#### Abstract

Using a shake-table, the effects of several stone pebble layer parameters (the layer thickness, the fraction of pebbles, the pebble compaction, the pebble moisture, the vertical contact stress below the foundation, and the effect of repeated excitations) on layer aseismic efficiency were investigated. For each considered parameter, a model of a rigid building on an aseismic layer was exposed to four different accelerograms, with three levels of peak ground acceleration (PGA), while all other layer parameters were kept constant. For each test, the characteristic displacements and accelerations were measured. Based on the test results, the main conclusions regarding the effect of the considered parameters on the effectiveness of the adopted aseismic layer are given.

#### 1. Introduction

In recent decades, intensive research has been carried out to reduce earthquake forces on buildings, bridges, and other structures to make them safer and more rational in seismically active areas. For this purpose, different approaches and principles of reducing seismic forces have been used, and they have resulted in different solutions in terms of efficiency, rationality, complexity, reliability, durability, and other important characteristics. The basic principle of seismic isolation is to “soften” the structure, i.e., to reduce the structure’s stiffness and increase the free oscillation period to minimize earthquake/inertial forces in the structure during earthquake.

For the purpose of practical application, simplicity of realization, and rationality, the possibility of applying the so-called low-cost and low-tech seismic base isolation for small and medium-sized economically developed countries is investigated. The possibility of using natural materials for seismic base isolation is of great importance. There are indications that ancient builders used natural materials (sand, stone, wood beams, etc.) for the purpose not only of increasing the soil bearing capacity but also for reducing earthquake forces on buildings. In this seismic isolation approach, dissipation of earthquake energy is achieved primarily by reducing friction under the foundation and its horizontal sliding on the substrate. It is expected that this type of seismic isolation can be useful in the case of rigid and medium-rigid low- to mid-rise buildings, where the effect of earthquake vertical component is not significant. Unfortunately, research in seismic base isolation is still at the beginning. Currently, there are very few studies related to this topic. Some are briefly described below.

The origin and early development of seismic isolation were presented by Makris [1]. Patil et al. [2] performed experiments and analytical work on a structural model with isolated footing using river sand and found encouraging results. Radnić et al. [3] and Banović et al. [4] found by shake-table study that a layer of limestone sand of appropriate thickness and compressibility can serve as seismic base isolation material. Experimental studies with dune sand and lightweight expanded clay as sliding layers in adobe buildings in Iran can be found in [5]. Zhao et al. [6] performed numerical simulation of the isolation layer consisting of gravel using a discrete element method. The isolation effect of the cushion is shown to increase with the increase of layer thickness and decrease with the increase of base pressure. Gravel and sand cushions have been used in some bridges such as the Rio–Antirio Bridge [7] in Greece, the Vasco de Gama Bridge [8] in Portugal, and the Izmit Bay Bridge [9] in Turkey. Anastasopoulos et al. [10] studied the seismic performance of a rocking-isolated bridge pier on surface foundations resting on sand. A series of reduced-scale shake-table tests were conducted, comparing the performance of a rocking-isolated system to that of a pier founded on a conventionally designed foundation. Development of seismic isolation technologies applicable to rural buildings under current rural economic conditions of China is presented by Zhang [11]. Doudoumis et al. [12] examined the concept of interposing an artificial soil layer between the superstructure and the foundation soil. Yegian et al. [13, 14] proposed smooth synthetic liners underneath the foundation of structures or between soil layers for dissipating seismic energy through sliding. Many numerical and experimental studies have been performed dealing with rubber-soil mixtures (RSM) for seismic base isolation of structures. Tsang et al. [15] proposed RSM around the foundation of structures for absorbing seismic energy and exerting a function similar to that of a cushion. Further work dealing with RSM can be found in [16–19]. Experimental studies based on shake-table tests by providing geotextiles and a smooth marble frictional base isolation system at the plinth level of a brick masonry building were performed by Nanda et al. [20–23]. Some papers dealing pure-friction base isolation systems can be found in [24–26].

