is obtained with an average weight of 2067 kg/m 3 and an equivalent shear wave velocity of 356 m/s. Subsequently, proper model materials are needed to simulate the idealized soil profile. There are two principles that the selected model soil should satisfy: (a) meet the requirements of similitude relations shown in Table 3, and (b) reproduce the dynamic properties of the prototype soil. Synthetic soil has the merits that it could be manipulated to meet the target stiffness and density by adjusting the proportions of constituents, for which it could be used as the soil model material. In this present study, the mixture of sawdust and dry sand with a mass ratio of which is 1:2.5 is selected as the model soil, which has a density of 860 kg/m 3 . Dynamic properties of the model soil are obtained by conducting a series of resonant column tests under different confining pressures (20, 50, 100 and 150 kPa). Test parameters include the small-strain (10 −5 or less) shear modulus G 0 , the relation of normalized shear modulus degradation with shear strain ( G∕G 0 -), and the relation of damping ratio with shear strain ( -). Based on the test results, the relation of the shear modulus G 0 and the confining stress ′ 0 of synthetic model soil can be derived by Eq. 6. The detailed derivation process refers to literature (Wu et al. 2020).
Theoretically, G 0 also can be determined by shear wave velocity V s and density of a given material.
The Eq. 7 can be used to estimate the shear modulus G 0 of prototype soil. Table 3 shows the properties of prototype soil and model soil. Comparation of the measured G∕G 0 -and -curves of the model soil and the prototype soil are depicted in Fig. 4. The model soil shows similar dynamic properties to the prototype one (fine sand, which is the most representative of the prototype conditions and near the interface). The model soil is filled into the model container layer by layer. Density of the model soil is controlled by thickness and weight.
As for the modelling of the surrounding rock, foam concrete could be an optional material due to its reproducibility of the mechanical properties of the rock and low density to meet the requirements of bearing capacity (Chen et al. 2020). The foam concrete is made of cement paste, foam, polypropylene fibre and water. Significant work is performed to test its properties with various densities, and then the specimen with a density of 550 kg/m 3 is selected. Table 4 shows the properties of the foam concrete and the prototype surrounding  Figure 6 shows the test scheme and instrumentation layout. Four accelerograms (A1-A4) are installed to record the seismic ground responses in both the transverse and longitudinal directions. Four sites are clearly distinguished according to their underlying strata. (a) A1 is located on the model rock, regarded as the outcrop rock. (b) A2 rests on a shallow soil deposit, with the underlying stratum mostly rock. (c) A3 is just situated above the soil-rock interface, and the dip angle of the rock edge is 30 degrees. (d) Different from A2, A4 is on a thick soil deposit. Shaking motions input from the shaking tables are recorded by A0, which acts as a "reference station" in the following analysis.  1 3

Input motions
Seismic motions are imposed in both transverse and longitudinal directions. As summarized in Table 5, five kinds of earthquake sequences are employed in this test. Among them, there are two artificially synthetic earthquake waves (representative of the construction site) and three real records from the PEER Strong Motion Database (Ranf et al. 2001).
To simulate the ground response excited by different level earthquakes, considering both weak and strong motions, three level intensities (0.12 g, 0.3 g and 0.5 g) are applied in this study. The seismic durations of all the records are adjusted according to the similitude ratio of time. Spectra of the motions are smoothed by the Hamming window (Blackman and Tukey 1958), with the smoothing parameter n = 5. The seismic excitations and their Fourier spectra are depicted in Fig. 7.

