Ground motion and structural vibration reduction using periodic wave bamer as a passive isolation A. Niousha, M. Motosaka Disaster Control Research Center, Graduate School of Engineering, Tolzoku University, Japan Abstract Seismic waves, machine foundation, traffic or blasting generates waves that adversely affect nearby structures and the operation of sensitive equipment. Various countermeasures have been advised to reduce the ground-transmitted vibration. conventionally the installation of trench. base isolation or active mass driver. In this study, the periodic wave barrier is introduced as a passive isolation to reduce the ground transmitted wave and the structural vibration. A one-dimensional soil model is first investigated for incident shear wave. The propagation and the attenuation zone of the periodic element are discussed. The effect of barrier's numbering, contrast, width and spacing are parametrically studied. A more realistic two-dimensional model is made based on this result. The reduction of the ground and structure response due to ground-transmitted wave by using the proposed device is investigated. It is concluded that periodic wave barrier can reduce transmitted waves in the range of attenuation zone of the periodic element. l Introduction Seismic waves. machine foundation, traffic or blasting generates waves that can adversely affect nearby structure and operation of sensitive equipments. Various countermeasures have been advised to reduce the groundtransmitted vibration, conventionally the installation of trench. base isolation or active mass driver. The problem of screening of incident wave by deep trenches. canyons or rock zone was observed in the past by the seismologists and earthquake engineers. These natural phenomena lead to the use of wave barrier (open or in-filled) to control the propagation waves due to vibration or seismic wave incidence.
192 Earthquake Resrstant Engineer~ng Strzmwes 111 The ground-transmitted wave can be isolated in a passive or active manner [l] by various type of wave barrier, such open trench or in-filed trench [2] or row of solid piles [3]. Barkan (1962), Dollings (1965), Neumeur (1963) were the first to report a number of practical cases of vibration isolation. The fist two authors also presented some field test results and suggest some guidelines. Woods (1968) perform a series of field experiments for active (near to source) and passive (far from the source) open trench and give some guideline to reduce the ground amplitude of 75% or more [l]. In 70th due to ever increasing of computational machine's speed, researchers have used various numerical techniques to study the vibration screening, such as FDM, FEM and BEM. Waas (1972) used frequency domain FEM with consistent boundary to study the screening effect of incident SH wave by the open trench. Aboudi (1973) used the FDM to discuss the effect of thin barrier in an elastic half space. Haupt (1977-78) used FEM method to investigate the used of solid trench for passive and active isolation, he performs some experimental model to verify his analytical results. Segol(1978) used FEM for 2-D model to study the screening by open or infill trench and his finding are some agreement with Woods (1968) results. Fuyuki and Matsumoto (1980) used FDM to investigate the Rayleigh wave scattering by rectangular trench and conclude that the effect of width and depth could be significant, whereas Woods (1968) and Segol(1978) concluded that the width is not important [2]. The use of row of piles is also studied by researchers to isolate the unwanted waves. Aviles [4] analytically studied the foundation isolation from vibration using piles as a barrier. Later Kattis [3] make a 3-D modeling of the pile barrier (BEM) replacing by an effective trenches to reduce the problem size. In all these researches, no attention was given to the possibility of screening the unwanted waves by a periodic wave barrier. A periodic system is well known for its filtering effects. Brillioun (1953) traced the history of this subject to 300 years ago to Sir Isaac Newton, but until 1887 the model consisted of lumped-mass joint with mass less spring. During 1900-1960, several mathematical techniques were developed for analyzing the system which lead to Mead [5] work who discussed theoretically the mono-couple and multicouple periodic element using the receptance (flexibility) matrix. He discussed the propagation zone and the attenuation zone of the periodic element This idea is well advanced in the mechanical engineering and acoustic [6]. This study aims to analytically investigate the possibility of screening of ground transmitted wave and reduction of structural vibration by periodic wave barrier. First a one-dimensional soil model is discussed and by using results obtained at this stage. Then a more realistic two-dimensional model is made. 2 Description of method 2.1 One-dimensional model For better understanding the effect of periodic wave barriers, a l-d model is first investigated (Fig.1). The results obtain at this stage will be used to select the 2-D