Banović et al. [27] performed an experimental shake-table study to investigate the possibility of using a layer of natural stone pebbles below the foundation for seismic base isolation of buildings. Models of stiff and medium-stiff buildings were tested with the model on different layers of pebbles and on the rigid base with the possibility of foundation uplifting. Four different horizontal accelerograms were applied. To exclude the influence of construction material nonlinearity on conclusions regarding the efficiency of this seismic base isolation concept, the tested model stress remained in the elastic area. The research results are very encouraging. Namely, depending on the type of applied excitation and some other parameters, compared to the rigid base case, a pebble layer reduced the strain/stress in the model up to 53%. For most applied excitations, compared to the rigid base case, the pebble layer reduced the horizontal displacement of the mass centre at the column top. However, firm conclusions require further research.

The base isolation concept in [27] can be categorised as a “Geotechnical Seismic Isolation (GSI) system,” as defined initially by Tsang [28] and also adopted by Brunet et al. [29] and Forcellini [30]. Namely, the dissipation of earthquake energy and the reduction of earthquake forces on the building in this concept are dominated by the sliding mechanism of the foundation on seismic isolation and between pebbles sublayers. Another way to describe mechanism of this isolation concept is the “distributed seismic isolation system,” which has been discussed by Tsang [31] and Mavronicola et al. [32].

This paper presents the results of a further research segment related to the concept of seismic base isolation using a layer of natural stone pebbles below the foundation presented in [27]. Namely, the research results of six different parameters related to the effectiveness of the adopted aseismic layer are presented. For simplicity, a rigid building model was adopted. This should have no impact on the conclusions made for cases of “softer” structure. Namely, as stated above, this concept is primarily intended for stiff and medium-stiff low- to mid-rise buildings, where maximum vertical stress below the foundation is adapted to the bearing capacity of the stone pebble layer. The effect of the following parameters was investigated: the layer thickness, the fraction of pebbles, the pebble compaction, the pebble moisture, the vertical contact stress below the foundation, and the effect of repeated excitations. For each considered parameter, the model of a rigid building on an aseismic layer was exposed to four different accelerograms with three levels of peak ground acceleration: PGA (0.2 g, 0.4 g, and 0.6 g). The effects of all parameters were evaluated based on the analysis of measured horizontal acceleration and displacement in the characteristic model points. For each considered parameter, all other layer parameters were kept constant. Since tests in this paper are conducted on the same small-scale model in order to investigate a relative effect of several parameters (parametric analysis), it is believed that conclusions obtained are representative for a real structure as well. The main conclusions of the research are presented at the end of the paper.

#### 2. Tested Models

The basic data regarding the adopted building model and aseismic layer are shown in Figure 1. As stated above and for simplicity, a rigid building model was adopted. This should not have an impact on the conclusions because this aseismic concept is primarily intended for stiff buildings, and in addition, research has been carried out to investigate the relative effect of several parameters on layer aseismic efficiency. The building is approximated by a rigid concrete block with mass *m* = 2000 kg and dimensions of 1.0 m × 2.0 m × 0.4 m. The concrete block is formed in height by prefabricated elements, rigidly coupled with prestressed bolts. The block has a reduced area in contact with the aseismic layer in order to achieve the desired contact stress under the foundation of the building.

An aseismic pebble layer with height *h*_{p} is formed within a frame with a plan size of 2.5 m × 2.5 m and fixed to the shake-table. The purpose of this study was to determine the effect of several adopted aseismic layer parameters (layer thickness, fraction of pebbles, pebble compaction, pebble moisture, vertical contact stress below the foundation, and the effect of repeated excitation) on the displacement and acceleration of the rigid structure model. The model was exposed to four different accelerograms, with three levels of PGA (0.2 g, 0.4 g, and 0.6 g).

#### 3. Analysed Stone Pebble Layer Parameters

##### 3.1. Aseismic Layer Thickness

In the conducted tests, the following two layer thicknesses were used: *h*_{p} = 0.3 m and *h*_{p} = 0.6 m, along with other constant parameters (Figure 2). Namely, in the event of proven effectiveness of this seismic base isolation concept, the intention was to form a relatively thin layer of stone pebbles below the building foundation in practice. To reduce the possible excavation and the amount of stone pebbles, from the aspect of rationality and speed of construction, it is desirable for the aseismic layer to be as thin as possible. It is assumed that aseismic layer thickness should not have greater impact on layer horizontal shear stiffness. The thicker layer would probably provide lower resistance than the thin layer to horizontal foundation displacement (lower friction) and larger vertical displacement (smaller flexural stiffness) upon rotation of the foundation. The use of a thicker aseismic layer also means raising the centre of the building mass above the top of the indigenous soil. This results in higher inertial force (acceleration) in the structure. The assumption is that a thin layer would be optimal for low buildings (approx. 1–3 floors), and a thicker layer would be optimal for slightly taller buildings (approx. 4–6 floors). An additional advantage of thin stone pebble layers, compared to thicker layers, is that they are easier to make and compact.

