Strength mobilization in clays and silts

A large database of 115 triaxial, direct simple shear, and cyclic tests on 19 clays and silts is presented and analysed to develop an empirical framework for the prediction of the mobilization of the undrained shear strength, cu, of natural clays tested from an initially isotropic state of stress. The strain at half the peak undrained strength (γM=2) is used to normalize the shear strain data between mobilized strengths of 0.2cu and 0.8cu. A power law with an exponent of 0.6 is found to describe all the normalized data within a strain factor of 1.75 when a representative sample provides a value for γM=2. Multi-linear regression analysis shows that γM=2 is a function of cu, plasticity index Ip, and initial mean effective stress p′0. Of the 97 stress-strain curves for which cu, Ip, and p′0 were available, the observed values of γM=2 fell within a factor of three of the regression; this additional uncertainty should be acknowledged if a designer wished to limit immediate foundation settlements on the basis of an undrained strength profile and the plasticity index of the clay. The influence of stress history is also discussed. The application of these stress-strain relations to serviceability design calculations is portrayed through a worked example. The implications for geotechnical decision-making and codes of practice are considered.

Comparison of constructions of irregular Gallager codes

The low-density parity check codes whose performance is closest to the Shannon limit are `Gallager codes' based on irregular graphs. We compare alternative methods for constructing these graphs and present two results. First, we find a `super-Poisson' construction which gives a small improvement in empirical performance over a random construction. Second, whereas Gallager codes normally take N2 time to encode, we investigate constructions of regular and irregular Gallager codes that allow more rapid encoding and have smaller memory requirements in the encoder. We find that these `fast encoding' Gallager codes have equally good performance.

Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check codes

We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with near-codewords, which cause problems for the sum-product decoder; The Ramanujan-Margulis construction gives a code with low-weight codewords, which produce an error-floor. © 2004 Elsevier B.V.

Performance of low density parity check codes as a function of actual and assumed noise levels

We investigate how sensitive Gallager's codes are, when decoded by the sum-product algorithm, to the assumed noise level. We have found a remarkably simple function that fits the empirical results as a function of the actual noise level at both high and low noise levels. © 2004 Elsevier B.V.

Performance of low density parity check codes as a function of actual and assumed noise levels

We investigate how sensitive Gallager's codes are, when decoded by the sum-product algorithm, to the assumed noise level. We have found a remarkably simple function that fits the empirical results as a function of the actual noise level at both high and low noise levels. ©2003 Published by Elsevier Science B. V.

Weaknesses of margulis and ramanujan-margulis low-density parity-check codes

We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with near-codewords, which cause problems for the sum-product decoder; The Ramanujan-Margulis construction gives a code with low-weight codewords, which produce an error-floor. ©2003 Published by Elsevier Science B. V.