M. D. Bolton

The fractal crushing of granular materials

Abstract A study has been made of the micro mechanical origins of the irrecoverable compression of aggregates which comprise brittle grains. The terms “yielding” and “plastic hardening” are used in the discipline of soil mechanics to describe the post-elastic behaviour of granular media. These “plastic” phenomena are here related to the successive splitting of grains. Grains are taken to split probabilistically; the likelihood increasing with applied (macroscopic) stress; but reducing with any increase in the co-ordination number and with any reduction in particle size. When the effect of the co-ordination number dominates; a simple numerical model confirms published findings that a fractal distribution of particle sizes evolves from the compression of an aggregate of uniform grains. Taking the production of new surface area from the particle size distributions produced by the numerical model; a work equation is used to deduce the plastic compression of voids; for one-dimensional compression of the aggregate. This too is shown to be in agreement with experimental data; and in particular confirms the linearity of plots of voids ratio versus the logarithm of stress. The gradient of these plots is for the first time related to fundamental material parameters.

Effects of brain ventricular shape on periventricular biomechanics: a finite-element analysis.

OBJECTIVE A computer simulation based on the finite-element method was used to study the biomechanics of acute obstructive hydrocephalus and, in particular, to define why periventricular edema is most prominent in the anterior and posterior horns. METHODS Brain parenchyma was modeled as a two-phase material composed of a porous elastic matrix saturated by interstitial fluid. The effects of the cerebrovascular system were not included in this model. The change in the shape of the ventricles as they enlarged was described by two variables, i.e., the stretch of the ependyma and the concavity of the ventricular wall. The distribution of stresses and strains in the tissue was defined by two standard mechanical measures, i.e., the mean effective stress and the void ratio. RESULTS With obstruction to cerebrospinal fluid flow, the simulation revealed that the degree of ventricular expansion at equilibrium depended on the pressure gradient between the ventricles and the subarachnoid space. Periventricular edema was associated with the appearance of expansive (tensile) stresses in the tissues surrounding the frontal and occipital horns. In contrast, the concave shape in the region of the body of the ventricle created compressive stresses in the parenchyma. Both of these stresses seem to be direct consequences of the concave/convex geometry of the ventricular wall, which serves to selectively focus the forces (perpendicular to the ependyma) produced by the increased intraventricular fluid pressure in the periventricular tissues. CONCLUSION The distribution of periventricular edema in acute hydrocephalus is a result not only of increased intraventricular pressure but also of ventricular geometry.

Stiffness of Clays and Silts: Normalizing Shear Modulus and Shear Strain

AbstractAn analysis is presented of a database of 67 tests on 21 clays and silts of undrained shear stress-strain data of fine-grained soils. Normalizations of secant G in terms of initial mean effective stress p′ (i.e., G/p′ versus log γ) or undrained shear strength cu (i.e., G/cu versus log γ) are shown to be much less successful in reducing the scatter between different clays than the approach that uses the maximum shear modulus, Gmax, a technique still not universally adopted by geotechnical researchers and constitutive modelers. Analysis of semiempirical expressions for Gmax is presented and a simple expression that uses only a void-ratio function and a confining-stress function is proposed. This is shown to be superior to a Hardin-style equation, and the void ratio function is demonstrated as an alternative to an overconsolidation ratio (OCR) function. To derive correlations that offer reliable estimates of secant stiffness at any required magnitude of working strain, secant shear modulus G is norma...

Communicating Hydrocephalus: The Biomechanics of Progressive Ventricular Enlargement Revisited

BACKGROUND This article investigates the physical mechanisms involved in the chronic ventricular enlargement that accompanies communicating hydrocephalus (CH)--including its normal and low-pressure forms. In particular, it proposes that this phenomenon can be explained by the combined effect of: (a) a reversal of interstitial fluid flow in the parenchyma, and (b) a reduction in the elastic modulus of the cerebral mantle. METHOD To investigate this hypothesis, these changes have been incorporated into a finite element computer simulation of CH, in which brain tissue is idealized as a sponge-like material. The fluid pressure in the lateral ventricles and the subarachnoid space has been set to 10 mmHg, while the fluid pressure inside the parenchyma has been set to 7.5 mmHg. The elastic moduli of white and gray matter have been set to the reduced values of 1 and 5 kPa, respectively. FINDINGS The simulation revealed a substantial ventricular distension (6.5 mm mean outward displacement), which was accompanied by the appearance of stress concentrations in the cerebral mantle. INTERPRETATION These results support the notion that a relative reduction in intraparenchymal fluid pressure coupled with low tissue elasticity can produce both a significant ventricular enlargement and periventricular solid stress concentrations.