##### 3.2. Pebble Fraction

The effect of three fractions of stone pebbles (Figure 3) was investigated: Φ_{b} = 4–8 mm (i.e., small pebbles), Φ_{b} = 8–16 mm (i.e., medium pebbles), and Φ_{b} = 16–32 mm (i.e., large pebbles). In fact, standardly separated pebble fractions in the exploitation of river gravel are used. It is expected that the pebbles of one fraction provide less friction between the foundation and the top of the aseismic layer. Therefore, no fractions with large differences in pebble grain size were used. Additionally, dust-free pebbles were used. The average compressive strength of the pebbles was approximately 80 MPa. The compressive strength of the pebbles did not affect the test results due to the small stresses in the aseismic layer. The larger pebbles are generally slightly cheaper than smaller pebbles.

##### 3.3. Pebble Layer Compaction

The compaction of the formed pebble layer was determined by measuring the compaction modulus (MS) at the top of the layer. The layers were formed in 0.10 m thick sublayers, with dynamic compaction using the shake-table and static compaction to the expected MS. Three MS values were studied (Figure 4): MS = 10 MPa, MS = 30 MPa, and MS = 60 MPa. It should be noted that there were variations of approximately 8% in the previously stated MS values for some base excitations and that the compaction was not completely uniform over the entire surface of the aseismic layer.

##### 3.4. Pebble Moisture

Although it is expected that pebble layers below the buildings are dominantly dry, it is possible that a smaller or larger part of the aseismic layer becomes wet. Assuming that pebble moisture has a certain effect on the friction between them, and thus on friction between the foundation bottom and aseismic layer top, the effects of two pebble moisture contents were analysed (Figure 5): *h* = 10% (i.e., dry pebbles) and *h* = 60% (i.e., wet pebbles). It should be noted that there were variations of approximately 10% within the previously stated *h* in the preparation of the aseismic layer. Additionally, it should be noted that pebble moisture was not completely uniform over the entire surface of the aseismic layer.

##### 3.5. Vertical Contact Stress below the Foundation

Considering the possible application of the proposed concept of seismic base isolation to lower buildings, depending on the foundation ground plan, relatively low vertical contact stress on top of the aseismic layer is expected. As already mentioned, maximum vertical stress below the foundation should be lower than the bearing capacity of the stone pebble layer. Three levels of contact stress due to gravity load were varied: *σ*_{v} = 0.04 MPa, *σ*_{v} = 0.10 MPa, and *σ*_{v} = 0.20 MPa. Equal vertical stress under the foundation can be realized in different ways: for example, with a different building height (weight) or the same building height (weight) and different foundation surface. A model with equal height (weight) and foundation different surface (Figure 6) was adopted, to achieve equal size and position of the tested model inertia force.

##### 3.6. Effect of Repeated Excitation on Aseismic Layer Efficiency

In reality, it is likely that similar earthquakes of moderate or high strength occur several times during the lifetime of a building. To investigate the effect of such a possibility on the behaviour and efficiency of the aseismic layer, as well as on the overall model displacements, tests were performed on the same model with six consecutive equal excitations, without updating the pebble layer. The accelerogram of the Ston earthquake and the artificial accelerogram with PGA = 0.6 g are applied, which generate the highest model accelerations and displacements (Section 4). All parameters of the aseismic layer are kept constant.

