Model test analysis of control effect of building foundation elastic pad on subway environmental vibration Yubin Wu, Ruixiang Song, yanan Wu 1 , Lei He, Bideng Liu, Qiong Wu, Dan Wu, Jing Zhang Institute of Urban Safety and Environmental Science, Beijing Academy of Science and Technology No.55, Taoranting Rd, Xicheng, Beijing, 100054, PR. China

ABSTRACT Building foundation elastic pad is one of the important measures for subway vibration control. In order to understand the subway vibration control effect of elastic pad on superstructure, two identical concrete test blocks were poured on site near a subway line. Taking the real subway vibration load as the input source strength, the vibration isolation effect of elastic pad on upper concrete mass block was compared and analyzed; At the same time, the influence of the backfill around the underground foundation of the building on the vibration isolation effect is simulated and analyzed. The backfill has a non negligible restraint effect on the building, improves the vertical natural frequency of the "building - elastic pad" system, and then reduces the vibration isolation effect of the elastic pad. Therefore, the influence of surrounding soil on vibration isolation effect should be fully considered in the application design of building foundation elastic pad engineering.

1. INTRODUCTION

The rapid development of urban rail transit has brought serious vibration and noise pollution to the surrounding environment [1] . Building foundation elastic pad is one of the important control measures of subway vibration [2-3] , At present, hundreds of buildings around the world have adopted this kind of vibration control measure, but there are few reports on the environmental vibration control effect and influencing factors of building foundation elastic pad, people still use the single degree of freedom vibration isolation theory to simply estimate the control effect.

In fact, the “building - elastic pad – soil” is a complex coupling system. The underground foundation of the building is constrained by the surrounding soil, and the lateral pressure generated by the soil around the underground foundation will inevitably affect the vertical natural frequency of the "building - elastic pad" system, so as to reduce the vibration isolation effect of the elastic pad on the superstructure, At the same time, the surrounding soil, as the propagation medium of vibration elastic wave, has an impact on the vibration response of buildings.

This paper systematically studies the influence law of the surrounding soil of building foundation on the vibration isolation effect by using the method of field model test. The research results can provide reference for engineering application.

2. MODEL TEST SCHEME

Concrete mass blocks with the same geometric dimensions are poured near the subway line site. Polyurethane elastic pads are pasted at the bottom and four sides of one mass block to simulate the building structure with elastic pad vibration isolation measures (referred to as test block 1 in this paper), and the other mass block is not paved with any elastic pads for comparison of vibration

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isolation effect and reference object (referred to as test block 2 in this paper). The length, width and height of the test block are respectively 1m × 1m × 1m, square concrete test box is poured around the outside of test block 1, with wall thickness of 0.2m and height of 1.1m; The inner wall of the test chamber is 0.5m away from the test block, and the middle is filled with backfill material. The site photos of concrete test block and test box are shown in Figure 1. There are two subway lines in operation around the model test site. The subway train running on the ground shows that it has a very obvious impact of environmental vibration. This test takes the actual subway environmental vibration as the excitation load, which can truly reflect the vibration isolation effect of the elastic pad under the subway vibration load.

Test block2 Test block 1

Test box

Back fill

Test box

Test block1

Test block2

Side pad

Bottom pad

Figure 1: Test model Figure 2: Schematic diagram of model test Based on the mass of the model test block and the physical and mechanical properties of the elastic pad, the experimental design of the vibration isolation performance of the elastic pad is carried out. The concrete test mass is about 2400Kg. Polyurethane elastic pads with side length of 13.4cm are laid at the four corners of the bottom of the concrete test block, and the thickness of the elastic pad is 5cm. Figure 2 is the schematic diagram of the model test. The maximum static load limit of the tested elastic pad material is 0.35N/mm 2 , the maximum short-time overload limit is 4N / mm 2 , the mechanical loss factor is 0.07, the static elastic modulus is 2.55N/mm 2 , and the dynamic elastic modulus is 3.35N/mm 2 . Figure 3 shows the stress deformation relationship curve of the elastic pad when the elastic pad is laid (shape factor q = 1.5), and Figure 4 is the relationship curve between the compressive stress of the elastic pad and the natural frequency. It can be seen from Figure 3 and Figure 4 that the compressive stress of the elastic pad in the model test in this paper is about 0.334 N / mm 2 , and the design load is within the reasonable working range of the elastic pad. Under the same load pressure, the thicker the elastic pad, the lower the natural frequency of the vibration isolation system. When the compressive stress in the model test in this paper is 0.334N/mm 2 and the thickness of the elastic pad is 5cm, the natural frequency of the vibration isolation system can reach 7Hz. In order to simulate the damping effect of the side pad of the underground foundation in the actual project, polyurethane and polystyrene board protective materials are pasted around the concrete test block.

