Study on the acceleration response of model soil using shaking table test

Ngày nhận bài: 28/11/2025; ngày sửa bài: 19/12/2025; ngày chấp nhận đăng: 25/12/2025

http://doi.org/10.64588/jc.07.12.2025

Abstract

This study evaluates the acceleration response of a soil foundation under seismic action through a shaking table test. The experimental setup involved designing a soil model - composed of a soil-sawdust mixture - and instrumenting it with accelerometers at various positions. The tests employed excitation waves with different intensities and frequency spectra, specifically the El Centro and Shanghai waves, as input motions. Acceleration responses were measured at various depths within the soil profile. The analysis results indicate that: (i) Peak acceleration within the model soil increased from the bottom to the surface; (ii) Under the same Peak Ground Acceleration level (e.g., PGA = 0.07 g), the recorded acceleration amplitudes were larger for the Shanghai wave than for the El Centro wave; (iii) At identical PGA levels, the seismic response of the model soil demonstrated greater sensitivity to input motions richer in low-frequency components.

Key words: Free field, shaking table, underground structure, earthquake, El Centro, Shanghai wave.

Tóm tắt

Bài báo trình bày ứng xử gia tốc của nền đất dưới tác động của động đất thông qua thí nghiệm bàn rung. Thí nghiệm được thiết kế gồm mô hình đất - là từ hỗn hợp đất và mùn cưa, hệ thống các cảm biến gia tốc để đo gia tốc dưới tác dụng của sóng kích thích tại đáy của mô hình. Sóng kích thích sử dụng là sóng El Centro và sóng Thượng Hải. Gia tốc nền được ghi lại tại các vị trí độ sâu khác nhau trong đất. Kết quả phân tích chỉ ra rằng: (i) Gia tốc đỉnh trong mô hình đất tăng dần từ đáy lên bề mặt; (ii) Ở cùng mức gia tốc đỉnh (ví dụ: PGA = 0.07 g), gia tốc ghi nhận được tại các điểm đo đối với sóng Thượng Hải là lớn hơn so với sóng El Centro; (iii) với cùng giá trị PGA = 0.07 g, ứng xử gia tốc của đất nền là lớn hơn đối với sóng kích thích có nhiều thành phần tần số thấp.

Từ khóa: Trường tự do, bàn rung, kết cấu ngầm, động đất, sóng El Centro, sóng Thượng Hải

1. Introduction

In densely populated cities today, underground structures have become an effective solution to urban space constraints, particularly in optimizing transportation systems with works such as subways, tunnels, etc. In areas with a historical record of earthquakes, research on seismic design solutions for underground structures is given special emphasis, becoming one of the critical tasks in the design and construction process. This urgency is further underscored by the severe damages to underground structures recently recorded worldwide, such as the Great Hanshin earthquake (1995), the Turkey Kocaeli earthquake (1999), the China Wenchuan earthquake (2008), the Pacific coast of Tohoku earthquake in Japan (2011), the China Lushan earthquake (2013), and the China Jiuzhaigou earthquake (2017)…[[1]-[19]].

In earthquakes, acceleration and its propagation through the soil foundation are among the critical parameters for assessing the severity of a seismic event. These parameters form the basis for seismic design and earthquake classification standards. One of the widely used contemporary methods for studying seismic effects involves physical modeling, specifically through the design of an earthquake simulation experiment using a shaking table and excitation waves with varying intensities and frequency spectra.

Based on that foundation, this paper presents a shaking table experiment to study the acceleration response of the soil foundation under excitation waves. A free-field shaking table experiment was conducted. The model soil was prepared as a mixture of natural soil and sawdust. The experiments were carried out at the National Key Laboratory of Earthquake Engineering at Tongji University (China). Experimental results serve as a reference for similar studies evaluating the behavior of underground structures during earthquakes.

2.  Testing apparatus

2.1. Shaking table

The test system was designed and installed by MTS Company, USA. The shaking table measures 4.0 x 4.0 m, with a maximum payload capacity of 25 tons. It can generate excitation waves simultaneously in three directions (X, Y, and Z). The generated excitation frequency ranges from 0.1 Hz to 50 Hz. The experimental system can install and acquire signals from up to 128 sensors. The displacement amplitude in the X, Y, and Z directions is ±100 mm, ±50 mm, and ±50 mm, respectively, with corresponding velocities of 1000 mm/s, 600 mm/s, and 600 mm/s.

2.2. Soil container

The soil container is a cylinder box made from a 4.0 mm in thickness rubber slab with good elasticity. The diameter of the box was 3.0m and the height was 1.5m. In order to keep its shape and sizes constant during carrying the tests, steel girths φ6mm steel girths were covered around the cylinder box with the gap between girths was 5cm. The soil box was put inside a steel frame that was welded by high-strength L-steel shape and I-steel shape.

2.3. Model soil

The model soil is a mixture of sand and sawdust to simulate the prototype soil. The characteristics of model soil were listed in Table 1 below.

Table 1. Main characteristics of the model soil.

During the preparation phase, the model soil was placed into the container in layers. Each layer had a thickness of approximately 10 cm and was leveled and compacted using a manual tamper. Sensors were installed at their predetermined locations as each layer was completed, prior to the placement of the subsequent layer.

2.4. Layout of Sensors

In the free-field shaking table test, accelerometers were deployed on the surface of the model soil, embedded within the soil mass, and positioned near the wall of the container, as illustrated in Figure 1 below.