#### 4. Applied Base Excitations

Applied dynamic horizontal base excitations and their spectral values are presented in Figure 7. The N-S accelerogram of the B. Luka earthquake (BiH, 1982): ABL [33] and the N-S accelerogram of the Ston earthquake (Croatia, 1996): AS [33] are characterized by short impact action with short predominant period. These excitations have small spectral velocity and displacement, i.e., they do not bring high earthquake input energy into the structure. The N-S accelerogram of the Petrovac earthquake (Montenegro, 1979): AP [33] and the artificial accelerogram: AA [34] characterize long-lasting action with pronounced accelerations (especially AA) and longer predominant periods (especially AP). An artificial accelerogram is created to match the elastic response spectra according to EC8 [34], for type 1 and soil type A. These excitations have higher spectral velocities and displacements, i.e., they bring higher earthquake input energy into the structure. The adopted excitations cover quite a wide spectrum of potential earthquake types. Each tested sample is exposed to sets of three successive base excitations (Figure 7(a)) with PGA = 0.2 g, PGA = 0.4 g, and PGA = 0.6 g, where PGA = *a*_{g,max}. After each set of three successive base excitations, the pebble layer and the model were updated for the next set of excitations. This approach, in which accumulation of displacements from previous excitations and eventual degradation of the pebble layer occurs, is possible in practice and is interesting in terms of monitoring the possible foundation eccentricity in relation to the aseismic layer. According to the seismic situation in Croatia, PGA = 0.2 g represents weak earthquakes, PGA = 0.4 g represents moderately strong earthquakes, and PGA = 0.6 g represents strong earthquakes.

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#### 5. Measured Quantities and Measuring Equipment

The behaviour of the tested rigid model during base excitation is best described by displacements and accelerations. The following values were measured on each tested sample (Figure 8): horizontal displacements *u*_{1} and *u*_{2}, vertical displacements and (rotation of the foundation), and horizontal acceleration of the mass centre *a*.

A uniaxial shake-table at the University of Split, Faculty of Civil Engineering, Architecture and Geodesy (Croatia), was used to test the models. Data acquisition from sensors during the shake-table test was ensured using the Quantum-X MX 840A (HBM) high-speed data acquisition system. The displacements were measured using analogue displacement sensors, type PB-25-S10-N0S-10C (Uni Measure). The accelerations were measured by a piezoelectric low-frequency accelerometer type 4610 (MS). The sampling rate during the shake-table test was 200 Hz. A video camera was used for test monitoring.

#### 6. Experimental Results

Only some obtained results are given hereafter. For each analysed parameter of the pebble layer, the results are shown separately for each applied accelerogram. The results are shown separately for the first lowest acceleration (PGA = 0.2 g) and for the last successive acceleration (PGA = 0.6 g). When evaluating the accuracy of the obtained results, it should be noted that there are possible minor deviations of the measured values of displacements and accelerations. Namely, the accuracy of the measured values affects a large number of parameters. Some parameters will be briefly commented upon below.

The analysed layer is an anisotropic medium, formed in sublayers with static and dynamic compaction, as a classical embankment. It is likely that in many reconstructions, in order to study various parameters, theoretically equal aseismic layers will not always be the same in reality. The behaviour of the adopted layer of unbound material is nonlinear even with low values of acceleration, with the possibility of occurrence and intensity of different nonlinearities in different places in a theoretically equal aseismic layer. When installing the model, it is possible that it was not always perfectly mounted considering the centre of the shake-table, as well as that the aseismic layer was not completely horizontal. The impact on measured results may also have the accuracy of repeated application of the same shake-table excitation, as well as the precision of the measuring equipment and the accuracy of the measurement. With regard to the previous years of experience in experimental testing, it can be assumed that the impact of the abovementioned possibilities was small. It can be comprehensively stated that the difference in declared values of the measured quantities and their real values is within acceptable limits and that the difference does not have any major influence on the conclusions. Hereafter, the results are presented separately for each considered pebble layer parameter, with the effect of the excitation type and PGA.

##### 6.1. Effect of Aseismic Layer Thickness

Some photos of the experimental setup before testing are shown in Figure 9, in accordance with Section 3.1. The effect of aseismic layer thickness on horizontal displacement *u*_{2} is shown in Figure 10, and peak *u*_{2} values are shown in Figure 11. It is noticeable that, independently of the pebble layer thickness, the results significantly depend on the type of applied excitation and PGA.

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The time-history displacement curves for *h*_{p} = 0.3 m and *h*_{p} = 0.6 m are approximately affine, especially for PGA = 0.2 g (where low nonlinearity in the layers is present). After the excitations with PGA = 0.2 g, small permanent *u*_{2} remained. The largest permanent *u*_{2} was produced by ABL and AA. For excitations with PGA = 0.6 g, permanent *u*_{2} was significantly higher (especially for AS, which is the result of the foundation slipping at the pebble layer top).