Earthquake Res~stant Engrneer~ng Strucrwes Ill 193 Y Element -1 Element -n Element Figure 1: One-dimensional periodic wave barrier. model. The transfer matrix method, which Fukuwa et al. [7] also used in their work, is applied to the propagation of shear wave. In this simple model, the flexibility (receptance) matrix is calculated and the propagation and attenuation zones are obtained. Let the amplitude of harmonic displacements at the left and the right hand side of the single element be g, and g, and corresponding forces at these co-ordinates be P, and P,, respectively. The transfer matrix of a system can be written as follow: where where Vs, and VJg are the shear velocity of the barrier and ground, respectively. The transfer matrix can be written in the form of flexibility matrix (eq.3)
194 Earthquake Resistant Engineering Structures 111 Finally by replacing qr= ep g, and PT = ep P, in eq.3 and solving the homogenous equation, the propagation and attenuation zone can be found using the following relation with the propagation constant of p: The propagation zone exists, where, that provided p is imaginary, and this occurs when -1 S coshp d. Effects of barrier's spacing, width, contrast and numbering are investigated. 2.2 'ho-dimensional model A 2-D model is considered to investigate the effect of periodic wave barrier in a more realistic model. The soil, the wave barriers and the strcture are assumed to model by a simple 2-D model. The hyperelement method is applied to the wave propagation analysis of the model. The method originally proposed by Kaussel and Roesset [g] for 2-D planar strain and axisymmetric case of layered stratum. The technique is based on the calculation by finite element method of the semidiscrete solution (modes of vibration) satisfying homogenous boundary conditions on the surface and the base. In this method an objective structure is divided into plural regions with horizontal layers. Each region is modeled using a hyperelement. The nodes of the hyperelement are placed at the interfaces of the thin layer elements on both sides of the region. Nagano and Motosaka [9] have extended it to a 3-D response of a 2-D model for the case of planar incident waves with an arbitrary azimuth and incident angle. To show the effectiveness of propose device, vertical point excitation are applied to the periodic vertical barriers model. The reducing factor (R), which is the ratio of amplitude of the observation point with barrier to the amplitude of the motion without barrier, is discussed. 3 Effects of model's parameters The effects of barrier's contrast, spacing, width and numbering are discussed at this part. Fig. 2 shows the variation of Icoshp I for the first three cases. A three barriers model is used at this stage. The ground shear velocity is assumed to be 250 m/s
Ear-thquake Resrstant Engrneerrnp Structur.es 111 195 0 1 2 3 4 Contrast VsbIVsg (a) 0 2 4 6 8 10 Barrier width (m) (b) Barrier spacing (m) Figure 2: variation of Icoshd for the effects of (a) contrast, (b) width and (c) spacing.
Earthquake Resistant Engineering Stlwttires 111.. 4. 1 2 3 number of barrier Figure 3: Variation of the transmitted wave amplitude for the effect of barrier's numbering. without damping. Fig 2(a) shows the effect of contrast (VsblVsg). The barrier wi~ dth is selected 4m and spacing 8m. It is shown that low velocity barrier is more effective in lower frequencies, while high velocity one can be used for higher frequencies screening. It is shown that increasing of contrast to more than 4 has almost not more effect in attenuation zone's range. A barrier shear velocity of 1004 s with spacing of 8m is selected for studying the effect of barrier's width. Fig 2(b) shows that by increasing of this parameter, lower frequencies range can be in attenuation zone. The effect of barrier spacing is studied next. The Barrier's velocity of 100 m/s and width of 4m are taken. It is observed (Fig.2(c)) that by increasing the barrier's spacing wider attenuation zone and lower frequencies in attenuation zone is obtained. The effect of barrier numbering is discussed in Fig.3. The amplitude of the transmitted wave through the system due to incident wave of unit amplitude is shown for different numbering of barriers. It is concluded that increasing the barriers numbering up to three barriers, the filtering can be more effective. Having this information a more realistic two-dimensional model is made, which will be discussed in the next part. 4 Application As an example to show the effectiveness of the propose device, the ground motion and structural response reduction using this passive isolation is study in this part. Based on the obtained results at the previous part, a two dimensional model with vertical periodic wave barrier is made Fig.4. The applied load is a harmonic unit amplitude vertical point excitation at 50m from the structure's side. The point excitation generatated wave that spread-out as a circular form from the source. A layered half space with depth of H=20m, Vs,=250m/s and Vs,=SOOm/s are considered. The structure is assumed to be model like the soil region, with dimension of hs=lom and width of b=30m, shear velocity of the 140m/s, density of 250kglm3
