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1DETERMINING THE EFFECTIVENESS OF SEISMIC BARRIERS BY CHANGING THEIR HEIGHT
1Yuldashev Sh.S., 2Abdunazarov A.Sh.
Professor of NamICI, d.t.s Researcher of NamICI https://doi.org/10.5281/zenodo.13623022
Abstract. In the article, the impact of seismic surface waves on the building was determined using the Plaxis 3D software complex using the Finite Element method. The highest displacement amplitudes at each point are determined. Seismic barriers with a height of 1 meter, 3 meters, 5 meters, and 7 meters are modeled, and their effectiveness by reducing seismic surface waves is studied and a comparative comparison is made.
Keywords: building, seismic surface waves, finite element method, theory of elasticity, seismic barrier.
Introduction
Seismic barriers are crucial for mitigating damage caused by natural disasters, particularly earthquakes. These barriers protect buildings and infrastructure from seismic activity, thereby safeguarding human lives. The primary function of seismic barriers is to absorb, reflect, or dissipate seismic energy, reducing the damage to the structural integrity of buildings and infrastructure.
Seismic surface waves can move through the ground and cause significant damage to structures. Seismic barriers play an important role, especially in high seismic activity areas. These barriers can be constructed using various materials and technologies, and their effectiveness depends on factors such as height, material quality, and construction methods. The performance of seismic barriers is largely influenced by their height, materials, and construction techniques. Height, for example, directly affects a barrier's ability to reflect or dissipate seismic waves, making it essential to evaluate properly and optimize this factor.
Research Materials and Methodology
This study aims to analyze the effectiveness of seismic barriers by varying their height to explore possibilities for improving their performance and enhancing seismic safety. The objective is to evaluate how changing the height of seismic barriers affects their effectiveness and to determine the optimal height. Through this analysis, we will investigate how barriers of different heights influence seismic waves and perform a comparative assessment.
The study focuses on determining how the placement of seismic barriers affects their ability to mitigate the impact of Rayleigh surface waves on buildings. This involves evaluating and comparing the performance of seismic barriers at different heights.
To solve the problem numerically, a finite model with dimensions of 200 m in length, 100 m in width, and 50 m in depth was selected. In the problem, groundwater is assumed to be at a depth of 20 m. The building is 24 m in length, 24 m in width, and 14.75 m in height, with a floor height of 3.3 m, and the basement part of the building is located at a depth of 3 m. The first layer of soil is modeled as 5 meters of loamy sand (Loam), and the second layer is modeled as 45 meters of gravelly soil (Pebble) (Figure 1).
Figure 1. Discretization of the soil model and residential building into finite elements.
b)
c)
d)
Figure 2. Seismic Barriers of Annular Shape with Thickness of 1 Meter and Heights of
1, 3, 5, and 7 Meters
The circular vertical seismic barrier is positioned 28 meters from the center of the building, with a thickness of 1 meter and a height of 1, 3, 5 and 7 meters (Figure 2).
In this problem, an infinite semi-space is replaced by a finite domain. The following conditions are imposed at the boundaries to ensure the waves approach infinity [1,2,3].
ax = apVpu
ryz = bpVsv rzy = bpVsw
Oy = apVpv л rxz = bpVsw rzx = bpVsii
(1)
az = apVpw" rxy = bpVsii xyx = bpVsV;
The research domain is divided into 47,109 finite elements and 86,147 nodes. The shapes of the finite elements are chosen as irregular tetrahedra (Figure 1).
