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0DETERMINING THE EFFICIENCY OF SEISMIC BARRIERS BASED ON THEIR HORIZONTAL AND VERTICAL
POSITIONING
1Yuldashev Sh.S., 2Abdunazarov A.Sh.
1Professor at NamECI 2Researcher of NamECI https://doi.org/10.5281/zenodo.13386720
Abstract. The article determines the effect of seismic surface waves on a building using the finite element method with the help of the Plaxis 3D software suite. The maximum displacement amplitudes at each point were determined. The efficiency of seismic barriers positioned horizontally and vertically was analyzed through contrastive comparison.
Keywords: building, seismic surface waves, finite element method, elasticity theory, seismic barrier.
Introduction. The idea of using horizontal barriers to protect against seismic surface waves was presented by Prof. S.V. Kuznetsov in his scientific research. The basis of the horizontal barrier concept is the Chadwick theorem, which states that Rayleigh waves cannot propagate along a compressed boundary of a semi-space. According to the conditions of the Chadwick theorem, a surface layer with physical-mechanical properties was considered. The principle of operation of the horizontal barrier is that the existence of such a surface layer with modified properties reduces the speed of Rayleigh waves passing through it, forming a "protected area" behind the barrier, which demonstrates the primary feasibility of using such a barrier for territorial seismic protection. The first results of experimental studies on vertical barriers were published in D.D. Barkan's book "Dynamics of Bases and Foundations." These studies examined linear barriers of finite depth. The experiments found a "protected" interval in the area behind the barrier.
Research Materials and Methodology Rayleigh waves propagate along the flat surface of a semi-space (Figure 1), attenuating with depth [1]. These waves transmit the most seismic energy and cause the greatest damage during an earthquake [1].
Reyle to'lqini
->
Figure 1. Schematic of Rayleigh surface wave propagation [1,2,3].
In the considered issue, the effectiveness of a seismic barrier in reducing the impact of Rayleigh surface waves on a building is determined and comparatively analyzed based on its positioning.
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 2).
Figure 2. Discretization of the soil model and residential building into finite elements.
Figure 3. Circular horizontal seismic barrier Figure 4. Circular vertical seismic barrier The circular horizontal seismic barrier is positioned 27 meters from the center of the building, with a thickness of 3 meters and a height of 1 meter (Figure 3).
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 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 = apVpù ryz = bpVsv rzy = bpVsw
ay = apVpv rxz = bpVsw rzx = bpVsu
az = apVpW" rxy = bpVsii ryx = bpVsv
(1)
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 2).
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
L
t _
|-3 ax 0 0 a dy 0 d dz
0 d dy 0 a dx d dz 0
0 0 d dz 0 d ay d dx.
(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, three components of stress corresponding to deformation are written as follows [1,2,3]:
{*} =
ox
T
xyj
The matrix [D] is determined from the following relationship between stress and deformation:
(£v) = —or +—ov;
\ JjQ £ X E y>
— ( \ — 1 —V £x ^^O = Effx EGy''
2 + (l + v) Yxy \YxyjQ = — T
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 computer process [3].
We adopt the time iteration coefficients for the Newmark method as 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 5. 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 6. Harmonic Force Law
[»10 J m]
ial
Figure 7. 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).
Table 2
Observation Points Coordinates (x,y, z) in Plane Horizontal Vertical
№ Displacement (mm) Displacement (mm) Displacement (mm)
1 100, 38, -3 1,527 1,459 1,305
(L> 2 100, 50, -3 1,518 1,477 1,291
<+H O 3 100, 62, -3 1,455 1,490 1,242
Is M & .5 ■o 2 4 112, 38, -3 0,912 0,706 0,503
5 112, 50, -3 0,825 0,596 0,467
§ ? 5 6 112, 62, -3 0,811 0,518 0,516
üg <D 7 124, 38, -3 0,722 0,648 0,630
H 8 124, 50, -3 0,772 0,686 0,678
9 124, 62, -3 0,859 0,753 0,779
10 100, 38, 0,75 1,539 1,470 1,312
11 100, 50, 0,75 1,535 1,493 1,301
12 100, 62, 0,75 1,465 1,499 1,254
!-H o 13 112, 38, 0,75 0,915 0,705 0,505
o G 14 112, 50, 0,75 0,819 0,589 0,465
K 15 112, 62, 0,75 0,809 0,515 0,513
16 124, 38, 0,75 0,729 0,651 0,633