Earthquake Reststanr Engrneerrng Structures 111 197 L=50m <. Screening area Figure 4: Two-dimensional analytical model. Table 1: Soil, barrier and structure properties. 500 1.80 Bamer 100 1.50.33.05 0.25.33.03 and damping of 5%. The soil, barriers and structure's physical properties are shown in Table 1. The calculation points are selected at the top of building and ground surface, behind the structure every 20m. First a single wave barrier with depth of 201x1 and width of 4 m is considered (barrier No.1). The reduction factor (R) of the horizontal and vertical response in the screening zone is shown in FigS(a) and (b). By repeating the barriers and using three periodic barriers with 8m spacing, the reduction factor (R) is calculated and shown in Fig.6(a) and (b). It is clearly shown that a periodic wave barrier is more effective than a single one. A reduction of 70-90% is observed at the screening zone. The structural responses at the top of structure for different investigated cases are also shown in Fig.7. It can be seen that the reduction is recognized in higher modes. These frequencies are in the range of attenuation zone of the periodic element. 5 Concluding Remarks A periodic wave barrier is presented as a passive isolation to reduce the ground transmitted waves. This device can reduce the wave's amplitude in the attenuation zone of the periodic element. It is shown from l-dimensional model that low velocity barrier is effective in
198 Ea~thqzlnke Reslstnr~t Engineering St~ucrures 111 20 40 60 80 100 120 140 160 Distance h m the barrier (m) [a) Horizontal motion 20 40 60 80 100 120 140 160 Distance from the barrier (m) h) Vertical motion Figure 5: Variation of reduction factor (R) for single bamers. (a) Horizontal motion - (b) Vertical motion lower frequency range, while a high velocity one can be used to reduce the higher frequency range. Although a single barrier can reduce the ground transmitted wave, but the use of periodic wave barrier can be more effective in the attenuation zone of the periodic system. The screening effect can increase with the number of barrier up to three. By changing the material property of the barrier, width or spacing one can define
Earthquake Resistant Engineering Structures I11 199 20 40 60 80 100 120 140 Distance from the barrier (m) 160 (a) Horizontal motion 20 40 60 80 100 120 140 160 Distance from the barrier (m) (b) Vertical motion Figure 6: Variation of reduction factor (R) for three barriers. (a) Horizontal motion - (b) Vertical motion the desired frequency range to reduce the structural response. References [l] Richard, F.E. et al., Vibrations of Soils and Foundations, Prentice-hall
200 Earthquake Resistant Engu?eerlng Strzlctures 111 30 20 10 No Barrier -..-. l Barrier 3 Barriers 0 I I I I l' 2 4 6 8 1 0 2 4 6 8 1 0 Freq. (Hz) Freq. (Hz) Figure 7: Response at the top of structure (bl2). (a) Horizontal motion (b) Vertical motion international series, 1970. [2] Ahmad, S. & Al-Hussaini, T.M, Simplified design for vibration screening by open and in-filled trenches, J. of Geotechnical Engineering, 117,1, pp. 67-88,1991. [3] Kattis, S.E. et al., Modeling of pile wave barriers by effective trenches and their screening effectiveness, Soil Dynamics and Earthquake Engineering, 18, pp. 1-10, 1999. [4] Avallis J. & Sanchez-Sesma FJ. Foundation isolation from vibration using piles as barriers, J. Engineering Mechanics ASCE, 114, pp.1854-1870, 1988 [5] Mead D.J., A general theory of harmonic wave propagation in linear periodic systems with multiple coupling, Journal of Sound and Vibration, 27(2), pp. 235-260,1973. [6] Mead, D.J., Wave propagation in continuous periodic structure: Research contributions from Southampton 1964-1995, J. of Sound and Vibration, 190(3), pp. 495-524, 1996. [7] Fukuwa N. et al., A study of the dynamic characteristics of the periodic structure using transfer matrix method, J. Structure and Construction Eng. AIJ, No.421, pp.101-108, 1991. [8] Kaussel E. and Roesset J.M., Semi-analytical Hyperelement for layered strata, J. Engineering Mechanics, ASCE, 103(4), pp. 596-588, 1977. [g] Nagano M. and Motosaka M.: Response analysis of 2-D structure subjected to obliquely incident waves with arbitrary horizontal angles, J. Structure and Construction. Eng. AIJ, No.474, pp.67-76, 1995.