Logarithm Function

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Yu-jun Cui - One of the best experts on this subject based on the ideXlab platform.

  • Influence of strain-rate on hydromechanical behavior of highly compacted GMZ01 bentonite
    Engineering Geology, 2015
    Co-Authors: Pengjun Qui, Yong-gui Chen, Bao Chen, Yu-jun Cui
    Abstract:

    During the long-term operation of a deep geological repository in crystalline rock, saturation of buffer/backfill materials will last for a long period of time. Investigation on time-dependent property of buffer/backfill materials is of great importance for long-term safety assessment of the repository. In this work, GMZ01 bentonite powder was statically compacted to specimens with a dry density of 1.70 g/cm3 and suction-equilibrated to their target values. Then, a series of suction-controlled constant rate of strain (CRS) tests (including single-stage and step-wise CRS tests) were conducted for the investigation of the strain rate-dependent compression behavior of highly compacted GMZ01 bentonite. Comparisons were made between the results of the single-stage and step-wise CRS tests under given suctions for the verification of the applicability of the isotache concept on the compacted GMZ01 bentonite. Based on that, the step-wise CRS compression tests were performed and results were presented in terms of vertical stress–vertical strain curves. Based on the test results, the virgin compression index λ and the yield stress p0 were determined. Analysis indicates that λ decreases, while p0 increases with increasing suction. Furthermore, p0 increases with increasing CRS, which is consistent with previous researches on saturated soils. Finally, a Logarithm Function proposed between α(s) and suction s is verified and several relevant parameters are fitted, which represents the coupling of suction, time and stress of GMZ01 bentonite.

  • An experimental investigation on the secondary compression of unsaturated GMZ01 bentonite
    Applied Clay Science, 2014
    Co-Authors: Xiaoling Lai, Yong-gui Chen, Bao Chen, Yu-jun Cui
    Abstract:

    The secondary compression behavior of compacted GMZ01 bentonite was experimentally investigated by conducting a series of suction-controlled high-pressure oedometer tests. GMZ01 bentonite powder was first exposed to suction controlled conditions at 110 MPa and then statically compacted to a dry density of 1.70 g/cm(3). Then, the compacted samples were hydrated to designed suctions using the vapor equilibrium technique and finally submitted to multi-staged loading oedometer tests. Corresponding results were presented in terms of stress-strain-time curves. Based on the test results, the incremental compression index C-c(*) and secondary compression index C-alpha were defined. Relationships between C-alpha(*),C-alpha, vertical stress and suction were analyzed. It is observed that both C-c(*) and C-alpha increase linearly with increasing vertical stress, which is different from the convex relationship reported by other researchers in saturated soils. Moreover, C-c(*) and C-alpha also increase with decreasing suction. The relationship between C-c(*) and C-alpha is linear in the considered stress range and the slope of this linear relationship (C-alpha/C-c(*)) increases with decreasing suction. Finally, a Logarithm Function is established between C-alpha(*)/C-c(*) and suction s, which represents the coupling of suction, creep and stress of GMZ01 bentonite.

Florent De Dinechin - One of the best experts on this subject based on the ideXlab platform.

  • Computing floating-point Logarithms with fixed-point operations
    2016
    Co-Authors: Julien Le Maire, Nicolas Brunie, Florent De Dinechin, Jean-michel Muller
    Abstract:

    Elementary Functions from the mathematical library input and output floating-point numbers. However it is possible to implement them purely using integer/fixed-point arithmetic. This option was not attractive between 1985 and 2005, because mainstream processor hardware supported 64-bit floating-point, but only 32-bit integers. Besides, conversions between floating-point and integer were costly. This has changed in recent years, in particular with the generalization of native 64-bit integer support. The purpose of this article is therefore to reevaluate the relevance of computing floating-point Functions in fixed-point. For this, several variants of the double-precision Logarithm Function are implemented and evaluated. Formulating the problem as a fixed-point one is easy after the range has been (classically) reduced. Then, 64-bit integers provide slightly more accuracy than 53-bit mantissa, which helps speed up the evaluation. Finally, multi-word arithmetic, critical for accurate implementations, is much faster in fixed-point, and natively supported by recent compilers. Novel techniques of argument reduction and rounding test are introduced in this context. Thanks to all this, a purely integer implementation of the correctly rounded double-precision Logarithm outperforms the previous state of the art, with the worst-case execution time reduced by a factor 5. This work also introduces variants of the Logarithm that input a floating-point number and output the result in fixed-point. These are shown to be both more accurate and more efficient than the traditional floating-point Functions for some applications.

