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0DETERMINING THE EFFECTIVENESS OF SEISMIC BARRIERS BY CHANGING THEIR THICKNESS
1Yuldashev Sh.S., 2Abdunazarov A.Sh.
1Professor at NamICI, t.f.d.
2Researcher at NamICI https://doi.org/10.5281/zenodo.13350631
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 of 0.4 meters, 0.6 meters, 0.8 meters and 1.0 meters of thickness 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 play a crucial role in reducing damage caused by natural disasters, especially earthquakes. By providing seismic protection to buildings and structures, seismic barriers help safeguard human life. The primary function of seismic barriers is to reduce damage to building structures by absorbing, reflecting, or dissipating seismic energy.
Seismic surface waves can move through a semi-space and cause significant damage to buildings. Seismic barriers, particularly in high seismic activity areas, play an important role. These barriers can be constructed using various materials and technologies, and their effectiveness depends on factors such as height, material quality, and construction methods. For instance, the height of the barrier directly affects its ability to reflect or dissipate seismic waves, making it crucial to evaluate and optimize this factor accurately.
Research Materials and Methodology
The goal is to analyze the effectiveness of seismic barriers by varying their thickness and to determine the optimal thickness. This analysis will help understand how thickness affects seismic waves and identify the most effective and cost-efficient thickness.
In the examined case, the dependence of the seismic barrier's effectiveness on its placement in relation to the impact of Rayleigh surface waves on the building is determined and compared.
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).
The circular vertical seismic barrier is positioned 28 meters from the center of the building, with a thickness of 0.4, 0.6, 0.8 and 1 meter and a height of 3 meters (Figure 4). 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 = apVvù\ ryz = bpVsv rzy = bpVsw
Gy = apVpv л rxz = bpVsw rzx = bpVsii
az = apVpw"
rxy = bpVsù (1)
xyx = bpVsv
The research domain is divided into 46,782 finite elements and 85,813 nodes. The shapes of the finite elements are chosen as irregular tetrahedra (Figure 2).
The order of the system of differential equations of motion is 85,813 x 3 = 257,439. The kinematic relations can be formulated as follows [1,2,3]:
e = Lu (2)
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-
Figure 1. Discretization of the soil model and residential building into finite elements.
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 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, the three components of stress corresponding to deformation are written as follows [1,2,3]:
{*} =
ax
Ол
T
xyj
The matrix [D] is determined from the following relationship between stress and
deformation:
_ ( \ — 1 —v £x (£x)0 = Effx EGy'' £%
_2 + (l + v) Уху \YxyjQ = — T
(sv) = — — Gv +— Gv\ \ VJq E x E y>
E
xy;
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, in 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 computational process [3].
We adopt the time iteration coefficients for the Newmark method coefficients 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 2. 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].
Time [s]
Figure 3. Harmonic Force Law
[*lDJm]
Figure 4. Process of Seismic Surface Waves Affecting the Building
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 reduce the impact of seismic surface waves on the building and determine the advantages of different seismic barrier thicknesses, seismic barriers with thicknesses of 0.4, 0.6, 0.8, and 1.0 meters were modeled. The maximum amplitudes of displacement along the building's uz axis at designated points (Table 2) were compared and analyzed.