For PGA = 0.2 g, the largest *u*_{2} was produced by AA (approx. 3.4 mm). For PGA = 0.6 g, the largest *u*_{2} was produced by AS (approx. 15.5 mm), while the same excitation for PGA = 0.2 g produced the lowest *u*_{2}. This is explained by the fact that the AS is characterized by a short impact action, with a more pronounced shear impact compared to bending. For the smallest PGA, there was no block sliding on the aseismic layer, and at the largest PGA, slipping was significantly larger than for other excitations. The effect of the adopted aseismic layer thickness on *u*_{2} is not particularly pronounced, except for excitations AS and AP at PGA = 0.6 g. In this case, *u*_{2} is partly higher for *h*_{p} = 0.3 m and partly for *h*_{p} = 0.6 m. For PGA = 0.6 g and excitations AS and AP, the thick layer had significantly higher maximum and permanent *u*_{2} than the thin layer. The effect of aseismic layer thickness on layer efficiency depends on the type of applied excitation and PGA.

The effect of aseismic layer thicknesses on horizontal acceleration *a* is shown in Figure 12, and peak acceleration values are shown in Figure 13. As with *u*_{2}, acceleration *a* significantly depends on the excitation type and the PGA. The time-history acceleration curves for *h*_{p} = 0.3 m and *h*_{p} = 0.6 m are almost affine. Compared to the excitations with PGA = 0.2 g, excitations with PGA = 0.6 g produced significantly higher *a*, but not proportionally with applied base accelerations. It is obvious that increasing PGA increased the nonlinearity in the aseismic layer. For PGA = 0.2 g, the highest *a* was produced by AP (approx. 10.1 ms^{−2}). For PGA = 0.6 g, the highest *a* was equal for AS, AP, and AA. The effect of adopted aseismic layer thickness on peak acceleration values is relatively small. For some excitations, the highest *a* was for a thin layer, and for others, it was for a thicker layer. The highest *a* is related to foundation slipping at the pebble layer top.

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In conducted tests, the maximum accelerations and displacements were produced by AS with PGA = 0.6 g and for layer thickness 0.6 m. Based on the aforementioned results, it can be stated that the aseismic layer with *h*_{p} = 0.3 m showed slightly better behaviour from the aspect of displacement and acceleration. As a thinner aseismic layer requires less excavation below the foundation, less pebbles, and simpler and faster construction, a layer thickness of 0.3 m is more optimal than 0.6 m.

##### 6.2. Effect of the Pebble Fraction

The effect of pebble fraction on horizontal displacement *u*_{2} is shown in Figure 14, and peak *u*_{2} values are shown in Figure 15. It is noticeable that, independent of pebble layer thickness, the results significantly depend on the type of applied excitation and PGA. The global overview of the effect of excitation type and PGA on *u*_{2} is considered in Section 6.1 and will not be repeated hereafter.

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The time-history displacement curves for all considered fractions are approximately affine, especially for PGA = 0.2 g. The small pebble fraction (Φ_{b} = 4–8 mm) for excitation ABL with PGA = 0.2 g and PGA = 0.6 g produced the smallest *u*_{2}, whereas AS with PGA = 0.6 g and AP with PGA = 0.2 g produced the largest *u*_{2}. The medium pebble fraction (Φ_{b} = 8–16 mm), for AS with PGA = 0.2 g and for AP with PGA = 0.6 g produced the largest *u*_{2}. The large pebble fraction (Φ_{b} = 16–32 mm) had the lowest *u*_{2} for AS with PGA = 0.2 g and PGA = 0.6 g and for AP at PGA = 0.6 g. The maximum *u*_{2} values of the large pebble fraction were for ABL and AA with PGA = 0.2 g and PGA = 0.6 g.

It is noticeable that the pebble fraction has a complex effect on the size of the model displacement, and no unique law exists. Namely, the maximum *u*_{2} values for each adopted pebble fraction depend on the type of applied excitation and PGA. However, all the adopted pebble fractions resulted in similar average model displacements.