Specific load / (N/mm 2 )

Specific load / (N/mm 2 )

Deflection / mm

Natural frequency / Hz

Figure 3: Stress-strain curve Figure 4: Curve of compressive stress-natural frequency The soil backfill is carried out between the test block 1 and the concrete frame. The test conditions of five backfill depths of 0.1m, 0.3m, 0.5m, 0.7m and 1m are compared and analyzed.

The three acceleration sensors are respectively arranged on the center of the upper surface of test block 1, the center of the upper surface of test block 2 and the ground between the two test blocks. The vibration isolation effect of the elastic pad at the bottom of the test block on the environmental vibration of the subway and the influence of the lateral backfill are compared and analyzed. Figure 5 shows the photos of the field model test.

Figure 5: Model test site

3. MODEL TEST RESULTS AND ANALYSIS

3.1. Test Excitation Load

Figure 6 shows the vibration acceleration time history curve obtained by the subway train passing the time ground surface test. It can be seen from the figure that the subway train has a relatively obvious impact on the environmental vibration. The measured peak vibration acceleration exceeds 0.2m/s2. The environmental vibration intensity generated by different subway lines or trains is different, and there are roughly two kinds of train loads with vibration intensity (referred to as large train load and small train load in this paper)

Large train load

Small train load

Figure 6: Time history curve of ground surface vibration acceleration

Time / s

3.2. Analysis of Vibration Isolation Effect

Figure 7 shows the comparison diagram of the measured vibration acceleration curves at the ground surface, concrete test block 1 and concrete test block 2 when the subway train passes through. It can be seen from the figure that the elastic pad can significantly reduce the subway vibration response of the concrete block. The peak acceleration of test block 1 with backfill depth of 0.1M, 0.3m, 0.5m, 0.7m and 1m can be reduced by 95%, 93%, 94%, 90% and 87% respectively compared with test block 2. The measured results show that the shallower the depth of backfill, the better the vibration isolation effect of elastic pad. The vibration of concrete test block 2 without elastic pad is slightly lower than that of the ground surface.

Fig. 8 shows the comparison diagram of vibration acceleration spectrum at three measuring points under typical working conditions. It can be seen from the figure that the vibration energy of subway environment is concentrated in the range of 40Hz ~ 80Hz, the vibration peak frequency is

about 40Hz ~ 50Hz, and test block 1 has a vibration amplification range at low frequency, which has obvious vibration isolation effect on high-frequency vibration above 20Hz.

GROUND TEST BLOCK 2. —TEST 810K

(a) 0.1m backfill (b) 0.7m backfill Figure 7: Comparison of acceleration time history of three measuring points

DD. —TEST BLOCK 2. —TEST BLOCK 1

oon OND —TETBLOCK? —TEsTALOcK! 5 Ot

(a) 0.3m backfill (b) 0.5m backfill

(c) 0.7m backfill (d) 1m backfill

Figure 8: Acceleration spectrum of three measuring points Figure 9 further shows the spectrum comparison diagram of five test conditions of test block 1. It can be seen from the figure that the measured results show obvious natural vibration frequency characteristics of "concrete block- elastic pad" system. With the increase of filling depth, the natural vibration frequency of the system gradually increases, and the vibration peak frequencies (system natural frequencies) corresponding to the five conditions are 7Hz, 10Hz, 11hz, 13Hz and 14Hz respectively, The test results prove the influence law of backfill on vibration isolation system

cD —TETALOGR?

(a) Measured acceleration spectrum (b) Acceleration spectrum normalization

Figure 9: Acceleration spectrum of test block 1

Building foundation elasticity is mainly used to reduce the impact of subway vibration on indoor personnel. Therefore, the maximum acceleration Z vibration level (VL Zmax ) is used as the evaluation quantity of vibration isolation effect in this paper. VL Zmax is the maximum value of the Z-weighted vibration level of the acceleration, VL Z , in the specified measurement duration time, t. VL Z is the vibration acceleration level, VAL, after correction by the human body vibration weighted factor in the Z direction, and the Z-weighted factor obtained from Code ISO 2631-1-1985 [4] . The calculation for VAL is shown in Equation (1):

VAL= 20 lg(a/a 0 ) (dB). (1) where a and a 0 denote the measured acceleration and the reference acceleration, respectively, which are often taken as 10 -6 m/s 2 . The units of the VAL, VL Z and VL Zmax are dB.

90 85 80 6 70 6 60 55 50 48 40 @-GROUND -e-TEST BLOCK2 —e-TEST BLOCK 1 be RL A LYN 123.45 6 7 8 9 1011 12 13 14 15 16 17 18 19 20 train

The VL Zmax of 20 consecutive trains is obtained in each test condition. The measured results of the VL Zmax under five test conditions are shown in Figure 10. It can be seen from the figure that the vibration of the measuring point of test block 2 is less than that of the measuring point on the ground surface. When the backfill buried depth is 0.1m and 0.3m, the vibration of all trains in test block 1 is less than that of test block 2. However, as the backfill depth increases, the vibration of more and more trains in test block 2 is greater than that of test block 1, It shows that the effect of elastic pad on human perception of vibration is getting smaller and smaller.

