The low-cost rolling base isolation system (RBIS) installed in the rubble stone masonry school buildings in rural areas in the Himalayan mountain range is shown in Figure 1. Except for the RBIS introduced at the bottom of the walls, the building composition and configuration are identical to real elementary schools (Figure 2) constructed in the mountainous regions by (Schildkamp and Araki, 2019b). The roads to access these schools are unpaved and rough as shown in Figure 3. Therefore, extra construction materials used for introducing the RBIS are restricted to being lightweight with small volume. The compositions of the proposed RBIS are developed considering such restriction in the materials used. The details of the superstructures of the constructed elementary schools by Schildkamp et al. are shown in the literature (Schildkamp and Araki, 2019a; Schildkamp and Araki, 2019b). We investigated the damages to these school buildings after the Gorkha earthquakes, and found that these buildings were almost intact although significant damages such as failure of the walls in out-of-plane direction were observed in the rubble stone masonry buildings nearby. Through this investigation, it was found that properly constructed masonry buildings by educated construction workers under good supervision can assure a certain level of seismic performance. The PGA at these buildings under the Gorkha earthquake is unknown due to the lack of records. The PGA recorded relatively close to the buildings was approximately 0.15g (Goda et al., 2015). Using this limited information, the proposed base isolation system is evaluated assuming that the superstructure can resist earthquakes with a PGA of 0.15g.

The section details of the wall bottom of the rubble stone masonry school building in Figure 1 are shown in Figure 4. The section details of the constructed buildings by Schildkamp et al. are shown on the left-hand side in Figure 4, and those with the proposed low-cost RBIS are shown on the right-hand side. The wall thickness is 350 mm. The wall is composed of natural mountain stones in the regions filled with mortar. There are three reinforced concrete (RC) beams between the RC grade beams and lintel beams as shown in Figure 1. There is no RC column. In the section details on the right-hand side in Figure 4, the tie beam is placed at the bottom of the wall. There is a styrofoam board and cast-iron balls under this tie beam. The thickness of the styrofoam board is 20 mm and the diameter of the cast-iron balls (Figure 5) is 30 mm. The styrofoam boards on the cast-iron balls are used for the ball embedment as well as the bottom part of the form panels for casting concrete of the tie beams. The cast-iron balls are an inexpensive product primarily used in ball mills to pulverize or mix materials into powder. The balls lie on the RC slab on the foundation, named the foundation slab. Two balls are placed under the tie beams at every 200 mm in the longitudinal direction of the beams. The styrofoam and cast-iron balls are placed continuously under the tie beams. Therefore, it is different from the standard base-isolation structure, where the weight between the bearings is transferred by the above beams. The details of this behavior are later discussed in Section 3.2.

In standard base isolation buildings in developed countries, relatively large beams are needed under and above the bearing devices which carry the weight of the superstructures to the foundations. The extra space for these large beams can disturb architectural planning, and the construction process can be more complex with extra cost. These additional requirements are barely acceptable for the small buildings in the Himalayan mountain range, and an alternative seismically isolated system is required.

Large beams under and above the isolation layer are not required in the RBIS, because the bearings are continuously placed under the walls. Consequently, changes in the construction procedures from the traditional rubble stone masonry buildings to introduce RBIS are limited. Figure 6 shows the possible sequence of the construction procedure of RBIS.

(1) The cast-iron balls are placed on the foundation slab at the specified locations and pinched with wooden bars so that the balls do not roll.

Under large earthquakes, the superstructure horizontally moves, while the cast-iron balls roll and horizontally squeeze into the styrofoam boards. Consequently, the induced inertial force on the superstructure during large earthquakes is reduced.

