THE ISSUE OF VOLUME
In the supervisor group of the TEPPFA project, an explanation for the fact that depth and traffic, as examples of increased load, has hardly any influence on the final pipe deflection was given. Looking at the installation at it's different phases and the measurements it was concluded that the soil undergoes significant changes during and after installation. Janson referred already to this phenomenon in 1990. In case of good soil and or in combination with proper compaction, these changes are very small. In case of loose soils however, these changes are considerable. But they are however not considered in the current design methods. They all work with constant soil stiffness independent of the changes occurring in the soil. Some reflect that higher in-situ stress results in higher grain stresses and hence higher soil stiffness. Nevertheless, they do not consider the change of volume in the soil by settlement.
The change of volume is first related to the change of relative density.
The relative density can be expressed as follows:
Dr = (nmax - nx) / (nmax-nmin)
n = (Vtot - Vsoil) / Vtot
In which :
Drrelative density [-]
VtotTotal volume = Vvoid + Vsoil[m3]
VsoilVolume of soil[m3]
VvoidVolume of voids[m3]
The change of the relative density depends very much on the type of soil. With well- graded gravel, the change from loosely packed soil and compacted soil hardly involves volume changes. Silty-sand however, involves considerable volume change when it changes from loosely packed to highly packed. Volume change is related to displacements and the soil stiffness related to load-displacement, hence in the latter case the changes affect the soil stiffness considerable. Due to artificial (traffic, groundwater etc) or natural compaction, the value of the relative density will increase up to 80%-100% in the course of time. The effect of the change of relative density on the soil modulus can be exercised with this porgramme. The graph is based on the observations in the TEPPFA project where the soil modulus was measured using several different methods for loose and well-compacted soils. In the literature other curves can be found, depending on the way they have been achieved. The tendency (slope) of the curve fits well with graphs found in literature. It is felt that more exact graphs can be obtained
From the comparison of the methods with the field experience it became clear that all design methods are able to predict the pipe deflection well when they consider well compacted soils. In this situation, the soil stiffness is not changing and hence the formulas are correct as far as the soil stiffness is concerned. It is also shown by all methods that in such case the pipe deflection or in case of the more rigid pipes the crown load, stay rather low and design of the ring performance is not important. Design gets more relevant when a good compaction can not be achieved because the soil is poorly graded, cohesive, or the field circumstances are poor.
In such cases most design methods do not represent the performance in a correct way. As an example, when pipes are buried in weak soils, one can no longer utilise the same load distribution around the pipe as with firm granular soils. The soil will slide immediately or in the course of time and hence changing the load distribution around the ring.
It shall be mentioned that some methods, like the one from Molin, has recognised that the deflection could not be explained by means of the Spangler formula only and therefore added installation and bedding factors, which cover the effects of uneven bed and installation.
THE VOLUME APPROACH
The volume approach is not a design method on itself, but an approach that can be used with all of the methods used. It introduces the effect of the changing soil properties on pipe deflection, which is by far more important than the effect of the changing geometry on the pipe deflection.
The volume of the soil (grains) does not change during the process and is related to the original porosity, so the porosity before the pipe starts to deflect. This volume can be determined by:
vsoil =(1-n0/100)* (b*d-pi/4*d*d)
The total volume changes when the pipe deflects and can be determined by:
vtotal =b*(d-delta)-( p/4*(d*d-delta*delta))
The volume of the voids changes affecting the porosity according:
Finally, a new relative density can be calculated, which introduces a new soil modulus, as was illustrated in figure 2.
In the following, this approach was utilised with a Spangler-like formula; the one proposed by Jan Molin. In order to simulate the process, small load steps are applied. After each step the pipe deflection and the effect on the relative density of the soil is calculated. The next load step is then applied using the increased soil modulus.
The best research approach, is to start with experiments before building mathematical models. Such models are only useful when they reflect the physics of a process. If not then they might become very misleading. Especially when the models also get less transparent. As a matter of fact, it shall never be accepted to utilise mathematical or numerical approaches if they have not been reflected against experimental results. Experimental results better come from fully true practice, or when that is not possible, from laboratory type of tests in which at least part of the model can be verified. In the TEPPFA / APME project both types of experimental work was performed. The field tests were carried out to obtain a good estimate of the actual values, and laboratory tests performed in order to verify the understanding of the physics. The test model used was a transparent box in which soil and pipe were built in. The soil was then loaded by means of a cantilever. Pictures were made after short time intervals. These pictures were used to measure the deflections and the pipe subsidence. Moreover, the pictures serve for running animations on this CD in order to obtain a better understanding of the pipe soil interaction process.
The load increase by means of a cantilever and the change of relative density is not accurately reflecting the change of density in real life. In real life the soil density changes from bottom to top, whereas in the experiments the density change progresses as a moving front from top to bottom. This also indicates that one shall be careful with the interpretation of results obtained in soil boxes and cells.