The order of the system of differential equations of motion is 86,147 x 3 = 258,441. The kinematic relations can be formulated as follows [1,2,3]:
e = Lu (2)
LT - Transposed differential operator
(3)
In general, each element material may have an initial deformation due to temperature changes, expansion, or crystallization [1,2,3]. If we denote this deformation by {£0}, the stress is determined by the difference between the current deformation and the initial deformation. Additionally, it is convenient to consider that there might be residual stress that can be measured
r3 0 0 а 0 а
9x ду dz
= 0 д 0 а д 0
ду дх dz
0 0 д 0 д д
dz ду дх-
at the time of observation [1,2,3]. This stress is added to the general expression for stress. When considering the material of the body as elastic, the relationship between stress and deformation is linear [1,2,3]:
{a} = [D]({s}-{s0})+{a0} (4)
Here, [D] is the elasticity matrix representing the material properties. In the case of plane stress, three components of stress corresponding to deformation are written as follows [1,2,3]:
{*} =
ax
It
xyj
The matrix [D] is determined from the following relationship between stress and deformation:
_ ( л — 1 —v
£x (£ж)0 = Effx Eay'
E"y, £y \£y)0 = Eax + Eay''
_2 + (l + v) Уху \YxyjQ = — Tf
E
uxy
From this:
[D] =
E
1-v2
1 V 0
V 1 0
1-v
0 0
2
(5)
The system of differential equations for the motion of a mechanical system subjected to dynamic loads is expressed as follows [1,3]:
Mu + Cù + Ku = F (6)
Here, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and F is the dynamic load vector. u is the displacement vector, ù is the velocity vector, and u is the acceleration vector, which are considered continuous functions of time [2,3].
In the numerical formulation of dynamic problems, the time iteration formulation is a crucial factor for the stability and accuracy of the computer processing [3].
We adopt the time iteration coefficients for the Newmark method a = 0.25 and fi = 0.5 [2,3]. The properties of the soil, building, and seismic barrier are provided in Table 1 [2,3].
Table 1
Parameter Unit of measure Designation Name of the soil
Loam Pebble
General Properties of the Soil
Model type - - Liner elastic Liner elastic
Soil parameter - - Dried Dried
The specific gravity of the upper layer of the soil under the influence of groundwater kN/m3 Yunsat 16 19
The specific gravity of the bottom layer of the soil under the influence of groundwater kN/m3 Ysat 17 20.5
Initial porosity coefficient - 0.5 0.5
Young's modulus kN/m2 E 50000 90000
Poisson's ratio - V 0.35 0.3
Longitudinal wave speed m/s VP 218.4 250.1
Transverse wavelength m/s Vs 104.9 133.7
General Properties of the Building
Model Type - - Elastic
Elasticity Modulus kN/m2 E 27500000
Poisson's Ratio - V 0.2
Density kN/m3 Y 24
General Properties of the Barrier
Model Type - - Elastic
Elasticity Modulus kN/m2 E 1000
Poisson's Ratio - V 0.3
Density kN/m3 Y 12
To determine and compare the impact of seismic surface waves on the building, 9 observation points per floor, totaling 54 points, were designated for the building (Figure 5) [3].
Figure 3. Observation Points
The propagation of seismic surface waves was generated using a harmonic force. The phase of the harmonic force is 0, with an amplitude of 1 and a frequency of 10 Hz, and a duration of 5 seconds (Figure 6) [3].
Figure 4. Harmonic Force Law When seismic surface waves impact the building, the maximum amplitude values of uz at the predesignated observation points in the building were determined and tabulated (Table 2).
To assess the reduction of seismic surface waves affecting the building and the advantages of varying the height of seismic barriers, seismic barriers with heights of 1, 3, 5, and 7 meters were modeled. The maximum amplitudes of displacement along the building's longitudinal axis at specified points (Table 2) were analyzed comparatively.
