Yatay yönde zorlanmış silindirik sıvı tanklarının zemin-yapı etkileşimi

Abstract

Bu çalışma, zemine oturan silindirik su tanklarının yatay zemin hareketi altındaki zemin-yapı etkileşimi üzerinedir. Tank, uniform duvar kalınlığına sahip olup, homojen yarı-uzay bir zemine oturtmaktadır. Hidrodinamik etkinin iki bileşeni olduğu düşünülmüştür: a)împulsif Tepki: Tank duvarıyla birlikte hareket eden sıvının tepkisi, b)Konvektif Tepki: Tank içindeki sıvının salınım (dalgalanma) hareketi. İmpulsif tepkide tank-sıvı sisteminin titreşimin temel modunda tek serbestlik dereceli bir sistem olarak davrandığı düşünüldü. Yer hareketi için, harmonik tepki, gerçek deprem kayıtları ve basit bir çarpma zoru gözönüne alındı. Öncelikle silindirik su tanklarında tank-sıvı arasındaki dinamik tepki incelendi. Tepkinin impulsif ve konvektif bileşenlerine ek olarak kabuktaki eksenel gerilmeleri veren ifadelere de yer verildi. Üçüncü bölümde tank-sıvı sistemine zemin ortamı da dahil edilerek üçlü bir sistem oluşturuldu ve bir model geliştirildi. Zemin ortamının idealize edilmiş şekli ve viskoelastik ortamda dinamik davranışın aldığı şekil anlatıldı. Dinamik tepkiler, harmonik ve sismik zora maruz sistemler için ele alındı. Dördüncü bölümde tepkinin konvektif bileşenini impulsif bileşenden bağımsız düşünme yaklaşımı üzerinde duruldu. Dinamik tepkinin konvektif bileşene etkisi incelendi. Beşinci bölümde ise tank ve zemin ortamını tek serbestlik dereceli bir sistem şeklinde idealize eden kütle-yay sistemi tanıtıldı. Bu sistemden elde edilen sonuçların doğruluğu araştırıldı.