Figure 1: Arrangement of accelerometers in the free-field test. Af1 to Af10 are bidirectional sensors. Af0 and Af11 are three-dimensional sensors. Unit is mm.

A total of 12 accelerometers were installed in the free - field shaking table test. In which, 4 accelerometers (designated Af1 to Af4) were placed on the soil surface, at a distance of 540 mm from the center line of the soil box along its longitudinal axis; 1 accelerometer was installed on the center line, 270 mm from sensor Af1; 6 accelerometers were embedded at depths of 450mm and 900 mm from the soil surface; 1 accelerometer (A0) was mounted on the shaking table platform to record its input acceleration. Regarding sensor type, accelerometers Af0 and Af11 were three-directional sensors, while all other sensors (Af1 through Af10) were bidirectional.

2.5. Ground motion input

The El-Centro earthquake acceleration record (N-S component) was employed as the prototype wave in this test. Besides, the Shanghai wave was also utilized as an input motion to investigate the differing effects of various seismic excitations on the soil response and underground structures.

The El Centro earthquake occurred on May 19th in California, near the US-Mexico border. With a surface wave magnitude (Ms) of 6.9, it featured an original peak ground acceleration (PGA) of 0.3g and a significant duration of strong motion of 30 seconds. For comparative analysis, the Shanghai artificial wave was selected in accordance with the local seismic design code for building structures (Code for Seismic Design of Buildings DGJ08-9-2013, Shanghai area). This wave has an original PGA of 0.04g and a duration of 10 seconds.

Figure 2 and Figure 3 present the acceleration time histories and corresponding Fourier spectra of the input motions used in the test. To study the effect of varying intensity, the PGA of these input motions was systematically scaled, while preserving their frequency content and temporal characteristics.

Fig 2: Original acceleration time-history and the Fourier spectra of El-Centro wave.

2.6. Test cases

Table 2 describes the six test configurations designed to investigate the propagation and variation of seismic acceleration in the soil medium, employing the El Centro and Shanghai waves as the input ground motions. The El Centro wave and Shanghai wave with PGAs of 0.07g. The direction of excitation wave was in transversal.

Table 2: Input motions for the free-field tests.

3.  Testing results

3.1. The acceleration response of the model soil

The acceleration response of the model soil was varied with depth from the bottom to the surface was shown in Figures 4.

a) Acceleration time history and Fourier spectra at the bottom of model soil for El2 case

b) Acceleration time history and Fourier spectra at the depth of 900mm for El2 case

c) Acceleration time history and Fourier spectra at the depth of 450mm for El2 case

d) Acceleration time history and Fourier spectra at the surface of model soil for El2 case

e) Acceleration time history and Fourier spectra at the bottom of model soil for SH3 case

f) Acceleration time history and Fourier spectra at the depth of 900mm for SH3 case

g) Acceleration time history and Fourier spectra at the depth of 450mm for SH3 case

h) Acceleration time history and Fourier spectra at the surface of model soil for SH3 case

Fig 4: Acceleration time histories and Fourier spectra for vibration in transversal direction of El Centro wave and Shanghai wave (PGAs = 0.07g).

These figures indicate that for transversal input motions with low PGA (0.07g), the peak accelerations of the model soil increased from the bottom to the surface. In terms of Fourier spectra, the dominant frequency of the model soil's acceleration response under the 0.07g PGA input ranged from 20 Hz to 30 Hz.

Furthermore, for input motions of the same PGA level, the acceleration amplitudes recorded within the model soil were larger under the Shanghai wave than under the El Centro wave. This suggests that the soil's acceleration response was more sensitive to input motions richer in low-frequency components. For instance, at PGA = 0.07g, the peak acceleration measured at point Af5x was approximately 0.044g for the El Centro excitation and about 0.075g for the Shanghai wave. This trend was consistent across all other accelerometers.

3.2. Peak acceleration amplification factor

The peak acceleration amplification factor is defined as the ratio of the peak acceleration recorded by sensors in the model soil to that recorded by the sensor on the shaking table (reference sensor). In this free-field test, it was calculated as the ratio of peak accelerations from sensors Af0x, Af5x, and Af9x to the peak acceleration from sensor A0x, as illustrated in Figure 5.

he Test results show that for input motions with a low peak ground acceleration (PGA = 0.07 g), the peak acceleration amplification factor increased with depth from the bottom to the surface. The maximum amplification factor occurred at the soil surface, with values of approximately 1.5 and 2.2 for the El Centro and Shanghai waves, respectively.

Furthermore, for low PGA input motions (0.07g), the amplification factors induced by the El Centro wave were smaller than those induced by the Shanghai wave. This suggests that the seismic response of the model soil is more sensitive to input motions richer in low-frequency components at the same PGA level, attributable to the wave propagation characteristics of the soil medium.

4.  Conclusions

The results of the free-field tests investigated the acceleration response of the model soil were consistent with previous studies.

With a low Peak Ground Acceleration (in the test is PGA = 0.07g), the peak acceleration of the model soil increased from the bottom to the surface.

For input motions of the same PGA level, the acceleration amplitudes recorded within the model soil were larger under the Shanghai wave than under the El Centro wave.

The seismic response of the model soil is more sensitive to input motions richer in low-frequency components at the same PGA level, attributable to the wave propagation characteristics of the soil medium.

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