[*10 m]
Figure 5. Process of Seismic Surface Waves Affecting the Building
Table 2
№ Observat ion Points Coordinates (x,y,z) No barrier Barrier
1 meter 3 meter 5 meter 7 meter
Displacemen t (mm) Displace ment (mm) Displace ment (mm) Displace ment (mm) Displace ment (mm)
The ground part of the building 1 100, 38, -3 1,527 1,702 1,305 1,266 1,096
2 100, 50, -3 1,518 1,662 1,291 1,220 1,128
3 100, 62, -3 1,455 1,626 1,242 1,242 1,113
4 112, 38, -3 0,912 0,633 0,503 0,410 0,360
5 112, 50, -3 0,825 0,655 0,467 0,398 0,367
6 112, 62, -3 0,811 0,705 0,516 0,402 0,366
7 124, 38, -3 0,722 0,744 0,630 0,689 0,643
8 124, 50, -3 0,772 0,841 0,678 0,674 0,657
9 124, 62, -3 0,859 0,937 0,779 0,626 0,641
1st floor 10 100, 38, 0,75 1,539 1,712 1,312 1,276 1,107
11 100, 50, 0,75 1,535 1,679 1,301 1,233 1,138
12 100, 62, 0,75 1,465 1,641 1,254 1,248 1,121
13 112, 38, 0,75 0,915 0,628 0,505 0,405 0,357
14 112, 50, 0,75 0,819 0,651 0,465 0,396 0,363
15 112, 62, 0,75 0,809 0,700 0,513 0,399 0,364
16 124, 38, 0,75 0,729 0,748 0,633 0,692 0,644
17 124, 50, 0,75 0,775 0,843 0,681 0,675 0,655
18 124, 62, 0,75 0,867 0,937 0,779 0,630 0,642
2nd floor 19 100, 38, 4,05 1,683 1,759 1,345 1,321 1,159
20 100, 50, 4,05 1,670 1,744 1,344 1,289 1,182
21 100, 62, 4,05 1,608 1,724 1,320 1,293 1,165
22 112, 38, 4,05 0,933 0,622 0,554 0,402 0,357
23 112, 50, 4,05 0,797 0,641 0,458 0,390 0,354
24 112, 62, 4,05 0,797 0,694 0,508 0,398 0,381
25 124, 38, 4,05 0,758 0,765 0,633 0,698 0,640
26 124, 50, 4,05 0,800 0,853 0,692 0,679 0,651
27 124, 62, 4,05 0,903 0,939 0,782 0,642 0,649
28 100, 38, 7,35 1,822 1,790 1,367 1,352 1,194
29 100, 50, 7,35 1,802 1,782 1,371 1,325 1,210
30 100, 62, 7,35 1,742 1,777 1,362 1,325 1,195
!-H o 31 112, 38, 7,35 0,950 0,617 0,587 0,399 0,357
o "Ö 32 112, 50, 7,35 0,785 0,637 0,455 0,387 0,349
!-h m 33 112, 62, 7,35 0,790 0,690 0,505 0,398 0,394
34 124, 38, 7,35 0,782 0,778 0,632 0,703 0,639
35 124, 50, 7,35 0,819 0,862 0,701 0,683 0,650
36 124, 62, 7,35 0,938 0,943 0,786 0,650 0,654
37 100, 38, 10,65 1,897 1,807 1,380 1,370 1,214
38 100, 50, 10,65 1,864 1,801 1,385 1,343 1,226
39 100, 62, 10,65 1,812 1,804 1,384 1,343 1,212
!-H 40 112, 38, 10,65 0,959 0,615 0,604 0,397 0,356
o o 41 112, 50, 10,65 0,782 0,635 0,454 0,386 0,346
42 112, 62, 10,65 0,787 0,688 0,503 0,398 0,399
43 124, 38, 10,65 0,795 0,786 0,633 0,707 0,640
44 124, 50, 10,65 0,828 0,868 0,706 0,686 0,651
45 124, 62, 10,65 0,960 0,947 0,790 0,654 0,657
M) C T3 46 100, 38, 13,95 1,919 1,812 1,384 1,376 1,220
m (L> 47 100, 50, 13,95 1,878 1,806 1,389 1,348 1,230
<+H O t eö d, O H 48 100, 62, 13,95 1,832 1,812 1,391 1,348 1,217
49 112, 38, 13,95 0,960 0,614 0,607 0,396 0,355
50 112, 50, 13,95 0,781 0,634 0,454 0,386 0,346
51 112, 62, 13,95 0,786 0,687 0,502 0,397 0,400
52 124, 38, 13,95 0,800 0,789 0,633 0,709 0,640
53 124, 50, 13,95 0,832 0,871 0,709 0,687 0,652
54 124, 62, 13,95 0,966 0,949 0,792 0,655 0,641
Figure 8. Contrastive Comparison Graph of Displacement ait Observation Point 54 In Figure 8, at the 54th observation point of the building without any surrounding barriers, the maximum displacement of the seismic surface wave along the uz axis is Uzmax= 0,966 mm. For the building with a seismic barrier of 1 meter height, Uzmax=0,949 mm; for the building with a seismic barrier of 3 meters height, Uzmax=0,792 mm; for the building with a seismic barrier of 5 meters height, Uzmax=0,655 mm; and for the building with a seismic barrier of 7 meters height, Uzmax=0,641 mm.