90 85 80 6 70 6 60 55 50 48 40 @-GROUND -e-TEST BLOCK2 —e-TEST BLOCK 1 123.45 6 7 8 9 1011 12 13 14 15 16 17 18 19 20 train

(a) 0.1m backfill (b) 0.3m backfill

90 85 80 6 70 6 60 55 50 48 40 @-GROUND -e-TEST BLOCK2 —e-TEST BLOCK 1 123.45 6 7 8 9 1011 12 13 14 15 16 17 18 19 20 train

（ c ） 0.5m backfill (d) 0.7m backfill

(e) 1m backfill Figure 10: Measured VL Zmax of subway Table 1 shows the average value of the measured maximum acceleration Z vibration level of 20 consecutive trains under five test conditions. It can be seen from the table that when the filling depth is 0.1m, the vibration isolation effect of the elastic pad is better, and the average value of the vibration isolation effect can reach 8.6db. When the filling depth increases to 0.5m, the average value of the vibration isolation effect of the elastic pad decreases to 2.1dB. When the filling depth is

90 85 80 6 70 6 60 55 50 48 40 @-GROUND -e-TEST BLOCK2 —e-TEST BLOCK 1 123.45 6 7 8 9 1011 12 13 14 15 16 17 18 19 20 train

90 85 80 6 70 6 60 55 50 48 40 @-GROUND -e-TEST BLOCK2 —e-TEST BLOCK 1 123.45 6 7 8 9 1011 12 13 14 15 16 17 18 19 20 train

0.7m and 1m, the elastic pad has no vibration reduction effect on the maximum acceleration Z vibration level due to the amplification effect of low-frequency vibration, Even negative effects

Table 1: Average value of VL zmax of 20 trains (dB)

Backfill depth(m) Ground Test block 1 Test block 1 Elastic pad effect 0.1 73.9 62.8 71.4 8.6 0.3 73.6 65.0 71.1 6.1 0.5 74.2 69.2 71.2 2.1 0.7 74.5 73.6 71.8 -1.8 1 74.3 74.0 71.9 -2.0 4. CONCLUSIONS

In this paper, taking the real subway environment vibration as the excitation load, the influence law of lateral backfill on the vibration isolation effect of building foundation elastic pad is studied by using the model test analysis method. The test results show that:

（ 1 ） The elastic pad at the bottom of the mass block has a great vibration isolation effect on the peak acceleration of subway ambient vibration. When the design natural frequency is 7Hz, the peak acceleration can be reduced by more than 90%;

（ 2 ） Under the excitation of subway ambient vibration, the vibration response of “mass block - elastic pad” vibration isolation system has obvious natural vibration characteristics. There is an amplification area in low-frequency vibration, and the vibration damping effect of high-frequency vibration is obvious;

（ 3 ） The vibration isolation effect of the elastic pad at the bottom of the mass block is obviously affected by the lateral backfill. With the increase of the backfill depth, the vibration isolation effect decreases gradually. Due to the low-frequency amplification effect, the maximum acceleration Z vibration level even has the amplification negative effect after backfilling to a certain depth. Therefore, in practical engineering application, the influence of the backfill on the vibration isolation effect of the elastic pad should be considered, and the buried depth and lateral restraint effect of the backfill should be reduced as much as possible;

（ 4 ） In addition to the buried depth of backfill, the type of backfill material and the laying method of side pad also have an impact on the vibration isolation effect of elastic pad. The research group will further carry out relevant experimental research work, 5. ACKNOWLEDGEMENTS

This work is partly funded by the BJAST Young Scholar Programs B No.YS202102 and the Beijing Financial Research Project (Grant No.11000022T000000468166 and 11000022T000000446408). 6. REFERENCES

1. Liu WeiNing, Ma Meng, Liu WeiFeng, Sun XiaoJing & Sun FangQiu. Overview on current

research of environmental vibration influence induced by urban mass transit in China. SCIENTIA SINICA Technologica, 46(6), 547–559 (2016). 2. Song Ruixiang , Zhang Xuegang ,Sun Guodong , Zhang Zhang , Wang Liang. Discussion on

theApplication of Two Foundation Isolation Measures in Buildings Receiving Excessive Vibration from Adjacent Subway Lines. Noise and Vibration Contrl, 38(5), 156–161 (2018). 3. MaNing ， Zhao Fuzhuang ， Wu Yubin ， Zheng Yongjun ， Song Ruixiang. Analysis of

Vibration Characteristics and Vibration Isolation Measures of Gas Equipment Adjacent to Metro. Urban Mass Transit, 24(7), 53–57 (2021). 4. International Organization for Standardization. ISO 2631-1:1985: Evaluation of human

exposure to whole-body vibration - Part 1: General requirements, (1985).