  • A flexible floating-point Logarithm for reconfigurable computers
    2010
    Co-Authors: Florent De Dinechin
    Abstract:

    The advent of reconfigurable co-processors based on field-programmable gate arrays has renewed interest in hardware architectures for elementary Functions. This article studies operators for the Logarithm Function in the context of this target technology. An old algorithm is generalized, fine-tuned and implemented as an architecture generator, exposing a wide range of trade-offs between resources (memory, logic and multipliers) and performance (frequency and pipeline depth). A single pipelined operator computes five times more double-precision floating-point Logarithms per second than a high-end processor core, while consuming only a few percents of the resources of a high-end FPGA. This generator is available under the LGPL as part of the FloPoCo project.

Yong-gui Chen - One of the best experts on this subject based on the ideXlab platform.

  • Influence of strain-rate on hydromechanical behavior of highly compacted GMZ01 bentonite
    Engineering Geology, 2015
    Co-Authors: Pengjun Qui, Yong-gui Chen, Bao Chen, Yu-jun Cui
    Abstract:

    During the long-term operation of a deep geological repository in crystalline rock, saturation of buffer/backfill materials will last for a long period of time. Investigation on time-dependent property of buffer/backfill materials is of great importance for long-term safety assessment of the repository. In this work, GMZ01 bentonite powder was statically compacted to specimens with a dry density of 1.70 g/cm3 and suction-equilibrated to their target values. Then, a series of suction-controlled constant rate of strain (CRS) tests (including single-stage and step-wise CRS tests) were conducted for the investigation of the strain rate-dependent compression behavior of highly compacted GMZ01 bentonite. Comparisons were made between the results of the single-stage and step-wise CRS tests under given suctions for the verification of the applicability of the isotache concept on the compacted GMZ01 bentonite. Based on that, the step-wise CRS compression tests were performed and results were presented in terms of vertical stress–vertical strain curves. Based on the test results, the virgin compression index λ and the yield stress p0 were determined. Analysis indicates that λ decreases, while p0 increases with increasing suction. Furthermore, p0 increases with increasing CRS, which is consistent with previous researches on saturated soils. Finally, a Logarithm Function proposed between α(s) and suction s is verified and several relevant parameters are fitted, which represents the coupling of suction, time and stress of GMZ01 bentonite.

  • An experimental investigation on the secondary compression of unsaturated GMZ01 bentonite
    Applied Clay Science, 2014
    Co-Authors: Xiaoling Lai, Yong-gui Chen, Bao Chen, Yu-jun Cui
    Abstract:

    The secondary compression behavior of compacted GMZ01 bentonite was experimentally investigated by conducting a series of suction-controlled high-pressure oedometer tests. GMZ01 bentonite powder was first exposed to suction controlled conditions at 110 MPa and then statically compacted to a dry density of 1.70 g/cm(3). Then, the compacted samples were hydrated to designed suctions using the vapor equilibrium technique and finally submitted to multi-staged loading oedometer tests. Corresponding results were presented in terms of stress-strain-time curves. Based on the test results, the incremental compression index C-c(*) and secondary compression index C-alpha were defined. Relationships between C-alpha(*),C-alpha, vertical stress and suction were analyzed. It is observed that both C-c(*) and C-alpha increase linearly with increasing vertical stress, which is different from the convex relationship reported by other researchers in saturated soils. Moreover, C-c(*) and C-alpha also increase with decreasing suction. The relationship between C-c(*) and C-alpha is linear in the considered stress range and the slope of this linear relationship (C-alpha/C-c(*)) increases with decreasing suction. Finally, a Logarithm Function is established between C-alpha(*)/C-c(*) and suction s, which represents the coupling of suction, creep and stress of GMZ01 bentonite.

Bao Chen - One of the best experts on this subject based on the ideXlab platform.

