Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo

Kasper Nikolaj Berntsen, Ove Dalager Ditlevsen

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    Abstract

    A two-dimensional silo pressure model-problem is investigated by molecular dynamics simulations. A plane silo container is filled by a granular matter consisting of congruent elliptic particles dropped one by one into the silo. A suitable energy absorbing contact force mechanism is activatedduring particle collisions and collisions against the walls. After a while the residual kinetic energy is small enough that the granular medium can be considered to be in equilibrium. The sample of contact forces along the wall and the averagevertical force components over the horizontal cross-sections through the granular matter in the silo are compared to thesolution of a stochastic equilibrium differential equation. In this equation the stochasticity source is a homogeneouswhite noise gamma-distributed side pressure factor field along the walls. This is a generalization of the deterministic side pressure factor proposed by Janssen in 1895. The stochastic Janssen factor model is shown to be fairly consistentwith the observations from which the mean and the intensity of the white noise is estimated by the method of maximumlikelihood using the properties of the gamma-distribution. Two wall friction coefficients are determined, one for transforming the expectation and the other for transforming theintensity of the transverse stress factor into the mean and the intensity of the vertical white noise shear stress factorfield along the walls. The latter is determined by the observed ratio of the standard deviations of the two fields. Thefirst is estimated by fitting the exponential expectation function for theaverage normal stress in the horizontal cross-sections to the observed sample function by the principle of least square.Knowing these, in total four, estimated parameter values, the stochastic model determines the expectation function of the stress field normal to the walls, and the covariance functions of all considered stress fields. The observed stress fieldrealizations are not contradicting these predictions. Thus it is demonstrated that molecular dynamics simulations can leadto valuable insight with respect to granular matter behavior even with the limited number of particles that can be handledwith practicable computer efforts. Most important is the observation that a gamma-distributed stochastic side pressurefield is a valid modeling assumption.
    Original languageEnglish
    Title of host publicationApplications of Statistics and Probability, Civil Engineering Reliability and Risk Analysis
    Place of PublicationRotterdam
    PublisherCRC Press/Balkema
    Publication date2000
    Pages57-64
    Publication statusPublished - 2000
    Event8th International Conference on Applications of Probability and Statistics to Civil Engineering - Sydney, Australia
    Duration: 12 Dec 199915 Dec 1999
    Conference number: 8

    Conference

    Conference8th International Conference on Applications of Probability and Statistics to Civil Engineering
    Number8
    CountryAustralia
    CitySydney
    Period12/12/199915/12/1999

    Cite this

    Berntsen, K. N., & Ditlevsen, O. D. (2000). Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo. In Applications of Statistics and Probability, Civil Engineering Reliability and Risk Analysis (pp. 57-64). Rotterdam: CRC Press/Balkema.
    Berntsen, Kasper Nikolaj ; Ditlevsen, Ove Dalager. / Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo. Applications of Statistics and Probability, Civil Engineering Reliability and Risk Analysis. Rotterdam : CRC Press/Balkema, 2000. pp. 57-64
    @inproceedings{2cbac3a764624c3aad40b90290081bcc,
    title = "Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo",
    abstract = "A two-dimensional silo pressure model-problem is investigated by molecular dynamics simulations. A plane silo container is filled by a granular matter consisting of congruent elliptic particles dropped one by one into the silo. A suitable energy absorbing contact force mechanism is activatedduring particle collisions and collisions against the walls. After a while the residual kinetic energy is small enough that the granular medium can be considered to be in equilibrium. The sample of contact forces along the wall and the averagevertical force components over the horizontal cross-sections through the granular matter in the silo are compared to thesolution of a stochastic equilibrium differential equation. In this equation the stochasticity source is a homogeneouswhite noise gamma-distributed side pressure factor field along the walls. This is a generalization of the deterministic side pressure factor proposed by Janssen in 1895. The stochastic Janssen factor model is shown to be fairly consistentwith the observations from which the mean and the intensity of the white noise is estimated by the method of maximumlikelihood using the properties of the gamma-distribution. Two wall friction coefficients are determined, one for transforming the expectation and the other for transforming theintensity of the transverse stress factor into the mean and the intensity of the vertical white noise shear stress factorfield along the walls. The latter is determined by the observed ratio of the standard deviations of the two fields. Thefirst is estimated by fitting the exponential expectation function for theaverage normal stress in the horizontal cross-sections to the observed sample function by the principle of least square.Knowing these, in total four, estimated parameter values, the stochastic model determines the expectation function of the stress field normal to the walls, and the covariance functions of all considered stress fields. The observed stress fieldrealizations are not contradicting these predictions. Thus it is demonstrated that molecular dynamics simulations can leadto valuable insight with respect to granular matter behavior even with the limited number of particles that can be handledwith practicable computer efforts. Most important is the observation that a gamma-distributed stochastic side pressurefield is a valid modeling assumption.",
    author = "Berntsen, {Kasper Nikolaj} and Ditlevsen, {Ove Dalager}",
    year = "2000",
    language = "English",
    pages = "57--64",
    booktitle = "Applications of Statistics and Probability, Civil Engineering Reliability and Risk Analysis",
    publisher = "CRC Press/Balkema",

    }

    Berntsen, KN & Ditlevsen, OD 2000, Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo. in Applications of Statistics and Probability, Civil Engineering Reliability and Risk Analysis. CRC Press/Balkema, Rotterdam, pp. 57-64, 8th International Conference on Applications of Probability and Statistics to Civil Engineering, Sydney, Australia, 12/12/1999.

    Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo. / Berntsen, Kasper Nikolaj; Ditlevsen, Ove Dalager.

    Applications of Statistics and Probability, Civil Engineering Reliability and Risk Analysis. Rotterdam : CRC Press/Balkema, 2000. p. 57-64.

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    TY - GEN

    T1 - Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo

    AU - Berntsen, Kasper Nikolaj

    AU - Ditlevsen, Ove Dalager

    PY - 2000

    Y1 - 2000

    N2 - A two-dimensional silo pressure model-problem is investigated by molecular dynamics simulations. A plane silo container is filled by a granular matter consisting of congruent elliptic particles dropped one by one into the silo. A suitable energy absorbing contact force mechanism is activatedduring particle collisions and collisions against the walls. After a while the residual kinetic energy is small enough that the granular medium can be considered to be in equilibrium. The sample of contact forces along the wall and the averagevertical force components over the horizontal cross-sections through the granular matter in the silo are compared to thesolution of a stochastic equilibrium differential equation. In this equation the stochasticity source is a homogeneouswhite noise gamma-distributed side pressure factor field along the walls. This is a generalization of the deterministic side pressure factor proposed by Janssen in 1895. The stochastic Janssen factor model is shown to be fairly consistentwith the observations from which the mean and the intensity of the white noise is estimated by the method of maximumlikelihood using the properties of the gamma-distribution. Two wall friction coefficients are determined, one for transforming the expectation and the other for transforming theintensity of the transverse stress factor into the mean and the intensity of the vertical white noise shear stress factorfield along the walls. The latter is determined by the observed ratio of the standard deviations of the two fields. Thefirst is estimated by fitting the exponential expectation function for theaverage normal stress in the horizontal cross-sections to the observed sample function by the principle of least square.Knowing these, in total four, estimated parameter values, the stochastic model determines the expectation function of the stress field normal to the walls, and the covariance functions of all considered stress fields. The observed stress fieldrealizations are not contradicting these predictions. Thus it is demonstrated that molecular dynamics simulations can leadto valuable insight with respect to granular matter behavior even with the limited number of particles that can be handledwith practicable computer efforts. Most important is the observation that a gamma-distributed stochastic side pressurefield is a valid modeling assumption.

    AB - A two-dimensional silo pressure model-problem is investigated by molecular dynamics simulations. A plane silo container is filled by a granular matter consisting of congruent elliptic particles dropped one by one into the silo. A suitable energy absorbing contact force mechanism is activatedduring particle collisions and collisions against the walls. After a while the residual kinetic energy is small enough that the granular medium can be considered to be in equilibrium. The sample of contact forces along the wall and the averagevertical force components over the horizontal cross-sections through the granular matter in the silo are compared to thesolution of a stochastic equilibrium differential equation. In this equation the stochasticity source is a homogeneouswhite noise gamma-distributed side pressure factor field along the walls. This is a generalization of the deterministic side pressure factor proposed by Janssen in 1895. The stochastic Janssen factor model is shown to be fairly consistentwith the observations from which the mean and the intensity of the white noise is estimated by the method of maximumlikelihood using the properties of the gamma-distribution. Two wall friction coefficients are determined, one for transforming the expectation and the other for transforming theintensity of the transverse stress factor into the mean and the intensity of the vertical white noise shear stress factorfield along the walls. The latter is determined by the observed ratio of the standard deviations of the two fields. Thefirst is estimated by fitting the exponential expectation function for theaverage normal stress in the horizontal cross-sections to the observed sample function by the principle of least square.Knowing these, in total four, estimated parameter values, the stochastic model determines the expectation function of the stress field normal to the walls, and the covariance functions of all considered stress fields. The observed stress fieldrealizations are not contradicting these predictions. Thus it is demonstrated that molecular dynamics simulations can leadto valuable insight with respect to granular matter behavior even with the limited number of particles that can be handledwith practicable computer efforts. Most important is the observation that a gamma-distributed stochastic side pressurefield is a valid modeling assumption.

    M3 - Article in proceedings

    SP - 57

    EP - 64

    BT - Applications of Statistics and Probability, Civil Engineering Reliability and Risk Analysis

    PB - CRC Press/Balkema

    CY - Rotterdam

    ER -

    Berntsen KN, Ditlevsen OD. Stochastic stresses in granular matter simulated by dripping identical ellipses into plane silo. In Applications of Statistics and Probability, Civil Engineering Reliability and Risk Analysis. Rotterdam: CRC Press/Balkema. 2000. p. 57-64