Table 2
No barrier Barrier
№ Observatio Coordinates 0,4 meter 0,6 meter 0,8 meter 1 meter
n Points (x,y,z) Displace Displace Displace Displace Displace
ment ment ment ment ment
(mm) (mm) (mm) (mm) (mm))
c T3 1 100, 38, -3 1,527 1,521 1,342 1,481 1,305
2 100, 50, -3 1,518 1,509 1,396 1,497 1,291
3 100, 62, -3 1,455 1,501 1,403 1,513 1,242
<+H 4 112, 38, -3 0,912 0,609 0,718 0,501 0,503
O t cä 5 112, 50, -3 0,825 0,660 0,584 0,556 0,467
SP 6 112, 62, -3 0,811 0,738 0,485 0,600 0,516
o !-H 7 124, 38, -3 0,722 0,772 0,782 0,747 0,630
M> (U 8 124, 50, -3 0,772 0,776 0,806 0,737 0,678
H 9 124, 62, -3 0,859 0,739 0,798 0,659 0,779
10 100, 38, 0,75 1,539 1,531 1,358 1,491 1,312
11 100, 50, 0,75 1,535 1,528 1,411 1,513 1,301
12 100, 62, 0,75 1,465 1,515 1,414 1,526 1,254
!-h o 13 112, 38, 0,75 0,915 0,609 0,716 0,498 0,505
o 14 112, 50, 0,75 0,819 0,662 0,574 0,550 0,465
Ui 15 112, 62, 0,75 0,809 0,740 0,483 0,597 0,513
16 124, 38, 0,75 0,729 0,775 0,784 0,749 0,633
17 124, 50, 0,75 0,775 0,778 0,807 0,736 0,681
18 124, 62, 0,75 0,867 0,739 0,800 0,662 0,779
19 100, 38, 4,05 1,683 1,595 1,439 1,548 1,345
20 100, 50, 4,05 1,670 1,597 1,473 1,579 1,344
21 100, 62, 4,05 1,608 1,640 1,467 1,597 1,320
!-H o 22 112, 38, 4,05 0,933 0,625 0,720 0,493 0,554
T3 23 112, 50, 4,05 0,797 0,660 0,550 0,537 0,458
c (N 24 112, 62, 4,05 0,797 0,752 0,482 0,592 0,508
25 124, 38, 4,05 0,758 0,797 0,789 0,758 0,633
26 124, 50, 4,05 0,800 0,787 0,813 0,734 0,692
27 124, 62, 4,05 0,903 0,744 0,815 0,668 0,782
!-H o 28 100, 38, 7,35 1,822 1,636 1,490 1,588 1,367
o T3 29 100, 50, 7,35 1,802 1,640 1,510 1,621 1,371
!-H m 30 100, 62, 7,35 1,742 1,729 1,499 1,645 1,362
31 112, 38, 7,35 0,950 0,633 0,725 0,490 0,587
32 112, 50, 7,35 0,785 0,660 0,537 0,531 0,455
33 112, 62, 7,35 0,790 0,764 0,482 0,589 0,505
34 124, 38, 7,35 0,782 0,813 0,796 0,765 0,632
35 124, 50, 7,35 0,819 0,795 0,820 0,734 0,701
36 124, 62, 7,35 0,938 0,748 0,827 0,673 0,786
37 100, 38, 10,65 1,897 1,659 1,517 1,609 1,380
38 100, 50, 10,65 1,864 1,661 1,529 1,643 1,385
39 100, 62, 10,65 1,812 1,781 1,518 1,671 1,384
S-H o 40 112, 38, 10,65 0,959 0,637 0,728 0,489 0,604
o 41 112, 50, 10,65 0,782 0,662 0,532 0,528 0,454
42 112, 62, 10,65 0,787 0,770 0,481 0,588 0,503
43 124, 38, 10,65 0,795 0,824 0,804 0,769 0,633
44 124, 50, 10,65 0,828 0,801 0,825 0,735 0,706
45 124, 62, 10,65 0,960 0,753 0,835 0,676 0,790
46 100, 38, 13,95 1,919 1,666 1,525 1,616 1,384
eg ö 47 100, 50, 13,95 1,878 1,669 1,533 1,649 1,389
2 48 100, 62, 13,95 1,832 1,797 1,523 1,680 1,391
03 49 112, 38, 13,95 0,960 0,638 0,727 0,488 0,607
£ 50 112, 50, 13,95 0,781 0,662 0,530 0,527 0,454
o 51 112, 62, 13,95 0,786 0,772 0,480 0,587 0,502
Ph &H 52 124, 38, 13,95 0,800 0,827 0,808 0,770 0,633
o H 53 124, 50, 13,95 0,832 0,804 0,828 0,736 0,709
54 124, 62, 13,95 0,966 0,754 0,837 0,677 0,792
Figure 5. Comparison Graph of Displacement ait Observation Point 14 In Figure 5, for the building model without any barriers, the maximum displacement along the uz axis at observation point 14 due to seismic surface waves was uzmax= 0,819 mm. For the model with a 0.4-meter thick seismic barrier, uzmax=0,662 mm; with a 0.6-meter thick barrier,
uzmax=0,574 mm; with a 0.8-meter thick barrier, Uzmax=0,550 mm; and with a 1.0-meter thick barrier, Uzmax=0,465 mm. Comparatively, the effectiveness of the seismic barriers was observed as follows: the displacement at observation point 14 with a 0.4-meter thick barrier was reduced by 19.17%, with a 0.6-meter thick barrier - by 29.91%, with a 0.8-meter thick barrier - by 32.84%, and with a 1.0-meter thick barrier - by 43.22%, compared to the model without barriers.