Fundamental frequency
A popular method to identify the site characteristics refers to the standard spectral ratios (SSR), introduced firstly by Borcherdt (1970). The SSR is calculated by taking the ratio of the Fourier spectrum of a single record to that of a reference-site record. Hence, the resulting spectral ratio is expressed as where F( ) i and F( ) R denote the horizontal Fourier spectra of the acceleration recorded from the interest and reference sites, respectively. Finding a proper reference site is crucial but challenging work for geologists to study the local site effect on prototype site, due to the strict selection standards. The reference site should satisfy two demands: (i) The distance between the site of interest and the reference site should be much smaller than their epicentral distance (i.e., the source and path effect in the records are identical). (ii) The reference should not be affected by any kind of site effect. Therefore, stations installed on the bedrock are generally used as the reference site. Otherwise, outcrops of bedrock sites are usually weathered, and that undoubtedly affects the reliability of the reference site, resulting in the inaccurate assessment of amplification effect. In this present study, accelerogram installed on the shaking tables (A0), which performs the same effect as the bedrock in actual project, is the optimal choice as the "reference site". The differences between the records on the ground surface and the shaking tables are solely caused by site effects. In total, five earthquakes with magnitude of 0.12 g are examined here (Table 4). Assumed that the ground accelerograms have recorded all the earthquake events, and each accelerogram has collected five earthquake sequences. The following approach to take the average of site effects at each sensor is adopted to minimize the accidental errors.
where the (SSR) i means the site effects of each accelerogram form a particular earthquake (denoted by i ), and N i represent the number of earthquake sequences recorded at that site.

Assessment of amplification effect compared with 1D analysis
In this section, two problems are explained by introducing one-dimensional (1D) propagating analysis. The first one is to identify the properties of site model materials. The experimental SSR is the ratio of the measured accelerations between the surface and input motion in the frequency domain. It is also theoretically a function of the shear wave velocity V s and damping ratio of ground medium. Thus, properties of ground medium can be roughly identified by adjusting V s and until the theoretical result that best matches the experimental SSR. Another one is to clarify the amplification effect caused by local site conditions, besides the 1D propagation effect, by comparing the response spectral ratios with the 1D analysis results. The analytical method to address the 1D seismic response is introduced by Kramer (1996), who adopted the Transfer Function (TF) to analyze the ground response. Based on the one-layer theory, a theoretical TF of the two-layer system can be derived, considering the strain compatibility and stress equilibrium at the boundary. The formula could be used in this present study (1D profiles are shown in Fig. 9a). The TF of two-layer system is as follows: where (10)  i = √ −1 ; h 1 and h 2 are the thickness of model soil and model rock, respectively; 1 and 2 are the damping ratios of model soil and model rock, respectively; 1 and 2 are the densities of model soil and model rock, respectively; f is the excitation frequency. Given a special case of V s1 = 0 (i.e., a single layer system), Eq. 10 yields the following: which is equivalent to the TF of one-layer homogeneous ground condition (Kramer 1996). The relationship between the fundamental frequency f 0 of the system and the shear wave velocity V s can be expressed as Note that for the rock site A1, the effective thickness h is 1.7 m, while the h for the soil site is 2 m. Given the f 0 of the model soil and model rock are 42 Hz and 7.75 Hz, respectively, the shear wave velocities of model rock V s2 and model soil V s1 are derived as 285 m/s and 62 m/s, respectively. 1 and 2 are adjusted simultaneously to match the magnitude of the first peak of the experimental SSR. The identified 1 and 2 are 8% and 12%, respectively. The results of theoretical TF are added to Fig. 9b represented by dashed red lines. The black and grey lines in Fig. 9b correspond to the mean SSR under transverse and longitudinal excitations, respectively.