Press-in piling: Ground vibration and noise during pile installation

Conventional dynamic piling methods are ill-suited to the urban environment. The press-in method offers an alternative technique of pile installation, which allows pre-formed piles to be installed with minimal noise and vibration. Field measurements of noise and ground vibrations during press-in piling are presented and compared to existing recommended limits. Based on this initial database, tentative prediction curves are presented. Equipped with these tools, designers can assess the relative environmental impact of each installation method when planning piling works.

Centrifugal and numerical modelling of reinforced embankments on soft clay installed with wick drains

Abstract Centrifuge models and finite element analyses of reinforced embankments on soft clay (with or without wick drains) are presented. The results obtained from the centrifuge tests were compared with those from the finite element analyses and were found to be in good agreement. For the case of reinforced embankments on soft clay installed with wick drains, it was found that the magnitude of maximum tension in the reinforcement was slightly higher than that for the case of no wick drains. Also, the distribution of tension in the reinforcement was much more localised under the shoulder of the embankment for the wick drain case as compared to the case of no wick drains. Base reinforcement of embankment is effective in situations, where the demanded shear strength of the clay foundation marginally exceeds the available shear strength. The presence of wick drains in soft clay increases the strength of the clay foundation significantly during the period of embankment construction. This gain in shear strength ensures better mobilization of tension in the reinforcement and contributes significantly towards the stability of the embankment.

CENTRIFUGE MODELLING OF AN EMBANKMENT ON SOFT CLAY REINFORCED WITH A GEOGRID

The behaviour of reinforced embankments on soft clay has been explored using the technique of centrifuge modelling. Controlled in-flight construction of the embankment was carried out in a geotechnical centrifuge over a soft clay layer reinforced with scaled-down and instrumented geogrid reinforcement and the behaviour of the subsoil and the response of the geogrid were observed. These observations are compared with those from another centrifuge test in which a scaled-down woven geotextile was used instead of the geogrid. A new technique for measuring the tension induced in the reinforcement was developed and used in the centrifuge tests. It was found that a geogrid reinforcement that is placed directly on top of the clay layer may not contribute significantly towards the stability of the embankment because of poor adhesion at the clay-reinforcement interface.

Effect of particle size distribution on pile tip resistance in calcareous sand in the geotechnical centrifuge

Abstract Until recently, the micro mechanical origins of soil behaviour have remained illusive, but it is now known that that the constitutive behaviour of a soil is largely determined by its particle size distribution. This paper examines the specific boundary problem associated with the penetration of a model pile into two different gradings of dry calcareous sand in a geotechnical centrifuge, in order to establish the effect of the inclusion of fine particles on the pile end bearing resistance. The first grading of sand comprised particles smaller than 0.5 mm; the second grading contained particles of nominal size d such that 0.15 mm < d < 0.5 mm. Each test was performed on each of two samples of each grading. Tip resistance was observed to rise to a peak at shallow depths, and then fall; a micro mechanical explanation is presented for this instability. Following the centrifuge tests, particles were retrieved from the centres of the soil samples, where the pile had previously been driven, for subsequent particle size analysis. It was found that insignificant crushing had occurred in the sand retrieved from depths less than the depth of peak resistance, but that significant crushing had occurred in the sand retrieved from greater depths. The peak in tip resistance was a factor of two larger for the well-graded sand, but the ultimate tip resistance at greater depths was found to be approximately independent of the initial particle size distribution for all four tests. A micro mechanical explanation is also proposed for this observation.

Large-scale modelling of soil-pipe interaction during large amplitude cyclic movements of partially embedded pipelines

As the development of offshore hydrocarbons moves into deeper water, pipelines form an increasingly significant part of the required infrastructure. High-temperature high-pressure pipelines must be designed to accommodate thermal ex- pansion and potential lateral buckling. A novel design approach is to control the formation of pre-engineered lateral buckles to relieve the expansion. The amplitude of these buckles is typically several pipe diameters. Assessment of the force-displace- ment interaction between the on-bottom pipeline and the seabed is crucial for design. A series of large-scale plane strain model tests has been conducted to measure the response of a pipe segment partially embedded in soft clay, during large ampli- tude cyclic movements, mimicking consecutive thermal expansion and contraction at a bend in a pipeline. Four key stages in the force-displacement response have been identified: (i) breakout, (ii) suction release, (iii) resistance against a steadily grow- ing active berm, and (iv) additional resistance during collection of a pre-existing dormant berm. A simple upper bound solu- tion is proposed to model the observed response. This solution captures the experimental trends including growth of the active berm and collection of dormant berms. This approach is the first attempt to quantitatively model the mechanisms underlying the response during large-displacement lateral sweeps of an on-bottom pipeline, accounting for the growth of soil berms.