This study is made of the effect of soil-structure interaction on the response of circular cylindrical tanks subjected to a horizontal component of ground shaking. The tanks are presumed to be of uniform wall thickness, filled with liquid and clamped to a rigid circular mat which is supported at the surface of a homogeneous elastic halfspace. The effect of foundation embedment is not considered. Both the foundation mass and the mass of the structure are assumed to be uniformly distributed over circular areas. The idealized structure may be viewed either as direct model of a one- storey building frame or, more generally, as the model of a single- degree-of-freedom in its fixed-base condition. The response quantities examined include the hydrodynamic pressures, the associated base shear and moments at sections immediately above and below the tank base. The irrelationship of the tank responses to horizontal and rocking actions of the foundation is established, and a model for laterally excited, rigid tanks supported on a non-deformable medium is generalized to permit consideration of the effects of tank and ground flexibilities and base rocking. The hydrodynamic effects are computed in two parts: (i) an implusive component, which represents the effect of the part of the liquid that may be considered to move in unison with the tank wall as a rigidly attached mass, (ii) a convective component, which represents the action of the part of the liquid that experiences sloshing motion. There are two aspects of interaction that must be considered: (i) the interaction between the tank and the contained liquid, (ii) the interaction between the tank-liquid system and the supporting medium. Fundamental to the formulation of the impulsive solution are the following assumptions: (i) in its fixed-base sondition, the tank-liquid system responses in its fundamental mode of vibration as a single- Xll degree-of-freedom, (ii) the impulsive effects are uncoupled from the convective effects. In this study, it was examined the consequences of soil-structure interaction on the convective components of response. The free-field ground motion investigated include a harmonic motion, a relatively simple pulse-type excitation and an actual earthquake record. Analyses of the seismic response of liquid storage tanks to horizontal ground shaking are normally carried out on the assumption that the tank base moves horizontally without any rotation. In reality, because of the flexibility of the supporting soils, the tank base experiences a rocking component of motion even under a purely translational free- field ground motion. The acceleration of this motion at any time, t, is denoted by yg(t), associated velocity and displacement are denoted by yg(t) and yg(t). The horizontal displacement of the foundation, x(t), is generally different from y(t). The foundation motion also includes a rotational or rocking component about a horizontal axis normal to the direction of the free-field ground motion. Denoted by 0(t), latter component would be expected to be particularly prominent for tall tanks and flexible soils. In this study, the effects of material damping of harmonically excited foundation was investigated. The halfspace is idealized as a linear viscoelastic solid and two models of viscoelastic action are considered: "The standard Voight model" and "the constant hysteretic model". The excitations investigated include a horizontal force and a moment about an axis in the plane of the foundation. The damping capacity of half-space material for "constant hysteretic solid is given by AW/W=2jt.tan8 where tan5=Q.G'/G G and Gy are the shear modulus of elasticity and viscosity, respectively. Q is circular frequency of excitation. For "Voight solid", the damping capacity is given by £=(l/a0).tan8 ao is dimensionless frequency parameter, defined as xm a0=(O.a)/c9 The dynamic response of a structure supported on soft soil may be different from the response of a similarly excited, identical structure supported on firm ground. There are two principal factors responsible for this difference: 1. The flexibly supported structure has more degrees of freedom and, consequently, different dynamic characteristics than the rigidly mounted structure. 2. A significant part of the vibrational energy of the flexibly supported structure may be dissipated by radiation of waves into the supporting medium or by damping in the foundation material. There is no counterpart of the latter effect in a rigidly mounted structure. The importance of the latter factor increases with increasing intensity of ground shaking. The response of the foundation-structure system obviously depends on the properties of the foundation and the supporting medium, the properties of the tank-liquid system and on the characteristics of the excitation. The effects of these factors can best be expressed in terms of dimensionless parameters. The three most important parameters of the problem are: 1. The wave parameter, o=c8/(f.h) f is the fixed-base natural frequency of the system in cycles per unit of time; cs is the speed of propogation of shear waves in the half-space;h is the distance from the base to the inertia forces for the asssumed mode. 2. The ratio H/a of the height of the structure to the radius of the foundation base. 3. The ratio fe/f of the excitation frequency to the fixed-base natural frequency of the system. The wave parameter a may be looked upon as a measure of the relative stiffness of the foundation and the structure. a=oo correspond to structure mounted on an infinitely rigid medium, whereas the remaining values are respresentative of systems in which the soil is relatively flexible in comparison to the structure. The other parameters are; * The material damping factor for the supporting medium, tanS. * The damping factor for the structure in its fixed-base condition, ç. * The relative mass density for the structure and the supporting medium, xiv y=m/(ps.7t.a h) * Poisson's ratio for the half-space material, vs. The response of the structure is generally intensitive to variations in these particular parameters. The interrelationship between x(t) and 8(t) may be established by two equilibrium; Equilibrium of horizontal forces requires that mf.x(t) + Qi(t) + Qs(t) = 0 Equilibrium of moments requires that lf.0(t) + Mi'(t) + Ms(t) =0 mf is the mass of the foundation; If is mass moment of inertia of foundation mat; Qs is the shear at the foundation-soil interface and Ms is the associated bending moment. Qs may be expressed in terms of x(t)- y(t) and Ms may be expressed in terms of 9(t). Qs and Ms depend on Kx and Ke respectively. Kx and Ke are the complex-valued stiffness of the foundation. For laterally excited foundation; Kx =K8X[kx(a0,vs) + i.a0nx(a0, vs)] For rocking motion; Ke =KSe[k6(ao,vs) + i.ao.ne(a0,vs)] K8X and KSe represent the static stiffnessof the foundation. Comprehensive response spectra are presented for a range of the parameters defining the problem and the results are used to assess the accuracy of a simple, approximate method of analysis in which the system is represented by a viscously damped, simple oscillator. In this system, the spring connected to the mass represents the elastic resistance of the structure, and its stifness, k, is equal to that of the fixed-base structure. The spring connected to the base accounts for the translational and rotational flexibilities of the foundation, whereas the dashpot accounts for the overall damping of the system. Two levels of approximation are used in the evaluation of the impulsive effects. In the precise method, the flexibility of the supporting medium is provided for directly by analysing the tank-liquid systems as an xv elastically supported system; whereas in the simpler, approximate procedure, it is provided for indirectly by modifying the dynamic properties of the system and evaluating the response of the modified system to the prescribed free-field ground motion considering the tank to be rigidly supported at the base. The simpler procedure is shown to be sufficient accuracy for most pratical purposes. The studies shown that soil-structure interaction decreases the resonant frequency of the system and modifies the magnitude of the peak response, decreasing the value for short squatty structures and increasing the values for tall, slender structures. For the squatty structure, the rocking of the foundation and the associated increase in response are quite important. The reduction in response due to the radiation effect is extremely small because the rocking component of the foundation response is more lightly damped than the horizontal component. Consideration of soil-structure interaction in a dynamic analysis is warranted for values of c less than 66.6. For values of a greater than about 66.6, the values of the frequency and damping are pratically equal to those for fixed-base systems. The interaction effects is negligible in this case (a value of 0=66.6 correspondens a soil with shear wave velocity, cs=600 m/sec). Soil-structure interaction has a negligible effect on the convective components of response and this may be evaluated for the free-field ground motion considering both the tank and the supporting medium to be rigid. The comparisons demonstrate that the convective solutions can be computed independently of the impulsive effects. It was shown that, the effect of material damping is two fold: It decreases the stiffness and increases the damping.