Ensemble Kalman Methods With Constraints

Ensemble Kalman methods constitute an increasingly important tool in both state and parameter estimation problems. Their popularity stems from the derivative-free nature of the methodology which may be readily applied when computer code is available for the underlying state-space dynamics (for state estimation) or for the parameter-to-observable map (for parameter estimation). There are many applications in which it is desirable to enforce prior information in the form of equality or inequality constraints on the state or parameter. This paper establishes a general framework for doing so, describing a widely applicable methodology, a theory which justifies the methodology, and a set of numerical experiments exemplifying it

Centrifuge Testing of Circular and Rectangular Embedded Structures with Base Excitations

We present data and metadata from a centrifuge testing program that was designed to investigate the seismic responses of buried circular and rectangular culverts. The specimen configurations were based on Caltrans Standard Plans, and the scope of research was to compare the experimental findings with the design method described in the NCHRP Report 611 as well as to formulate preliminary recommendations for Caltrans practice. A relatively flexible pipe and a stiff box-shaped specimen embedded in dense sand were tested in the centrifuge at the Center for Geotechnical Modeling at University of California, Davis and were subjected to a set of broadband and harmonic input motions. Responses were recorded in the soil and in the embedded structures using a dense array of instruments. Measured quantities included specimen accelerations, bending strains, and hoop strains; soil accelerations, shear-wave velocities, settlements, and lateral displacements; and accelerations of the centrifuge's shaking table. This data paper describes the tests and summarizes the generated data, which are archived at DesignSafe.ci.org (DOI: 10.17603/DS2XW9R) and are accessible through an interactive Jupyter notebook

Reduced order modeling of soil structure interaction problems

This dissertation is focused on creating the key ingredients of a numerical platform for reduced order modeling of soil structure interaction (SSI) problems. Specifically, a computer code is developed for forward simulation of wave propagation in the two-dimensional (plane-strain and axisymmetric) semi-infinite heterogeneous solid media. Perfectly matched layers (PMLs) are used for absorbing the outgoing waves. The computationally efficient symmetric hybrid PML formulation available for the plane-strain setting is extended to axisymmetric problems. The domain reduction method (DRM) is used for translation of the remote excitation within a PML-truncated medium. The methodologies are devised for using this finite element (FE) solver to (i) compute the soil impedance functions and (ii) the modified input motions (a.k.a. foundation input motion) of rigid and flexible interfaces embedded in heterogeneous half-spaces numerically. Existing semi-analytical solutions are used to verify these methods comprehensively. The verified framework is validated using data from a large-scale field test as well as centrifuge experiments. In order to demonstrate the framework's application: (i) the impedance functions and kinematic interaction transfer functions (KITFs) of a number of SSI problems---for which existing analytical solutions are limited---are computed; and (ii) the reduced order model of a buried structure in an elastic half-space is constructed. In order to avoid integro-differential equations, stable discrete-time filters are used for devising time-domain representations of the computed soil impedance matrix. The dynamic response of the resulting spatio-temporal reduced order model is compared against those obtained from solving the same problem using the direct modeling approach, and excellent agreement is observed

Reduced order modeling of soil structure interaction problems

This dissertation is focused on creating the key ingredients of a numerical platform for reduced order modeling of soil structure interaction (SSI) problems. Specifically, a computer code is developed for forward simulation of wave propagation in the two-dimensional (plane-strain and axisymmetric) semi-infinite heterogeneous solid media. Perfectly matched layers (PMLs) are used for absorbing the outgoing waves. The computationally efficient symmetric hybrid PML formulation available for the plane-strain setting is extended to axisymmetric problems. The domain reduction method (DRM) is used for translation of the remote excitation within a PML-truncated medium. The methodologies are devised for using this finite element (FE) solver to (i) compute the soil impedance functions and (ii) the modified input motions (a.k.a. foundation input motion) of rigid and flexible interfaces embedded in heterogeneous half-spaces numerically. Existing semi-analytical solutions are used to verify these methods comprehensively. The verified framework is validated using data from a large-scale field test as well as centrifuge experiments. In order to demonstrate the framework's application: (i) the impedance functions and kinematic interaction transfer functions (KITFs) of a number of SSI problems---for which existing analytical solutions are limited---are computed; and (ii) the reduced order model of a buried structure in an elastic half-space is constructed. In order to avoid integro-differential equations, stable discrete-time filters are used for devising time-domain representations of the computed soil impedance matrix. The dynamic response of the resulting spatio-temporal reduced order model is compared against those obtained from solving the same problem using the direct modeling approach, and excellent agreement is observed