  • Influence of strain-rate on hydromechanical behavior of highly compacted GMZ01 bentonite
    Engineering Geology, 2015
    Co-Authors: Pengjun Qui, Yong-gui Chen, Bao Chen, Yu-jun Cui
    Abstract:

    During the long-term operation of a deep geological repository in crystalline rock, saturation of buffer/backfill materials will last for a long period of time. Investigation on time-dependent property of buffer/backfill materials is of great importance for long-term safety assessment of the repository. In this work, GMZ01 bentonite powder was statically compacted to specimens with a dry density of 1.70 g/cm3 and suction-equilibrated to their target values. Then, a series of suction-controlled constant rate of strain (CRS) tests (including single-stage and step-wise CRS tests) were conducted for the investigation of the strain rate-dependent compression behavior of highly compacted GMZ01 bentonite. Comparisons were made between the results of the single-stage and step-wise CRS tests under given suctions for the verification of the applicability of the isotache concept on the compacted GMZ01 bentonite. Based on that, the step-wise CRS compression tests were performed and results were presented in terms of vertical stress–vertical strain curves. Based on the test results, the virgin compression index λ and the yield stress p0 were determined. Analysis indicates that λ decreases, while p0 increases with increasing suction. Furthermore, p0 increases with increasing CRS, which is consistent with previous researches on saturated soils. Finally, a Logarithm Function proposed between α(s) and suction s is verified and several relevant parameters are fitted, which represents the coupling of suction, time and stress of GMZ01 bentonite.

  • An experimental investigation on the secondary compression of unsaturated GMZ01 bentonite
    Applied Clay Science, 2014
    Co-Authors: Xiaoling Lai, Yong-gui Chen, Bao Chen, Yu-jun Cui
    Abstract:

    The secondary compression behavior of compacted GMZ01 bentonite was experimentally investigated by conducting a series of suction-controlled high-pressure oedometer tests. GMZ01 bentonite powder was first exposed to suction controlled conditions at 110 MPa and then statically compacted to a dry density of 1.70 g/cm(3). Then, the compacted samples were hydrated to designed suctions using the vapor equilibrium technique and finally submitted to multi-staged loading oedometer tests. Corresponding results were presented in terms of stress-strain-time curves. Based on the test results, the incremental compression index C-c(*) and secondary compression index C-alpha were defined. Relationships between C-alpha(*),C-alpha, vertical stress and suction were analyzed. It is observed that both C-c(*) and C-alpha increase linearly with increasing vertical stress, which is different from the convex relationship reported by other researchers in saturated soils. Moreover, C-c(*) and C-alpha also increase with decreasing suction. The relationship between C-c(*) and C-alpha is linear in the considered stress range and the slope of this linear relationship (C-alpha/C-c(*)) increases with decreasing suction. Finally, a Logarithm Function is established between C-alpha(*)/C-c(*) and suction s, which represents the coupling of suction, creep and stress of GMZ01 bentonite.

Xiaoling Lai - One of the best experts on this subject based on the ideXlab platform.

  • An experimental investigation on the secondary compression of unsaturated GMZ01 bentonite
    Applied Clay Science, 2014
    Co-Authors: Xiaoling Lai, Yong-gui Chen, Bao Chen, Yu-jun Cui
    Abstract:

    The secondary compression behavior of compacted GMZ01 bentonite was experimentally investigated by conducting a series of suction-controlled high-pressure oedometer tests. GMZ01 bentonite powder was first exposed to suction controlled conditions at 110 MPa and then statically compacted to a dry density of 1.70 g/cm(3). Then, the compacted samples were hydrated to designed suctions using the vapor equilibrium technique and finally submitted to multi-staged loading oedometer tests. Corresponding results were presented in terms of stress-strain-time curves. Based on the test results, the incremental compression index C-c(*) and secondary compression index C-alpha were defined. Relationships between C-alpha(*),C-alpha, vertical stress and suction were analyzed. It is observed that both C-c(*) and C-alpha increase linearly with increasing vertical stress, which is different from the convex relationship reported by other researchers in saturated soils. Moreover, C-c(*) and C-alpha also increase with decreasing suction. The relationship between C-c(*) and C-alpha is linear in the considered stress range and the slope of this linear relationship (C-alpha/C-c(*)) increases with decreasing suction. Finally, a Logarithm Function is established between C-alpha(*)/C-c(*) and suction s, which represents the coupling of suction, creep and stress of GMZ01 bentonite.