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When Romeo observed how the animals reacted to extended periods of stress — 30 minutes of restraint each day for seven days — the pattern was different.

After the animals were released from the restraint s, stress hormones surged higher in young rats than in adults. The rats endured the minute restraint each day for seven days.

The restraint is banned according to NYPD regulations but it is not illegal. He would have probably done both in much the same way: with elegance and restraint , yet radically.

Yet responses so far have been muted, with some activists calling for restraint. Even the provocateurs, it would seem, recognize the need for some restraint.

But an injured Israeli spirit is not one known for restraint. Attacking the brain, they warp the judgment, and weaken the power of restraint.

Numerical analysis using a sequential finite-element FE program in which the excavation, casting and restraining of the slab, and long-term changes of stress are all modelled.

This has been used extensively in the industry and is considered by many engineers to be intuitively correct. It is described in Section 2.

The non-FE process described in more detail later is ideally intended to achieve the same results as the FE process, using simpler forms of calculation, often with approximations to model some of the complexities listed earlier.

It will be shown, by means of a very simple example, that the non-FE process is fundamentally flawed and its results are meaningless in most cases.

Regardless of any approximations involved in modelling the complexity of the real situation, the process itself is wrong.

It will then be shown that the long-term EHPs are dependent on various properties of the ground, but not on the magnitude of stiffness.

The non-FE process uses elastic theory to compute stress or displacement distributions, with either linear or non-linear assumptions for the stress—strain behaviour of the clay.

Its application for calculation of heave pressures, the subject of this paper, is noted by Ellis and O'Brien , but a detailed procedure is not provided.

Calculations of this type can be carried out using computer programs such as Oasys PDisp Oasys, This paper is concerned with the process in which such programs are used, not with the programs themselves.

In the non-FE process, two calculations are carried out separately rather than in sequence. The main driver of the displacement is the removal of the weight of excavation, which may be modelled by upwards tractions on the clay surface at the level of the excavation.

The clay behaviour may be modelled by a range of constitutive models, although linear elasticity is often assumed at this stage. In some cases, additional components of heave may be added to this undrained calculation to allow for loss of suction and desaturation, or a certain amount of swelling of the clay if the excavation process is fairly slow.

The calculation is repeated assuming the clay to be fully drained, to represent the long-term state.

The behaviour of the clay is sometimes represented as linear elastic, or alternatively more complicated constitutive models may be adopted.

In the latter case, a series of calculations is needed, imposing different heave pressures, to establish the relationship between drained heave and long-term EHP.

If linear elastic behaviour is used, the stiffness may not necessarily be related to the undrained stiffness assumed in a on the basis of a consistent elastic material; this provides a simple way of introducing the non-linear behaviour of the clay, modelling reduced stiffness during swelling.

In separate calculations, the stiffness of the structural system i. The heave of the soil surface that occurs during excavation due to undrained constant volume deformation of the ground h 1 , as computed in a above.

Additional heave of the excavated surface that occurs before the slab is cast related to expansion of the soil due to swelling or loss of suction h 2.

The long-term deflection of the slab due to EHP, which gives the gradient of BC, related to the stiffness of the slab and of its restraints.

In the non-FE process, it is then assumed that the intersection of the dashed line and the solid curve point C shows the final state, indicating the EHP acting on the slab.

In practical situations, the response of the clay will not be the same at all points on the site as it will be affected by the proximity of piles and retaining walls, and possibly by excavations of differing levels.

Figure 3 shows a simple case of the more general situations represented by Figure 2. This is the case that will be studied in this paper.

By showing that the non-FE process yields the wrong result for a simple case, the process itself will be shown to be fundamentally flawed.

The following simplifications are adopted in Figure 3. The heave assumed before the slab is cast is taken to be only that due to undrained constant volume deformation of the clay h 1.

The slab is assumed to be rigid and rigidly restrained, so once it has been cast and restrained it has no vertical displacement.

As a result, component h 3 in Figure 2 is zero in Figure 3 , and the broken line representing displacement of the slab due to EHP is horizontal in Figure 3.

The behaviour of the clay is assumed to be linear elastic in both the undrained and drained phases, and its stiffness is assumed to be uniform and isotropic.

That is, different drained stiffnesses result in different final EHPs. In this illustrative example, the undrained stiffness is the same for all three cases, so point B does not change.

The type of problem represented by Figure 3 was analysed by both the FE process and the non-FE process described earlier. The water table was taken to be at ground level, with hydrostatic pressures in the initial and final, long-term states.

In the FE analyses, only the soil beneath the excavation was modelled, with the overburden above represented by surcharge; this replicates the normal procedure of the non-FE calculations.

The restrained slab, shown cross-hatched, was not included in the model, but its effect was represented by restraining the nodes at the surface of the clay.

For reference, all the material parameters used in the paper are recorded in Table 2. As will be apparent from the plotted results, a very coarse FE mesh was used for these analyses; the purpose was to demonstrate principles, not to produce accurate analyses of a real situation.

The base of the mesh was fixed in both horizontal and vertical directions, whereas the centre-line and the remote boundary, at distance 10 R , were allowed to slide vertically.

Figure 4. Computed water pressures in kPa after undrained excavation. In the non-FE process, the second calculation is a drained analysis starting from the initial state before excavation and ending at the long-term state, with the final heave of the slab and final EHPs.

Because it is assumed in this simple example that the slab is rigid and rigidly restrained, this can be achieved by imposing the vertical displacements derived from the undrained analysis on a separate drained analysis.

No horizontal restraint is provided, however, since none is available when the process is carried out in the programs normally used for the non-FE process.

Figure 5 shows the computed final EHPs. In the FE process, the second stage, representing the long-term state after the slab has been cast and restrained, is carried out sequentially from the undrained stage.

Since the slab was to be rigid, this was modelled by fixing the nodes vertically at the excavated surface in the positions they had reached in the undrained stage, changing the stiffness parameters to drained values and returning the water pressures to their initial hydrostatic values.

In order to be consistent with the non-FE process, the nodes at the excavated surface were not restrained horizontally in this analysis.

Figure 5 shows that the computed long-term EHPs were the same for these two runs. This leads to conclusion 1: for a consistent elastic material, the non-FE process successfully reproduces the results of the FE process.

It was found that the computed long-term EHPs were identical in these three runs using the FE process. Hence the second conclusion for this simple problem is: for the FE process, the long-term EHP is independent of the stiffness of the ground, E d , after the slab is cast and restrained.

This finding is directly contradictory to the assumption shown for the non-FE process in Figure 3 and verified in Figure 5.

This leads to conclusion 3: if the undrained and drained stiffnesses are not those of a consistent elastic material, the non-FE process is not successful in reproducing the results of the FE process.

It was noted earlier that the computed stress state at the end of undrained excavation is independent of the undrained stiffness E u.

As this stress state is the only driver for setting up the heave pressures, conclusion 3 can be extended to give conclusion 4: for the FE process, the long-term EHP is independent of both the undrained and drained stiffnesses E u and E d.

Figure 6 shows the computed displacements during transfer from undrained to drained stages in run FE1. Although the stress states at the end of the three FE runs were the same, the computed displacements were very different, being inversely proportional in magnitude to the drained Young's modulus E d.

Figure 6. Computed displacements during transfer from undrained to drained stages run FE1. The non-FE process represented by Figures 2 and 3 has been in use for many years and is thought to be intuitively correct.

However, consideration from a dimensional point of view shows that this is not so. This is now considered for the simplified linear elastic case investigated in this paper.

The resulting change of water pressure has the same units, so must be proportional to this.

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