Seismic Input Motion Identification in a Heterogeneous Halfspace

This paper presents a new time domain method for reconstructing unknown incident seismic input waves entering into a truncated heterogeneous soil domain from a soil surface response. The problem is cast into a partial differential equation (PDE)–constrained optimization problem where a misfit between a measured response at a sensor on the ground surface induced by a target signal and a computed wave solution induced by an estimate signal is minimized. Using this method allows for fast and accurate evaluation of the sensitivity of a misfit functional (i.e., gradient or Fréchet derivative) with respect to control parameters. Both forward and adjoint problems are solved by using the finite-element method (FEM). The numerical results prove that the presented method can identify a targeted incident seismic input signal into a truncated soil domain without providing the numerical optimizer with any hint about the target. In presence of noise in measurement, this inversion process recovers a target signal more accurately than the deconvolution does

Seismic Input Motion Identification in a Heterogeneous Halfspace

This paper presents a new time domain method for reconstructing unknown incident seismic input waves entering into a truncated heterogeneous soil domain from a soil surface response. The problem is cast into a partial differential equation (PDE)–constrained optimization problem where a misfit between a measured response at a sensor on the ground surface induced by a target signal and a computed wave solution induced by an estimate signal is minimized. Using this method allows for fast and accurate evaluation of the sensitivity of a misfit functional (i.e., gradient or Fréchet derivative) with respect to control parameters. Both forward and adjoint problems are solved by using the finite-element method (FEM). The numerical results prove that the presented method can identify a targeted incident seismic input signal into a truncated soil domain without providing the numerical optimizer with any hint about the target. In presence of noise in measurement, this inversion process recovers a target signal more accurately than the deconvolution does

A quantitative assessment of the NCHRP 611 method for soil-structure interaction analysis of buried circular structures & a proposed improvement

The recent National Cooperative Highway Research Program (NCHRP) Report 611 titled “Seismic Analysis and Design of Retaining Walls, Buried Structures, Slopes, and Embankments” has been widely adopted as a guideline in the analysis design of buried/embedded structures due to its computational simplicity and broadly accepted accuracy for simple soil-structure configurations. However, the method is not without shortcomings. In particular, the NCHRP method is not sensitive to the inherently broadband frequency content of seismic input excitations, soil heterogeneities, and potential kinematic interaction effects. The present study seeks to quantitatively assess the brackets of the validity of the NCHRP 611 method—specifically, for soil-structure analyses of buried circular structures, and offers an improvement that is simple to implement. This is achieved through parametric studies using detailed nonlinear finite element simulations involving a broad range of ground motions, and soil and structural properties. The simulations are carried out with models that are parametric variations of a model that has been validated in a prior centrifuge testing program on embedded structures. A refined version of the NCHRP 611 method, which uses maximum shear strains obtained through one-dimensional site response analyses, is shown to produce fairly accurate results for nearly all of the different cases considered in the parametric studies. The basic version of the method, however, which is based on rough estimates of maximum shear strain and effective soil modulus, is observed to be highly inaccurate

A quantitative assessment of the NCHRP 611 method for soil-structure interaction analysis of buried circular structures & a proposed improvement

The recent National Cooperative Highway Research Program (NCHRP) Report 611 titled “Seismic Analysis and Design of Retaining Walls, Buried Structures, Slopes, and Embankments” has been widely adopted as a guideline in the analysis design of buried/embedded structures due to its computational simplicity and broadly accepted accuracy for simple soil-structure configurations. However, the method is not without shortcomings. In particular, the NCHRP method is not sensitive to the inherently broadband frequency content of seismic input excitations, soil heterogeneities, and potential kinematic interaction effects. The present study seeks to quantitatively assess the brackets of the validity of the NCHRP 611 method—specifically, for soil-structure analyses of buried circular structures, and offers an improvement that is simple to implement. This is achieved through parametric studies using detailed nonlinear finite element simulations involving a broad range of ground motions, and soil and structural properties. The simulations are carried out with models that are parametric variations of a model that has been validated in a prior centrifuge testing program on embedded structures. A refined version of the NCHRP 611 method, which uses maximum shear strains obtained through one-dimensional site response analyses, is shown to produce fairly accurate results for nearly all of the different cases considered in the parametric studies. The basic version of the method, however, which is based on rough estimates of maximum shear strain and effective soil modulus, is observed to be highly inaccurate