Compared to the building without any surrounding barriers, the effectiveness of the seismic barriers is recorded as 1.79% for the 1-meter height barrier, 18.06% - for the 3-meter height barrier, 32.21% - for the 5-meter height barrier, and 33.66% - for the 7-meter height barrier.
Figure 9. Contrastive Comparison Graph of Velocity at Observation Point 54
In Figure 9, the maximum value of the velocity of the seismic surface wave along the vz axis at observation point 54 of the building without any obstacles around it is vzmax=6,50 cm/s, in the building with a 1-meter-high seismic barrier Vzmax=4,59 cm/s, Vzmax=4,\9 cm/s in a building with a 3-meter-high seismic barrier, Vzmax=2,06 cm/s in a building with a 5-meter-high seismic barrier, a 7-meter-high seismic barrier Vzmax= 1,82 cm/s in a densely located building. In a contrastive comparison, the speed at observation point 54 of a building with a 1-meter-high seismic barrier is 29.38% compared to a building without any barriers around the building, 35.53% in a building with a 3-meter-high seismic barrier, and 68.31%in the building with a 5-meter-high seismic barrier, and 72.00% in the building with a 7-meter high seismic barrier.
Figure 10. Contrastive Comparison Graph of Acceleration at Observation Point 54
In Figure 10, at observation point 54 of a building with no barriers around it, the maximum acceleration of the seismic surface wave along the az axis is aZmax=54,49 cm/s2. For a building with a 1-meter-high seismic barrier, aZmax=45,65 cm/s2; with a 3-meter-high barrier, aZmax=38,29cm/s2; with a 5-meter-high barrier, aZmax=24,00 cm/s2; and with a 7-meter-high barrier, azmax= 16,83 cm/s2. In comparison, the effectiveness of the seismic barriers is noted as follows: a 1-meter-high barrier reduces the acceleration by 16.22%, a 3-meter-high barrier - by 29.73%, a 5-meter-high barrier - by 55.95%, and a 7-meter-high barrier - by 69.11% relative to the building with no barriers.
To reduce the impact of seismic surface waves on the building, a circular seismic barrier with a radius of 28 meters and a thickness of 1 meter was modeled with heights of 1, 3, 5, and 7 meters to examine the process of reducing seismic surface waves.
Conclusion:
Based on the obtained results and the graphics in the figures, it is evident that compared to a building with no barriers around it, the building with a seismic barrier of 1 meter height, located at the center of the building with a radius of 28 meters and a thickness of 1 meter, shows an average reduction in displacement of 3.15%, velocity of 37.98%, and acceleration of 21.09%. For a building with a seismic barrier of 3 meters height, the average reductions are 24.05% in displacement, 56.53% in velocity, and 50.13% in acceleration. For a seismic barrier of 5 meters height, the reductions are 29.26% in displacement, 63.93% in velocity, and 51.58% in acceleration. For a seismic barrier of 7 meters height, the reductions are 34.94% in displacement, 66.13% in
velocity, and 62.66% in acceleration. This indicates a significant decrease in the oscillation level of seismic surface waves.
According to this analysis, it is clear that the effectiveness of seismic barriers in reducing the impact of seismic surface waves is dependent on the height of the barriers. The results suggest that increasing the height of seismic barriers can significantly reduce the level of seismic surface wave oscillations. As the height of the seismic barrier increases, a decrease in displacement, velocity, and acceleration is observed. This implies that taller seismic barriers are more effective in resisting and reducing the spread of surface waves, thus minimizing damage to the building. The modeling results indicate that a seismic barrier with a height of 7 meters is most effective in reducing the oscillation of surface waves. In summary, increasing the height of seismic barriers results in a significant reduction in the impact of seismic surface waves on the building, highlighting its importance in enhancing seismic safety. Utilizing such seismic barriers in construction, especially in highly seismically active areas, can significantly improve the safety of buildings.
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