The effect of Φ_{b} on horizontal acceleration *a* is shown in Figure 16, and peak acceleration values are shown in Figure 17. Obviously, the discussed Φ_{b} also has an impact on model acceleration, but this impact is significantly lower than that for the previously considered model displacements. Namely, the time-history acceleration curves for some Φ_{b} are even more affine, and the difference in peak accelerations is significantly lower. It can be stated that all considered Φ_{b} generate similar inertial forces in the model for the same excitation and equal PGA. The highest/lowest maximum *a* values for a particular fraction depend on the type of excitation and PGA. Based on the aforementioned results, for *u*_{2} and *a*, it can be stated that all considered pebble fractions result in similar displacement and rigid model acceleration. As larger pebble factions are regularly cheaper than smaller fractions, Φ_{b} = 16–32 mm can be considered more favourable than other pebble factions.

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##### 6.3. Effect of Pebble Layer Compaction

The time-history *u*_{2} curves for adopted test samples are shown in Figure 18, and peak *u*_{2} values are shown in Figure 19. The time-history displacement curves are approximately affine for all considered compaction modules. For different compaction modules (MS), excitations with PGA = 0.6 g resulted in a greater difference in maximum *u*_{2} (Figure 19) than with PGA = 0.2 g. The largest difference is for AS. The largest *u*_{2} values were for the smallest MS (10 MPa), whereas the smallest value was for the highest MS (60 MPa). This was expected because a high MS reduces the aseismic layer bending and shear stiffness.

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Horizontal acceleration *a* is shown in Figure 20, and peak *a* values are shown in Figure 21. The shape of the time-history acceleration curve depends primarily on the type of excitation and is very similar for all adopted MS values. The maximum *a* values generally increase with increasing MS, which is expected because a higher MS results in a stiffer substrate.

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Based on the aforementioned results, it can be concluded that a smaller MS results in a larger displacement and smaller acceleration of the rigid building. Consequently, it can be stated that lower MS is optimal, with limited maximum displacement, as it reduces construction costs for the aseismic layer. However, a certain level of compactness is necessary for the substrate under the foundation to have sufficient bearing capacity for all relevant structural loads and to minimize pebble layer settlement from long-term load.

##### 6.4. Effect of Pebble Moisture

To shorten the paper, only maximum values of displacements *u*_{2} and accelerations *a* are presented. For PGA = 0.2 g, the maximum *u*_{2} (Figure 22) slightly depends on pebble moisture, whereas the *u*_{2} values were mostly higher for *h* = 10% moisture than for *h* = 60% moisture. For PGA = 0.6 g, the aseismic layer showed similar behaviour. For ABL and AA excitations, the dry pebble layer (*h* = 10%) had larger maximum displacement *u*_{2}, whereas for AS and AP excitations, the wet pebble layer (*h* = 60%) had the larger maximum displacement.

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For PGA = 0.2 g, based on the average values of displacement *u*_{2}, it can be stated that the dry pebble layer case resulted in larger average displacement *u*_{2}. At PGA = 0.6 g, both pebble moisture cases resulted in similar maximum displacement *u*_{2}. In general, the pebble moisture has no major influence on the aseismic layer efficiency.

The average maximum *a* (Figure 23) for all excitations is higher for dry pebbles. Thus, compared to the wet pebble layer, higher inertial forces are generated for dry pebbles. Based on the aforementioned results, it can be stated that pebble moisture has no major impact on the rigid building model displacement and acceleration. The average acceleration *a* for all considered excitations was only slightly higher for dry pebbles. Thus, in the case of applying the proposed concept of seismic base isolation, pebble moisture factor would not be relevant to the effectiveness of the considered aseismic concept.

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##### 6.5. Effect of Vertical Contact Stress below the Foundation

The time-history *u*_{2} curves are shown in Figure 24, with peak *u*_{2} values shown in Figure 25. At low PGA (0.2 g), the largest *u*_{2} was produced by ABL and AA for low contact stress (*σ*_{v} = 0.04 MPa), whereas for excitations AS and AP, the largest *u*_{2} was for medium contact stress (*σ*_{v} = 0.10 MPa). At high PGA (0.6 g), the largest *u*_{2} for all excitations was for *σ*_{v} = 0.10 MPa. It is obvious that the level of contact stress from gravitational load has a significant impact on the rigid model displacement size, but the behaviour of that effect is complex. However, it can be stated that for the majority of different excitations, the displacements *u*_{2} will be larger for high gravitational contact stress.