The aggravation effect induced by the local site condition is investigated by introducing the aggravation factor approach, which is defined as the ratio between the site-specific SSR and 1D amplification result of the measure point. Since all the scaled input motions have a main-energy frequencyband in 0-30 Hz (Fig. 7), higher frequency parts (30-50 Hz) are not in the study interest. Moreover, the high-frequency part of the recorded acceleration is easily polluted by the ambient noise. According to the analysis results (Fig. 9b, c), the following conclusions are worth listing.
(a) A1 presents a low SSR amplitude in the frequency range of less than 30 Hz, indicating the rock site has a minor amplification effect on the input motion. This evidence generally shows the rationality to pick the outcropping rock as "reference site" in real engineering site. The aggravation effect observed in the longitudinal direction, can also be regarded as a warning that buildings on the margin of rock site, near the soil deposit, are more vulnerable than those in the center of rock site during earthquakes along the given direction. (b) As for the A2 records, pronounced peaks in the spectral amplifications correspond to the fundamental frequency of f≈22 Hz. The SSR results fit well with the 1D theoretical results in transverse and longitudinal excitation directions, indicating a solely 1D seismic response. The high amplification factor means that this site can suffer significant damage when earthquake motions with abundant amplitude at the 15-30 Hz range. The aggravation effect is confined to a limited area with a paltry amplitude. (c) There is an "anomalous" observation for A3. Not only does it have two adjacent peaks in each excitation direction, and the second peak shows a higher amplitude, but the fact that 1D wave propagation analysis fails to explain the amplification effect in this site. In the transverse direction, the first amplified band is located at 5-9 Hz, and the second is at 10-15 Hz, with peak amplitudes of 3.5 and 4.5, respectively. It is distinct in the longitudinal direction, which shows a continuous amplified band at 5-23 Hz, with the two peak amplitudes of 3.5 and 6, respectively. Compared with the 1D analysis, apronounced shadow zone, where aggravation factors are less than 1, is observed in the range of 8-13 Hz, precisely the amplified area of 1D analysis. This phenomenon offers at least a warning that factors other than 1D wave propagation may have played a role. The possibility that these differences could be the product of the 2D/3D response is examined in the sequel. (d) A4 is installed on the soil site, and the observed amplification effect is the most significant. The ground responses at records A4 in two excitation directions are distinct. The amplification peaks in the transverse excitation case occur at a narrow frequency range of 5-10 Hz, similar to the 1D wave propagation results, while it shows a broader amplification range (5-18 Hz) in the longitudinal excitation case. High aggravation factors exist in 8-30 Hz, and the longitudinal aggravation effect is more prominent. It is likely the result of seismic waves, generated at the edge and propagating to the surface (A4), causing the aggravation of ground acceleration response, in terms of amplitude and frequency content.
As mentioned above, there are two "anomalous" phenomena when examining the amplification effect of A3 and A4 records. One is the total inconsistent behavior with 1D analysis in A3, and another is the extra amplification of high-frequency components in A4, especially in the longitudinal direction. It can be attributed to the scattering effect generated at the soft-hard strata boundary. As shown in Fig. 10, when the up-propagated waves reach the boundary, partial waves are reflected from the edge and propagated to the surface. Considering the large ratio between S-wave velocities of the model rock and model soil, almost equal to 5, the reflected angles can be determined as close to 90 degrees, i.e., perpendicular to the edge. Assumed that the rock edge works as the bedrock, the amplification effect caused by the refracted waves could be approximately estimated by Eq. 14. The difference is that the h should be adjusted as the distance that the refracted waves actually travel, represented by the grey arrows.
Since A3 is located in the area where there are no direct-arrival waves, as shown in Fig. 10, the 1D analysis that assumed the vertical propagating condition does not fit this condition, making the difference between the experimental and 1D theoretical results. Given the fact that the arrived waves actually propagated 1.2 m from the edge to A3,