There are multiple reasons why RBIS is suitable for rubble stone masonry buildings in rural areas. Firstly, the residual displacement after large earthquakes is not a primary concern in these buildings because there is no water supply nor any other equipment vertically continuing from the foundation to the superstructure. The masonry buildings with RBIS should be designed such that the maximum displacement during large earthquakes would be small enough for the superstructures to stay on the foundation slabs. However, there is no other building nor obstacle close to the building as shown in Figure 2 so that there is no risk that the superstructures could collide during their horizontal movements under large earthquakes. The limitation of the maximum displacement is not specified; however, 150–200 mm is acceptable with the sufficient width of the lower slab as seen in Figure 2 without the superstructure falling off from the lower slabs. (Relative displacement of 150–200 mm was observed in the shaking table experiment later described in Section 4.4.) Secondly, the system is low-cost with limited additional procedures from the traditional construction of rubble stone masonry buildings. The cast-iron balls are continuously placed under the walls, and the materials needed for RBIS are inexpensive and available in cities nearby. The total volume of these material is relatively small and it is possible to transport them to the building locations in mountainous regions.

The cost increase of introducing RBIS to the school buildings is estimated as being less than approximately 15% of the overall building cost. This number is based on the cost study of the building construction by Schildkamp (Schildkamp and Araki, 2019a) as well as the material and transportation cost derived from our experience creating specimens in experiments and visiting the Himalayan mountainous regions.

The reasons for selecting styrofoam board as the material under the tie beams are listed below:

(a) The styrofoam board is useful both for the embedment of the cast-iron balls and the form panel for casting concrete.

Quasi-static cyclic loading experiments were conducted in order to investigate the performance of RBIS. The specimen is shown in Figure 7A, and the loading facility is shown in Figure 8 and Figure 7B. The materials composing the specimens from the bottom to the top are cast concrete slab (lower slab), four cast-iron balls and precast concrete slab (upper slab) with styrofoam board. The lower slab is a 300 × 300 mm² with a thickness of 80 mm. The upper slab is 250 × 250 mm² with a thickness of 50 mm glued to a 20 mm thick styrofoam board. The diameter of the cast-iron balls is 30 mm. The cyclic lateral displacement in the loading schedule shown in Figure 7C was imposed under the constant vertical load. The red and blue lines in the figure indicate the range at which to calculate the rolling coefficients which are described later. The loading velocity was a constant 1.73 mm/s. A single test was defined as the set of displacement loading of three cycles with 50 mm amplitude after one cycle with 10 mm amplitude. The constant vertical load was set as the equivalent load carried by four cast-iron balls in Figure 4.

The test parameter is the constant vertical loads. The names of the specimen are shown in Table 1. In addition to these three specimens, two more specimens were created and tested. The surface of the lower slab concrete was finished with a wooden piece in one specimen to investigate the influence of the concrete surface conditions, and rusted cast-iron balls were used in the other specimen. These changes did not affect the test results significantly. Therefore, the three specimens listed in Table 1 are discussed below.

The last numbers in the specimen names in Table 1 indicate the target values of the constant vertical loads (target vertical load) in kN. The vertical loads carried by one cast-iron ball placed at the bottom of walls in Figure 1 in the longitudinal direction with the spacing of 200, 300 and 400 mm are 2.4, 3.6 and 4.8 kN, respectively. The numbers in the specimen names are four times these loads considering the number of cast-iron balls in one specimen (=4). The specimen SN-9.6 is the base, because the most possible spacing of the cast-iron balls is 200 mm. The reasons for conducting the tests with SN-14.4 and SN-19.2 increasing the target vertical loads are to investigate the influence of the vertical load in the RBIS performance and the risk of damages such as cracks in the lower slabs. As discussed later, it was found in the experiments that the influence is limited and no damage was observed. The rolling coefficients in Table 1 are later discussed in Section 3.2.

Concrete mixing is shown in Table 2, and the composition of the cast-iron balls is shown in Table 3. The four-week compressive strength of the mortar is 25.3 N/mm². The compressive and flexural strength of the styrofoam tested according to JIS K 7220 and JIS K 7221-2 are 0.29 N/mm² and 1.1 N/mm², respectively.