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The effect of vertical contact stress below the foundation on acceleration *a* is shown on Figure 26, and the peak values of *a* are shown in Figure 27. At PGA = 0.2 g, the highest *a* was for *σ*_{v} = 0.04 MPa, followed by *σ*_{v} = 0.10 MPa, and the minimum was for *σ*_{v} = 0.20 MPa. At PGA = 0.6 g, the highest *a* value depends on excitation type. For *σ*_{v} = 0.04 MPa, the highest *a* was produced by ABL and AA, whereas for *σ*_{v} = 0.20 MPa, the highest *a* was produced by AS and AP. Like *u*_{2}, the effect of contact stress level on acceleration *a* is ambiguous. For low PGA, it is expected that the low levels of contact stress will produce higher acceleration (lower aseismic layer efficiency). For high PGA, high levels of contact stress produce higher acceleration.

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##### 6.6. Effect of Repeated Excitation on Aseismic Layer Efficiency

The effect of repeated excitation AS with PGA = 0.6 g on displacement *u*_{2} is shown in Figure 28. The increase in overall *u*_{2} after the action of each excitation is evident, due to the permanent displacement from the previous excitation. However, the relative displacement for each repeated excitation was approximately equal. With respect to the initial state, the maximum *u*_{2} after the first excitation was approximately 14 mm, whereas after the last (sixth) it was approximately 45 mm (i.e., approx. 3.5 times larger). The effect of repeated excitation AA with PGA = 0.6 g on displacement *u*_{2} is shown in Figure 29. Compared to the AS case, the model behaviour is analogous, only overall and relative displacement *u*_{2} is far smaller for AA. The reason is that AS is a short impact excitation with a more pronounced shear-force effect on the model causing large foundation slipping at the pebble layer top. Excitation AA exerts a longer oscillatory effect with greater bending impact.

The effect of repeated excitation AS with PGA = 0.6 g on acceleration *a* is shown in Figure 30. It is noticeable that the time-history acceleration curves are affine, wherein each successive excitation increases the peak acceleration.

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At the first excitation, the maximum *a* was approximately 14.8 ms^{−2}, and at the sixth, it was approximately 18 ms^{−2}, i.e., an increase of approximately 20%.

The effect of repeated excitation AA with PGA = 0.6 g on *a* is shown in Figure 31. Obviously, these diagrams are analogous to those in Figure 30, except that here, the largest *a* increase was only approximately 6%.

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It is notable that a large number of strong earthquake repetitions can result in large permanent horizontal displacement and reduce aseismic layer efficiency (increase acceleration). The influence of six equal consecutive strong earthquakes on aseismic layer efficiency was tested, and this can occur very rarely in reality. For that unlikely event, at the end of the most unfavourable considered excitation, the initial displacement increased by approximately 3.5 times and initial maximum acceleration by approximately 20%.

For eliminating the displacement effect, it is necessary that the aseismic layer is sufficiently wider than the foundation. Regarding the reduction of the initial aseismic layer efficiency, it is within acceptable limits even in the case of a large number of strong earthquake repetitions.

The cause of the aforementioned unfavourable aseismic layer behaviour is successive foundation slipping on the pebble layer top and successive foundation penetration into the aseismic layer.

The effects of repeated excitation AS with PGA = 0.6 g on vertical displacements and are shown in Figure 32. It is notable that the permanent total displacement (settlement) = 9.1 mm and = 13.3 mm remained after the sixth repetition. Different and indicate that a steady angle of rigid model rotation (tilt) has occurred. In the successive repetition of the excitation, substrate compaction and vertical displacement reduction occurred. As the largest vertical displacement is approximately 4.3% of the aseismic layer thickness, this effect can be practically ignored. The effect of repeated excitation AA on vertical displacements and is significantly smaller (Figure 33).

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#### 7. Conclusions

Previous research [27] has suggested that a natural stone pebble layer below the foundation can significantly reduce strain/stresses of stiff and medium-stiff building models under earthquake load. Namely, depending on the type of applied excitation and some other parameters, compared to the rigid base case, a pebble layer reduced the strain/stress in the MSB model from 28% to 53% and in the MSSB model from 8% to 47%.

