【正文】 esive, . sand.Even dynamic problems may be studied by such a scale model, by noting that in that case the equations of motion contain terms of the type. These terms will be the same in the model and in the prototype if the time is scaled according to the square root of the length scale, ()Here it has been assumed that the density is the same in the model as in the prototype, which is easy to acplish, by using the same material. It may be noted that dynamic effects are important only for special problems, such as earthquakes and high speed trains. In the standard engineering problems dynamic effects usually play a minor role. Even in the cyclic loading of an offshore platform the dynamic effects are small because the period of the cycles (about 10 seconds) is so large.Problems of consolidation can also be studied in 1gmodels, at least in a first approximation. In the consolidation equation, ()all terms should then be scaled by the same factor. If all the stresses are scaled on the same scale (nL) as a length, in order to model equilibrium, and the deformations on scale 1, the term in the left hand side of the equation can be in agreement with the other terms only if time is scaled on the length scale, ()The first term in the right hand side of the equation then is not scaled correctly, because this term consists of a ratio of two factors at length scale. But in many cases this is a small term anyway, as the pressibility of the water () is very small. This means that the error in scaling the consolidation process will be very small.It follows from the considerations given above that it is impossible to take both consolidation and dynamic effects into account, as these two phenomena lead to different requirements for the time scale. An ingenious way to solve this difficulty is to scale the permeability, without changing the porous material, by using a different fluid in the model, having a different viscosity, such that the two terms scale in the same way.As mentioned before, all this does not apply if the material behavior is more plex than is indicated by eq. (). This will be so in the majority of problems, for instance in case of simultaneous elastic and plastic deformations, or in case of a cohesive material. This means that simple scale tests on clays are not representative for the behavior in the prototype. They can be used only if friction is the dominant property in the mechanical behavior, and the plastic deformations are relatively large.Centrifuge testingA general way of describing the relation between stresses and strains in a soil is ()where f is an arbitrary function, and hk indicates that there may be some other physical parameters involved in the functional relationship,such as the cohesion c, or the stiffness parameters K and G. Equation () states that the incremental strains are determined by the stresses and the incremental stresses, in a not yet specified manner. Various types of behavior can be described by relations of the type (), such as elastic and plastic deformations. Of particular importance is that the incremental strains depend upon the actual stresses. This means that the stiffness may depend upon the stresses, which is a typical property of many soils. Dilatancy and contractancy can also be described by the general relation (). And elastic deformations, in which the incremental strains are fully determined by the incremental stresses can also be described by (), of course.Assuming the validity of the general relationship (), model testing is possible only if the stresses and the strains are all modelled at scale 1, and that the same soil is used, to ensure that the properties are the same. This implies that the stresses caused by the weight of the material must also be modelled at scale 1. In the equations of equilibrium terms of the type appear with a term. In order to model both these terms at the same scale, the volumetric weightmust be inversely proportional to the length scale, ()This can be realized by rotating the model very fast, in a centrifuge. Gravity then appears to be magnified, see Figure . The facility consists of an arm that can be rotated around a central axis.Figure : Geotechnical centrifuge.At the two ends of the arm containers are placed, one containing the model, and the other containing a counter weight (or another model), to balance the arm. If the arm rotates a centrifugal force acts on the material in the two containers, which will rotate around a hinge. If the rotation is very fast the bottom of the two containers will be practically vertical.For safety, the centrifuge must be protected by heavy steel plates and concrete walls, to prevent damage in case of failure of a part of the system. For this reason the centrifuge is often located in the basement of a geotechnical laboratory.An elementary consideration of the motion of a body moving along a circular path, of radius R, indicates that an acceleration perpendicular to the path occurs, of magnitude ()This is called the centripetal acceleration. In the case of a container filled with soil that rotates in a centrifuge this acceleration is caused by the force from the container on the soil, and transmitted through the soil, in upward direction. If the soil were not contained by the container, it would fly on, in a straight path, but it is retained in its circular path by the container. This requires a very large force, and this force is larger if the velocity is larger, or the radius smaller (at the same velocity). The stress state would be the same if the container w。體積小，節(jié)約占地，造型美觀；造價比較低，具有良好的經(jīng)濟效益。（2）施工方便快捷。有荷載時： 有載土壓力計算(2) 抗滑穩(wěn)定性驗算無載時： 有載時：(3) 抗傾覆穩(wěn)定性驗算則無載時：有載時：（4） 地基應(yīng)力驗算無載時：則有荷載時：則所以加筋土擋土墻設(shè)計符合要求。（2） 由軌道和列車換算