When the upper slab horizontally moves on the lower slab, the cast-iron balls move in two ways, roll and slip. The balls roll horizontally squeezing into the styrofoam, and slip on the surface of the lower slab. During the moving process, these rolling and slipping movements are not clearly separated; however, the rolling is more dominant. The approximate ratio of these movements with respect to the overall lateral movement can be evaluated from the trace on the lower slab. Figure 9 shows the trace on the surface of the lower slab after the third SN-14.4 test. The cast-iron balls make the trace when they roll and slip. There is no clear difference in the trace by rolling and slipping; however, the length of trace is different. The trace length by rolling is half of the relative lateral displacement between the lower and upper slabs, while that by slipping is equal to the relative displacement. Using this fact, the ratio of rolling and slipping movement in the overall lateral movement can be estimated. The abovementioned relationships are expressed in Equations 1, 2. L A = L R + L S (1) L T = L R 2 + L S (2) where L A is the relative lateral displacement between the lower and upper slabs in the experiment. L A is 100 mm, which is twice as large as the amplitude shown in the loading schedule in Figure 7C. L R and L S are the displacement in rolling and slipping movements, respectively. L T is the trace length (= L T N − B T N in Figure 9), which is the relative lateral displacement between the cast-iron balls and the lower slab. The mean value of L T in the tests listed in Table 1 is nearly 50 mm. Using Equations 1, 2, L R is close to L A . Therefore, most of the lateral movement is estimated as rolling.

The relationships between the lateral displacements and F/N in SN-9.6. Are shown in Figure 10. The horizontal axis is the relative lateral displacement between the lower and upper slabs. The vertical axis is F/N, which is the ratio of the resisting lateral force F with respect to the normal force N. The normal force N can be the weight of superstructure mg of the building. In this experiment, N is the vertical load which is the difference between the recorded data from the load-cell connected in series to the actuator and the weight of the lower slab and its base in the facility. During the experiments, the recorded vertical load was not kept constant and changed with the lateral movements due to the performance of the loading facility and changed up to 20%. The plot is colored in yellow, cyan, red and blue with respect to the first to fourth loading cycles in Figure 7C, so that the change of F/N under increasing cycles is clearly observed. The relationships in SN-9.6, SN-14.4 and SN-19.2 are similar and those in SN-9.6 are shown in the figure. No significant difference was observed in these relationships not only in these three specimens, but also in the two tested specimens with rusted cast-iron balls and different surface conditions of lower slab concrete. Four cast-iron balls in each specimen did not carry the vertical force evenly, but it did not affect these relationships. This fact shows the relatively stable RBIS performance with limited influence from the surface conditions of the cast-iron balls and slabs.

The absolute mean value of F/N corresponding to the red lines in Figure 7C (named the “initial loading displacements”) is denoted as μ₁ and, similarly, that corresponding to the blue lines (“preloaded displacements”) is denoted as μ₂. μ₁ and μ₂ are the “rolling coefficients” in the initial loading displacements and preloaded displacements, respectively. The values of F/N are relatively stable when the lateral displacements are greater than 10 mm as seen in Figure 10. It is especially true in the initial loading displacements. The values of μ₁ and μ₂ are shown in Table 1. The difference between the specimens is relatively small; however, the difference between μ₁ and μ₂ is large. Specifically, μ₁ is around 0.14 and μ₂ is around 0.06. The reason for the difference is that the cast-iron balls squeeze into the styrofoam in the initial loading displacements and roll with smaller resistance in the preloaded displacements. The equivalent viscous damping ratio h _eq is 55% in the initial loading displacements, and is 25% and 19% in the first and second cycle of preloaded displacements, respectively.

This section discusses the bearing strength of concrete and the stress under the cast-iron balls. The weight carried by one ball in Figure 4 is 2.4, 3.6 and 4.8 kN in cases of 200, 300 and 400 mm of the ball spacing in the longitudinal direction of the wall, respectively. Assuming that the diameter of the circle where the ball contacts the lower slab is 6 mm, which is the mean value of B _TN as shown in Figure 9, the bearing stress is 85, 127 and 170 N/mm², respectively. The four-week compressive strength of the lower slab is 24 N/mm². Therefore, the bearing stress with 200 mm spacing is more than three times larger than the compressive strength. The bearing stress under the ball is not uniform and it is not considered. On the other hand, existing research shows that the bearing strength of concrete in a small loading area can be more than three times greater than the compressive strength (Hyland and Chen, 1970). Also, no damage in the lower slab was observed even at the highest bearing stress in the SN-19.2 specimen, where the vertical force corresponds to 400 mm of ball spacing in the buildings. Further investigation regarding the bearing strength and stress may be required; however, this paper continues to discuss the performance of RBIS, mainly focusing on the 200 mm of the ball spacing design.