17 124, 50, 0,75 0,775 0,686 0,681
18 124, 62, 0,75 0,867 0,754 0,779
19 100, 38, 4,05 1,683 1,545 1,345
20 100, 50, 4,05 1,670 1,556 1,344
21 100, 62, 4,05 1,608 1,549 1,320
!-H o 22 112, 38, 4,05 0,933 0,695 0,554
G T3 23 112, 50, 4,05 0,797 0,570 0,458
c (N 24 112, 62, 4,05 0,797 0,512 0,508
25 124, 38, 4,05 0,758 0,656 0,633
26 124, 50, 4,05 0,800 0,685 0,692
27 124, 62, 4,05 0,903 0,766 0,782
28 100, 38, 7,35 1,822 1,592 1,367
29 100, 50, 7,35 1,802 1,593 1,371
30 100, 62, 7,35 1,742 1,581 1,362
!-H o o c 31 112, 38, 7,35 0,950 0,693 0,587
32 112, 50, 7,35 0,785 0,561 0,455
-a !-H 33 112, 62, 7,35 0,790 0,511 0,505
34 124, 38, 7,35 0,782 0,660 0,632
35 124, 50, 7,35 0,819 0,686 0,701
36 124, 62, 7,35 0,938 0,779 0,786
37 100, 38, 10,65 1,897 1,617 1,380
38 100, 50, 10,65 1,864 1,611 1,385
39 100, 62, 10,65 1,812 1,598 1,384
i-H o 40 112, 38, 10,65 0,959 0,691 0,604
o r! 41 112, 50, 10,65 0,782 0,557 0,454
42 112, 62, 10,65 0,787 0,510 0,503
43 124, 38, 10,65 0,795 0,663 0,633
44 124, 50, 10,65 0,828 0,688 0,706
45 124, 62, 10,65 0,960 0,786 0,790
46 100, 38, 13,95 1,919 1,624 1,384
eg 47 100, 50, 13,95 1,878 1,615 1,389
is '3 48 100, 62, 13,95 1,832 1,604 1,391
m 49 112, 38, 13,95 0,960 0,689 0,607
£ t+H 50 112, 50, 13,95 0,781 0,555 0,454
O "Ë 51 112, 62, 13,95 0,786 0,510 0,502
c3 PH 52 124, 38, 13,95 0,800 0,664 0,633
C o H 53 124, 50, 13,95 0,832 0,689 0,709
54 124, 62, 13,95 0,966 0,789 0,792
When modeling horizontal and vertical seismic barriers to reduce the impact of seismic surface waves on the building, the values of uz at the nodes were compared using the pre-designated observation points of the building (Table 2).
0,00 1,00 2,00 3,00 4,00 5,00
Figure 8. Contrastive Comparison Graph of Displacement at Observation Point 5
In Figure 8, for the building model without any barriers, the maximum displacement along the uz axis at observation point 5 due to seismic surface waves was Uzmax=0,825 mm. When a horizontal seismic barrier was present, Uzmax=0,596 mm, and with a vertical seismic barrier, Uzmax=0,467 mm.
Comparatively, the effectiveness of seismic barriers was observed as follows: the displacement at observation point 5 with a horizontal seismic barrier was reduced by 27.81% compared to the model without barriers, and with a vertical seismic barrier, it was reduced by 43.38%.
0,00 1,00 2,00 3,00 4,00 5,00
Figure 9. Contrastive Comparison Graph of Velocity at Observation Point 5 In Figure 9, for the building model without any barriers, the maximum velocity along the vz axis at observation point 5 due to seismic surface waves was Vzmax=5,501 cm/s. When a horizontal seismic barrier was present, Vzmax=3,767 cm/s, and with a vertical seismic barrier, Vzmax=2,674 cm/s. Comparatively, the effectiveness of the seismic barriers was observed as follows: the velocity at observation point 5 with a horizontal seismic barrier was reduced by 31.52% compared to the model without barriers, and with a vertical seismic barrier, it was reduced by 51.39%.
Figure 10. Contrastive Comparison Graph of Acceleration at Observation Point 5 In Figure 10, for the building model without any barriers, the maximum acceleration along the az axis at observation point 5 due to seismic surface waves was azmax=43,23 cm/s2. When a horizontal seismic barrier was present, azmax=37,15 cm/s2, and with a vertical seismic barrier, azmax= 17,74 cm/s2. Comparatively, the effectiveness of the seismic barriers was observed as follows: the acceleration at observation point 5 with a horizontal seismic barrier was reduced by 14.06% compared to the model without barriers, and with a vertical seismic barrier, it was reduced by 58.96%.
Conclusion. Compared to a building without any barriers, the seismic barriers showed the following effectiveness at the same coordinates: For the model with a horizontal seismic barrier, the average displacement was reduced by 15.13%, velocity - by 23.68%, and acceleration - by 33.11%. For the model with a vertical seismic barrier, the displacement was reduced by 24.05%, velocity - by 56.53%, and acceleration - by 50.13%. The effectiveness of both horizontal and vertical seismic barriers in reducing the impact of seismic surface waves was determined and
comparative analyses were conducted. Based on the results, it can be stated that vertical barriers are more effective than horizontal barriers, providing greater protection against damage to buildings and structures.
REFERENCES
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