Soil consolidation associated with grouting during shield tunnelling in soft clayey ground

J. N. Shirlaw, Land Transport Authority, Singapore The authors have provided a very interesting paper, with a case study, laboratory testing and finite element analysis of the effects of grouting during EPB tunnelling. However, little detail is given on the monitoring and tunnelling in the case study, and further information would help to provide a fuller record of their work. For the monitoring, were settlements measured using an array orthogonal to the direction of advance, to measure the width of the consolidation settlement trough? Based on my experience in Singapore with grout injected after tail void closure, I would expect the settlement troughs during consolidation for arrays B and C, and possibly A, to follow an ‘error function’ shape with a width similar to that of the initial settlement trough. Consolidation settlements due to this type of grouting have the effect of delaying the immediate settlement due to tunnelling, but the final effect is the same as immediate settlement. Using an i value of half the depth to tunnel axis, this would imply that the total volume loss due to tunnelling was 5·7%, 7·5% and 7·9% for cases A, B and C. These are relatively high values, but would be consistent with the closure of a gap of about 60 mm all around the tunnel. It would be useful to know the size of the tail void (the diameter cut by the machine minus the external diameter of the lining), to allow comparison with these volume loss figures. The volume loss figures given above are high for an EPB machine operating in a firm clay. The stability number with no support pressure is 3·49. The total settlements recorded are high for such a stability number, even disregarding the support provided by the EPB machine. It would be useful to know the range of face pressures used during tunnelling, and whether the face was over-pressurised, which could lead to remoulding of the very sensitive clay. The volume loss figures given above can also be expressed as volume losses of 0·405–0·558 m=m of tunnel. Trials B and C involved the injection of 3·8 and 6 m of grout. Comparing these figures, I presume that the conventional tail void grouting was discontinued for several metres of the tunnel, but it is not stated over what length of tunnel the tail void grouting was replaced by the alternative grouting. This is important, because it appears that the settlement over Trials B and C was not just related to the effects of the trials. The surface settlement over the two trials would be due to the cumulative effects of tunnelling from a point about 21 m before the settlement point to about 21 m beyond the settlement point. It would therefore appear that the surface settlements over trials B and C would have included effects both from the trial injection and from the more conventional grouting as used in Trial A. I would note that the ‘immediate’ settlement identified in the paper does not allow for the time necessary for the full development of the immediate settlement trough, owing to this threedimensional effect. The conventional tail void grouting appears to have been more effective than the trial injections at controlling total surface settlement. However, the settlement was still large for this size and type of machine operating in firm clay. The authors do not state whether the tail void grouting was carried out using grout pipes laid along the tail skin, to allow grouting simultaneously with machine advance, or through the lining. The former of these has been found to be much more effective at filling the tail void before it closes (in soft clays) than the latter. I was very interested in the high compressibility of the cement/silicate grout (Type I) used, and the significant reduction in grout compression using the Type II grout. This is clearly an area that warrants further investigation. However, I would appreciate some clarification on some of the items in the paper. The authors report a 120 s gel-hardening time for the Type I grout, but for the identical grout used in the tunnelling trial report a 20 s gel time. In the consolidation testing of the grouts, the authors report that Type I lost 30% of its original volume ‘after hardening’. I am not clear whether the 30% loss was measured on hardened grout, or during the interval between injection and hardening. I also note that with Type I grout the laboratory trials show an initial volume expansion of very close to 100% of the grout volume used in all but one case. For the Type II grout the initial volume expansion is well below 100% of the grout volume used in three out of seven cases, implying some other losses in the system. The authors also do not state the mix used for grouting in trial A: it would be useful to know whether this grout was also prone to significant loss of volume. As a final comment, I question the normalisation of the grout volume by initial soil volume in Figs 10 and 12. Within the laboratory trials the soil volume is defined by the size of the container. However, for wider application, this method of presentation is of limited value. Did the authors consider expressing the data in terms of rþ 3 r=r, where r is the radius of the initial injection cavity, and rþ 3 r is the radius of the expanding bulb (assuming expansion as a sphere)?