Using the specimen shown in Figure 11, the dynamic behavior of RBIS was investigated in one-directional shaking table experiments (Figure 12). The lower slabs were attached to the shaking table and the superstructure with RBIS was placed on them. Two upper slabs were connected with the steel frame composed of two parallel I-shaped steel beams (H-100 × 100) in the superstructure. The upper slabs were tightened to the frame with bolts, so that the upper slabs could be replaced.

The weights made of steel plates were placed on the steel beams in the middle of the length. The sizes of the upper slab are 600 × 350 mm² with a thickness of 150 mm. These sizes of thickness and width (=350 mm) are the same as those in the tie beam section in the school buildings in Figure 1. The slabs were created using the styrofoam board as the form panel for the casting concrete so that the building procedure in Figure 6 was examined. The details of the procedure are described later in Section 4.2. Precast concrete slabs with 600 × 300 mm² with a thickness of 60 mm were used for the lower slabs. Two lower slabs were used for one upper slab. Therefore, four lower slabs in total were used for a single test.

Two cast-iron balls were placed under one upper slab. Therefore, the superstructure was supported by four balls in total. The tilting of an upper slab at about the line between the two balls below is constrained by the two beams in the above steel frame. The combinations of initial locations of cast-iron balls under the upper slab are shown as “Ball locations for shaking table experiments” in Figure 13. Three tests were conducted in one testing case and the initial ball locations were changed in every test, because it was observed in the quasi-static experiments that the rolling coefficients in the initial loading displacements are greater than those in the preloaded displacements.

The test parameters are the weight and input motions. The weight of the superstructure was changed by the steel plates (weight) on the frame. The test case with five steel plates is named SNWKC and that without the plate is named SNLKC. The weight of the superstructure in SNWKC is 9.04 kN including the weight of the upper slabs. The vertical load supported by one cast-iron ball is 2.26 kN (=9.04/4 kN). This load is close to 2.4 kN that is the vertical load on one ball in the rubble stone masonry building in Figure 1 with the 200 mm spacing of the balls in the longitudinal direction of the walls. The weight of the superstructure in SNLKC is 3.14 kN, and the vertical load supported by one ball is 0.79 kN.

The details of the upper slabs are shown in Figure 13, and their construction procedure is shown in Figure 14. The cast-iron balls and styrofoam are the same as those used in the quasi-static experiments. As shown in Figure 13, there are six balls placed under the upper slab in the construction experiments, simulating the ball placement in the building in Figure 1. On the other hand, there are two balls placed under one upper slab in the shaking table experiments changing the locations, simulating the supporting weight by one cast-iron ball in the building without excessively increasing the weight of the superstructure. The concrete mixing is shown in Table 2. The tested four-week compressive strength is 24.1 N/mm². The construction procedure of the upper slab is essentially the same as that for the building as shown in Figure 6. The styrofoam was placed on the cast-iron balls which were pinched with wooden bars and the form panels on the sides were nailed on the bar facing the styrofoam without gaps. The side form panels were greased for demolding but the styrofoam was not greased for attaching the styrofoam to the cast concrete.

No damage was observed on the styrofoam during the concrete casting. A simple experiment was conducted for investigating the strength of styrofoam by applying loads via the cast-iron balls. The styrofoam did not fail under 10 kN/m² which is approximately 2.8 times larger than the weight of the tie-beam. The weight of walls above the tie-beams does not load onto the styrofoam once the beam concrete is hardened. Therefore, the styrofoam has sufficient enough strength to serve as the form panel for the tie-beams.