Model soil Model Rock
Reflected wave Fig. 10 Schematic illustration of the mechanism of the wave interference at the soil-rock interface then the recalculated fundamental frequency is 13 Hz, which is identical to the transverse test result (Fig. 9a). For the same reason, it can be expected that the resonant frequencies induced by these refracted waves range from 7.75 to 25 Hz, because the distances from the edge to surface vary from 0.6 to 2 m. These refracted waves with specific amplification frequencies propagate to A4, resulting in the aggravation effect of frequency components in a certain range (7.75-25 Hz, seen in Fig. 9).

Effects of soil nonlinearity
Another advantage of experimental analysis is that both the weak and strong motions can be easily obtained by adjusting the amplitude of input motions. There are so many evidences show that the soil nonlinearity has a significant effect on the ground response (Hartzell 1998;Régnier et al. 2016a, b). Figure 11 shows the spectral ratios of the four sites excited by motions with amplitudes of 0.12 g, 0.3 g, and 0.5 g. Overall, the amplification ratios decrease with the input amplitudes increase, and all the peaks in the SSR drift left, indicating the fundamental frequencies of these sites are reduced. This phenomenon is attributed to the non-linear response of the soft sediments induced by high-level earthquake.
Besides the general observations, there are some unique characteristics among these records. (a) A2 shows a sharper decline of amplitude with the increase of excitation intensity than in other sites. (b) As for A3, the amplitude drop is not significant, while the aforementioned second-peak dominant phenomenon is gone, accompanied by the slightly left-shift first peak. (c) For the case of weak motion, A4 presents a high amplification amplitude in a broad frequency range at 8-30 Hz, especially in the longitudinal direction. This amplification effect is gradually disappeared with the increase in earthquake intensity, denoted by the narrowed peak. There are two main reasons that account for the above phenomena. (1) Due to soil nonlinearity, the shear stiffness of the model soil decreases to a substantially lower secant value, corresponding to a lower effective shear-wave velocity. This decrease produces lower wavelengths and subsequently, amplifies the predominant period of site. As a result, the amplification effects of the high-frequency content are weakened. (2) Based on the previous analysis, the 2D amplification effect observed at the A3 and A4 sites can be attributed to the scattering effect, caused by the reflection/refraction of waves generated at the soil-rock interface. The aggravation results from these reflection/refraction waves, which propagate and reach the ground surface, and then composite with the up-propagating waves (1D response) that arrive surface simultaneously. Therefore, as the shaking intensity increases, reflection/refraction waves generated at the interface are substantially dampened before they reach the ground surface due to soil nonlinearity, mitigating the 2D amplification effect.

Estimation of other parameters describing site-specific ground motion
Other site-specific parameters to describe the ground characteristics, such as the peak ground acceleration, arias intensity, and acceleration response spectra, are discussed in this section. These parameters are not scalable because they are the products of the interaction of ground and input motions. In other words, these parameters calculated from one earthquake would be different from that calculated from another earthquake. Cases of two real records and an artificial wave are analyzed in this section.

Peak ground acceleration
The most commonly used measurement of the amplitude for a particular ground motion is the peak ground acceleration (PGA). The acceleration amplification factor is defined as the ratio of the peak acceleration of the measured point to the input peak ground acceleration. Then the amplification factor in this test is defined as A , which could be calculated as follows where a(t) and a base (t) are the surface and input accelerations (referring to A0), respectively. Figure 12 shows the acceleration amplification of the four observed sites under excitation of earthquake records with different amplitudes. According to Fig. 12, PGA observed in the rock site A1 shows limited amplification with respect to the input motion, and the increased intensity has little influence on the amplification factor, meaning the model rock keeping elastic state during the test. The observation points A2 and A4 show more significant PGA amplification effects than other measured points. This is the result of the inherent site amplification effect discussed preceding. With the shaking intensities increase, the site amplification effects decrease. It's evident that soil nonlinearity plays an important role. Besides the amplification pattern max a base (t) determined by the sites, there are also variations in amplification factor at the same point due to different earthquake events. PGA excited by the W-N wave presents lower amplification ratio with respect to the Taft wave and the Arti-#1 wave, indicating that the seismic wave forms have great influences on the PGA of ground surface.

Arias intensity
Ground motions with high peak accelerations are usually, but not always, more destructive than motions with low peak accelerations. Very high peak accelerations that last for only a very short period of time may cause little damage to many tapes of structures (Kramer 1996). Arias intensity ( I A ) (Arias 1970) is defined as the cumulative energy per unit weight absorbed by an infinite set of undamped single-degree-of-freedom oscillators at the end of an earthquake. I A could be expressed as in which a 2 (t) is the acceleration time history in the interest direction, g is the acceleration of gravity, and T d is the total duration of ground motion. The virtue of I A is that it can simultaneously reflect the effects of ground motion amplitude and duration, making it a more effective indicator of the potential destructiveness of an earthquake event.
Arias intensities of the four observed sites are presented in Fig. 13. For the sake of comparability, all records are prolonged to reach the same end time, and the acceleration in extended time is zero, not influencing the amplitudes of Arias intensity results. Generally, when the earthquake motions input along the transverse direction, A2 shows the largest I A , while it occurs at A4 in the longitudinal excitation direction. Moreover, the I A of A4 (17) in the longitudinal direction shows two times that in the transverse direction, indicating the amplification effect caused by the local site effect of the slope rock edge is more significant in the longitudinal direction. The results excited by different seismic motions differ widely. For example, I A inspired by the Arti-#1 wave have relatively larger values than those inspired by the other two waves, and it act faster to reach the peak values with less than 4 s. With the tremendous energy released in a relatively short time, ground seismic response caused by the Arti-#1 wave can be highly destructive.