However, the practical application of this concept requires further research. This paper presents experimental study results regarding the effect of several stone pebble layer parameters on layer aseismic efficiency. The main conclusions are outlined below:(i)Generally, aseismic layer efficiency and the effects of all observed layer parameters are significantly dependent on the type of applied excitation and PGA.(ii)Regarding the effect of aseismic layer thickness (*h*_{p} = 0.3 m and *h*_{p} = 0.6 m), thinner layers had more favourable response for some excitations, whereas for others it was opposite. The aseismic layer is considered more efficient if the generated accelerations (inertial forces) are lower and the displacements have acceptable values. As the aseismic effectiveness of the considered layers was almost equal, for rationality and faster construction, a thinner layer is considered more favourable.(iii)In terms of the effect of the considered pebble fraction (Φ_{b} = 4–8 mm, Φ_{b} = 8–16 mm, and Φ_{b} = 16–32 mm), different pebble fractions result in similar model displacements and accelerations, i.e., have the same efficiency. The fraction Φ_{b} = 16–32 mm is considered optimal because it is cheaper than smaller fractions.(iv)Regarding the effect of the pebble layer compaction modulus (MS = 10 MPa, MS = 30 MPa, and MS = 60 MPa), a lower MS results in smaller model accelerations and larger displacements. The test results show that different MS values do not result in significant differences in model displacements and accelerations. Therefore, a lower compaction modulus can be considered more favourable, if the structure displacements are within acceptable limits. A certain level of compactness is necessary for the substrate under the foundation to have sufficient bearing capacity for all relevant structural loads and limited displacements in the case of earthquake load.(v)In terms of the effect of pebble moisture (*h* = 10% and *h* = 60%), slightly higher inertial forces are generated for dry pebbles, whereas the model displacements are similar. It can be stated that pebble moisture has no major impact on the pebble layer aseismic efficiency but may be relevant to more easily achieving the required layer compaction modulus.(vi)Regarding the effect of gravitational load contact stress level (*σ*_{v} = 0.04 MPa, *σ*_{v} = 0.10 MPa, and *σ*_{v} = 0.20 MPa), it cannot be precisely defined even for the same excitation. The probable reason is the inconsistency of the declared initial compaction modulus on the entire surface of the aseismic layer, as well as the change of compactness during each excitation. For low PGA values, it can be expected that low levels of contact stress produce higher accelerations (lower aseismic layer efficiency). For high PGA, high levels of contact stress produce higher accelerations.(vii)For the effect of successive strong earthquake repetition (six consecutive repeats of two different types of earthquakes with PGA = 0.6 g), the conducted tests have shown that large permanent horizontal building displacement can occur (up to 3.5 times the initial displacement) and increase the initial building horizontal acceleration (up to 20%), i.e., reduction of aseismic layer efficiency. The impact of accumulated horizontal displacements can be annulled by an adequate extension of the aseismic layer in relation to the foundation. Aseismic layer efficiency reduction can be considered acceptable, even in the case of large strong earthquake repetitions. Vertical settlement and building tilt can occur in strong earthquake repetition, but this impact can be practically neglected.

#### Abbreviations

a: | Horizontal acceleration of the mass centre |

a_{g}: | Ground (shake-table) acceleration |

a_{g,max}: | Peak ground (shake-table) acceleration |

b: | Width of the model foundation |

h: | Pebble layer moisture |

h_{p}: | Pebble layer thickness |

MS: | Compaction modulus of the pebble layer |

u: | Displacement |

u_{1}: | Horizontal displacement of the model foundation |

u_{2}: | Horizontal displacement of the mass centre |

: | Velocity |

: | Vertical displacement of the model on left side |

: | Vertical displacement of the model on right side |

σ_{v}: | Vertical contact stress on top of the aseismic layer |

Φ_{b}: | Pebble fraction. |

#### Data Availability

All data underlying the findings of the study are presented in this paper.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

This work was fully supported by the Croatian Science Foundation under the project “Seismic base isolation of a building by using natural materials: shake-table testing and numerical modelling” (IP-06-2016-5325). The work of doctoral student Ivan Banović was fully supported by the “Young researchers' career development project: training of doctoral students” of the Croatian Science Foundation funded by the European Union from the European Social Fund. The authors are grateful for the support.