Two input motions were used for the shaking table experiments, which were the sine wave and scaled north-south component of the Imperial Valley Earthquake recorded at El Centro (hereafter referred to as the 1940 El Centro NS). As shown in Figure 15, the sine wave is defined as the constant velocity, 0.4 m/s with increasing acceleration. The constant maximum velocity is controlled by the capacity of the maximum displacement of the shaking table. The recorded El Centro NS motion was scaled so that the maximum velocity is 0.5 m/s. The recorded Gorkha earthquake, which includes the long-period components, was considered for the input motion; however, it was not used because the maximum acceleration is less than 2 m/s² in the scaled Gorkha motion so that the maximum displacement of the shaking table reaches its capacity. With this small acceleration, the performance of RBIS is not evaluated. The proposed RBIS is developed for reducing the maximum acceleration in short periods and is not effective against long-period ground motions. The buildings applying RBIS are small as shown in Figure 1, and the first natural period is short. Unlike the high-rise buildings, the system is not expected to reduce the response to the long-period ground motions.

Figure 16 shows the recorded accelerations and displacements of SNWKC and SNLKC under the sine wave motions as well as SNWKC under the El Centro motions. The blue lines in the figure show the acceleration of the table and the black lines show that of the superstructure. The recording locations of the displacement and accelerations are shown in Figure 11. The acceleration of the superstructure shown in the figure was low-pass filtered with a cut-off of 10 Hz.

The recorded acceleration on the superstructure is lower than 0.2g. The maximum acceleration remained nearly constant in the heavier specimen, SNWKC, under the sine wave motion with increasing acceleration. As shown in Figure 16A, the maximum response acceleration in El Centro NS motion was also around 0.2g, and its ratio with respect to the maximum acceleration in the input motion is smaller than that in the sine wave motion. On the other hand, the response acceleration in the lighter specimen, SNLKC, is relatively large at around 0.25g as shown in Figure 16C, because the resisting force for the cast-iron balls horizontally bearing onto the styrofoam is relatively large. It was observed in most test cases that the displacements accumulated in one direction. The maximum displacement was around 250 mm. Figure 17 shows the bottom surface of the styrofoam in SNWKC after the test with El Centro NS motion. The traces of the cast-iron balls horizontally squeezing into the styrofoam were confirmed.

In the quasi-static cyclic loading experiments described in Chapter 3, it was observed that the rolling coefficients in the initial loading displacements, μ₁, and in the preloaded displacements, μ₂, are around 0.14 and 0.06, respectively. On the other hand, the maximum response acceleration in the shaking table experiment is around 0.2g, which is greater than the predicted maximum acceleration when taking into account the rolling coefficients, μ₁ and μ₂. During the experiment, the cast-iron balls horizontally squeezed into the embedded styrofoam. The resisting forces on the balls from the styrofoam are dependent on the relative velocity between the shaking table and specimen. Consequently, the maximum acceleration of the superstructure was greater than that corresponding to the rolling coefficient obtained from the quasi-static experiments.

In this section, the shaking table experiment was numerically simulated and the damping ratio was calibrated for evaluation of the velocity-dependent effect. The response history analyses (RHAs) were performed for a single-degree-of-freedom (SDOF) model representing the specimen shown in Figure 11. Figure 18 shows the restoring force relationships of the RBIS of the experiment, superimposed on the relationships between the lateral force and displacement obtained in the SN-9.6 (third test) quasi-static cyclic loading experiments in Figure 10. The restoring force relationships represent the difference of μ₁ and μ₂, as well as the pinching behavior. The RHAs were performed using the numerical simulation software, OpenSees (Pacific Earthquake Engineering Center (PEER), 2024a). The restoring force relationships are defined in Table 4 by using the Pinching 4 model, which is a material library (Pacific Earthquake Engineering Center (PEER), 2024b) prepared in OpenSees. The relationships are symmetrical with respect to the origin. The symbols for the forces and displacements in Table 4 are shown in Figure 18. The damping ratio h was defined as proportional to the tangent stiffness with respect to the initial natural period. The ratio was calibrated as 6% with the recorded responses in the experiment. The mass of the SDOF model is 0.922 ton (=9.04 kN/g), corresponding to the SNWKC experiment. The Newmark-β method (β = 1/6) was used with the 0.02 s time interval in the numerical integration. Figure 19 compares the accelerations and relative displacements of the tested record in SNWKC El Centro NS and simulation with h = 6% and 0%. As is shown, the simulation under h = 6% reasonably agrees with the recorded responses.