Acceleration response spectra
The response spectrum describes the maximum response of a single-degree-of-freedom system (SDOF) to a particular input motion as a function of the natural frequency and damping ratio of the SDOF system (Kramer 1996). It's an important parameter for earthquake-resistant design of aboveground structures. The 5% damped response spectra at the ground surface versus period are plotted in Figs. 14, 15, as well as their spectral ratio to the input motions. As can be seen, in the transverse direction (Fig. 14), the resonant peak of spectral ratio at A2 and A4 are comparable, while the absolute value of spectral acceleration at A2 is much more prevailing. Because different from the A4 site, the period of which the significant amplification occurs is more than 0.1 s, the maximum amplification period of the A2 site is in the range of 0.05-0.1 s, and the input motions are rich in components of such period range. In the longitudinal excitation case, the spectral ratio at A4 shows a larger amplification factor with respect to A2 site, and period components in 0.05-0.1 s are amplified simultaneously, resulting in the largest absolute value of spectral  Fig. 13 Arise intensity at the ground surface of the four observed sites: a transverse excitation and b longitudinal excitation acceleration A4. This is the evidence that the local site effect plays an important role in broadening the risk period range and amplifying the seismic response of surface buildings. Additionally, the amplification functions obtained by the response spectral ratio are comparable to those obtained by the SSR method, since the converted period ranges are identical to the frequency band at the place where the spectral ratios show high amplitude. That is why some researchers use the response spectral ratios to characterize site amplification (Bindi et al. 2017).

Conclusions
In this present work, a shaking table test considering laterally soil-rock strata is conducted to study the local site effect on the ground surface response. Detailed set up of the experiments, design of the similitude relation, and preparation of the ground with model soil and model rock, have been described, providing the references for further investigation.
Balancing between the limitation of play-load of the shaking table and the requirement to satisfy the similitude ratios, artificial model soil and foam concrete are used to simulate the prototype soil and rock, respectively. Laboratory tests are carried out to verify the availability of the model material. Artificial waves and real records are employed to reproduce the bedrock motion and they are input form the table in both transverse and longitudinal directions. Effect of the soil nonlinearity is realized by increasing the intensity of the inputted motion. The ground is classified to four local sites according to the combination of the soil deposit and rock strata. The following main conclusions can be drawn from the recorded acceleration date presented in this paper.
(a) The standard spectral ratio (SSR) is introduced to identify the fundamental frequency and the amplification amplitude of the four sites. The results show significant discrepancies in different sites and the same site excited in different directions. The sites located on the shallow soil deposit (A2) and the thick soil deposit (A4) both present high amplitudes, indicating the high amplification of ground motions. (b) Subsequently, 1D theoretical analysis is developed, based on the analytical solution derived by Kramer. The 1D wave propagation results fit well with the experimental results of A1 and A4 in the transverse direction, while A2 in the two directions. The additional amplification effect is presented by comparing the 1D wave propagation results and the experimental results, defined as the aggregation factor. There are two "anomalous" phenomena, i.e., the total inconsistent behavior with 1D analysis in A3 and the extra amplification of high-frequency components in A4. These phenomena are explained by wave propagation theory and attributed to the scattering effect at the rock edge. (c) Soil nonlinearity has a significant influence on the amplification pattern of ground motion. In general, the fundamental frequencies and amplification amplitudes of all the sites show a decreasing tendency as the nonlinearity increases. Specifically, the soil nonlinearity can diminish the aggravation effect caused by the scatter wave generated at the rock edge, resulting in the vanishing of the second-peak dominant phenomenon in A3 and the elimination of high-frequency amplification in A4. (d) Other site-specific parameters, such as the peak ground acceleration, arias intensity, and acceleration response spectra, are discussed at the end of this work. Results indicate that besides the inherent amplification effect caused by the local site condition, the wave form of the base motions also dramatically influences the ground acceleration response.