Stefan Van Baars

Numerical check of the Meyerhof bearing capacity equation for shallow foundations

Most geotechnical design codes and books use the equations of Meyerhof or Terzaghi to calculate shallow foundations. These equations are based on the failure mechanism published by Prandtl for shallow strip foundations. The common idea is that failure of a footing occurs in all cases according to a Prandtl-wedge failure mechanism. To check the failure mechanism and the equations of the currently used bearing capacity factors and correction factors, a large number of finite-element calculations of strip and circular footings have been made. The finite-element calculations show that in cases of soils with high friction angles, soils without cohesion or a surcharge, footings with inclined loading or circular footings, not the Prandtl-wedge failure mechanism, but other failure mechanisms occur. In addition, the currently used equations for the bearing capacity factors and correction factors are too high. Therefore, new equations have been presented in this article. For some correction factors, for example, the inclination factors and the cohesion slope factor, an analytical solution is found.Most geotechnical design codes and books use the equations of Meyerhof or Terzaghi to calculate shallow foundations. These equations are based on the failure mechanism published by Prandtl for shallow strip foundations. The common idea is that failure of a footing occurs in all cases according to a Prandtl-wedge failure mechanism. To check the failure mechanism and the equations of the currently used bearing capacity factors and correction factors, a large number of finite-element calculations of strip and circular footings have been made. The finite-element calculations show that in cases of soils with high friction angles, soils without cohesion or a surcharge, footings with inclined loading or circular footings, not the Prandtl-wedge failure mechanism, but other failure mechanisms occur. In addition, the currently used equations for the bearing capacity factors and correction factors are too high. Therefore, new equations have been presented in this article. For some correction factors, for example, the inclination factors and the cohesion slope factor, an analytical solution is found.

Numerical Check of the Meyerhof Bearing Capacity Equation for Shallow Foundations

In 1920 Prandtl published an analytical solution for the bearing capacity of a strip load on a weightless infinite half-space. This solution was extended with a surrounding surcharge by Reissner and with the soil weight by Keverling Buisman. It was Terzaghi who wrote this with three separate bearing capacity factors for the cohesion, surcharge and soil-weight. Meyerhof extended this to the equation which is nowadays used; with shape and inclination factors. He also proposed equations for the inclination factors, based on his own laboratory experiments. Since then, several people proposed updated equations for the soil-weight bearing capacity factor, and also for the shape and inclination factors.

PROPAGATION OF HARMONICAL VIBRATIONS IN PEAT

In order to check the reliability of man-made vibration prediction methods, vibration tests were performed on one of polders in the North-West of the Netherlands. The polder was chosen because it has a rather homogenous, thick and soft peat top layer. Here sufficient harmonical vibrations could be generated by a rather small shaker. The shaker was designed and manufactured in order to produce harmonical vibrations at the soil surface. It consists of two counter rotating electric vibrators (with rotating eccentric masses) in order to produce a vertically oscillating force. For the recordings of the vibrations, six 2D or 3D geophones were placed on the soil surface and one 2D geophone was placed on top of the shaker. The measured vibration amplitudes of the vertically oscillating shaker were compared with 1. Two different analytical methods used for the design of vibrating machine foundations, 2. The Confined Elasticity approach and 3. The Finite Element Method, for which Plaxis 2D software was used. Also the measured vibration amplitudes at the soil surface were compared with Barkan- Bornitzs solution and Finite Element Modeling.

Landslides in Urban Areas of Luxembourg, Caused by Weak Rheatian Clay

Luxembourg is geologically divided into two parts: Oesling in the North and Gutland in the Middle and South. Oesling is part of the Ardennes plateau. Gutland was formed in the Triassic and Jurassic ages and is much younger than Oesling. It consists mainly of sedimentary rocks. Luxembourg has a variety of interesting, weak or problematic soils, such as the swelling gypsum layers, the layered schists of Wiltz and especially the weak Keuper-Rhaetian-clay. The Rhaetian clay layer is mostly rather thin and is found at a relatively constant altitude and the band where it comes to the surface is identified by the varying erosion erratically found throughout Gutland. Approximately two third of all landslides are found along this line. Hence it was decided to investigate the Rhaetian clay in the geotechnical laboratory of the University of Luxembourg. Samples were taken from a pit at Rue de Muhlenbach on the north side of the city of Luxembourg and from a sliding slope of a building pit in Schutrange. The friction angle was found to be ϕ = 8° at Muhlenbach and ϕ = 13° at Schuttrange, which are both record low friction angles, which explains the high number of landslides in Luxembourg.

Seismic Techniques for Surveying the Underground of Shallow Foundations

For civil structures founded on shallow foundations, the ground underneath the foundation often holds the greatest risks of the total structure. This can be due to of a very soft soil layer, an inhomogeneous subsurface or a hidden dangerous object. It would be most favorable when a cheap and quick kind of seismic “tap-and-listen” technique can be used to detect those risks. The problem is however that an applied pulse or blast always creates a combination of compression-, shearand surface-waves. These types of waves have different wave velocities and will return therefore at different time intervals. For a shallow subsurface technique, all these waves will overlap, which makes the interpretation very hard. Both the single pulse technique and the single-frequency, multiple wave technique (constant vibration) have been studied, but both techniques have their limitations. It can be concluded from finite element calculations that it will be difficult or even impossible to design good seismic techniques for surveying the underground of shallow foundations for hidden shallow objects like water pipelines, undetonated bombs, dead bodies, coffins, potholes, etc.. The main reason is that the relative amount of reflected energy is simply too low in comparison to the energy of the still present original wave.