Figure 6. Comparison Graph of Velocity at Observation Point 14 In Figure 6, for the building model without any barriers, the maximum velocity along the vz axis at observation point 14 due to seismic surface waves was vzmax=5,64 cm/s. For the model with a 0.4-meter thick seismic barrier, Vzmax=4,32 cm/s; with a 0.6-meter thick barrier, Vzmax=3,94 cm/s; with a 0.8-meter thick barrier, Vzmax=2,20 cm/s; and with a 1.0-meter thick barrier, Vzmax= 1,59 cm/s. Comparatively, the effectiveness of the seismic barriers was observed as follows: the velocity at observation point 14 with a 0.4-meter thick barrier was reduced by 23.40%, with a 0.6-meter thick barrier - by 30.14%, with a 0.8-meter thick barrier - by 60.99%, and with a 1.0-meter thick barrier - by 71.81%, compared to the model without barriers.
Figure 7. Comparison Graph of Acceleration at Observation Point 14 In Figure 7, for the building model without any barriers, the maximum acceleration along the az axis at observation point 14 due to seismic surface waves was azmax=92,29 cm/s2. For the model with a 0.4-meter-thick seismic barrier, azmax=67,59 cm/s2; with a 0.6-meter-thick barrier, azmax=60,32 cm/s2; with a 0.8-meter-thick barrier, azmax=32,55 cm/s2; and with a 1.0-meter-thick
barrier, azmax=28,70 cm/s2. Comparatively, the effectiveness of the seismic barriers was observed as follows: the acceleration at observation points 14 with a 0.4-meter-thick barrier was reduced by 16.22%, with a 0.6-meter-thick barrier - by 29.73%, with a 0.8-meter-thick barrier - by 55.95%, and with a 1.0-meter-thick barrier - by 69.11%, compared to the model without barriers.
Conclusion
This study investigated the impact of various thicknesses of seismic barriers placed around a building, with a radius of 28 meters and a height of 3 meters, on the seismic surface wave oscillation levels. The results led to the following conclusions:
Impact of Thickness:
For a seismic barrier with a thickness of 0.4 meters, the average reduction in seismic surface wave displacement is 8.40%, velocity is 18.00%, and acceleration is 22.75%.
For a seismic barrier with a thickness of 0.6 meters, the average reduction in displacement is 14.95%, velocity is 36.77%, and acceleration is 33.42%.
For a seismic barrier with a thickness of 0.8 meters, the average reduction in displacement is 15.38%, velocity is 51.98%, and acceleration is 37.77%.
For a seismic barrier with a thickness of 1.0 meters, the average reduction in displacement is 24.05%, velocity is 56.53%, and acceleration is 50.13%.
Effectiveness of Thicker Barriers:
Thicker seismic barriers are more effective at reducing the propagation of surface waves and significantly enhance the seismic safety of buildings.
A 1.0-meter-thick seismic barrier provides the highest level of reduction in surface wave oscillations, thus aiding in improving the safety of buildings in high seismic activity areas.
Practical Significance:
Thicker seismic barriers play a crucial role in protecting buildings from seismic damage, especially in areas with high seismic activity. The findings provide essential information for construction practices aimed at ensuring seismic safety. In summary, increasing the thickness of seismic barriers leads to a significant reduction in seismic surface wave oscillation levels around buildings. This demonstrates their importance in enhancing seismic safety and indicates that using thicker seismic barriers is an effective method for protecting buildings from seismic damage.
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