Coupled Surge-Heave Motions of a Moored System. I: Model Calibration and Parametric Study

Model calibration and parametric studies of the coupled, complex surge-heave motions of a medium-scale experimental, nonlinear, submerged, moored structural system are presented here. The experimental system excited by periodic wave fields consists of a spherical buoy and attached multipoint mooring lines. Sources of nonlinearity include complex geometric restoring forces and coupled fluid–structure interaction exciting forces. The sphere moves mainly in a two-dimensional fashion [or two degrees of freedom (2DOF)] of surge and heave, with negligible pitch. Characteristic experimental results include harmonic, subharmonic, and superharmonic responses. As an extension of single-degree-of-freedom, independent-flow-field (IFF) models, a 2DOF, IFF model is derived and employed. Good agreement is shown between the analytical predictions and experimental results. Existence of complex nonlinear responses, including chaos and multiple coexisting steady states, are numerically identified when the coupling is strong and damping is light. Degree of complexity and nonlinearity of responses diminish with decreasing coupling and/or increasing damping.     

Stochastic Analysis of a Single-Degree-of-Freedom Nonlinear Experimental Moored System Using an Independent-Flow-Field Model

Stochastic characteristics of the surge response of a nonlinear single-degree-of-freedom moored structure subjected to random wave excitations are examined in this paper. Sources of nonlinearity of the system include a complex geometric configuration and wave-induced quadratic drag. A Morison-type model with an independent-flow-field formulation and a three-term-polynomial approximation of the nonlinear restoring force is employed for its proven excellent prediction capability for the experimental results investigated. Wave excitations considered in this study include nearly periodic waves, which take into account the presence of tank noise, noisy periodic waves that have predominant periodic components with designed additive random perturbations, and narrow-band random waves. A unified wave excitation model is used to describe all the wave conditions. A modulating factor governing the degree of randomness in the wave excitations is introduced. The corresponding Fokker–Planck formulation is applied and numerically solved for the response probability density functions (PDFs). Experimental results and simulations are compared in detail via the PDFs in phase space. The PDFs portray coexisting multiple response attractors and indicate their relative strengths, and experimental response behaviors, including transitions and interactions, are accordingly interpreted from the ensemble perspective. Using time-averaged probability density functions as an invariant measure, probability distributions of large excursions in experimental and simulated responses to various random wave excitations are demonstrated and compared. Asymptotic long-term behaviors of the experimental responses are then inferred.     

Stochastic Response and Stability of a Nonintegrable System

For determining the stochastic response and stability of a strongly nonlinear single-degree-of-freedom system using the stochastic averaging technique, the size of excitations should be small such that the response of the system converges weakly to a Markov process. This condition is not often met with practical problems, and therefore, application of this method for obtaining their responses becomes difficult. Further, for systems with nonlinearities that cannot be integrated in closed form, stability analysis by examining the conditions of the two boundaries of the problem is not possible. A semianalytical method along with a weighted residual technique is presented here to circumvent these difficulties and to determine the response and stability of a strongly nonlinear system subjected to sizable stochastic excitation. The weighted residual technique is employed to correct the errors in averaged drift and diffusion coefficients resulting due to the size of the stochastic excitation. Two example problems are solved as illustrations of the method.     

Analysis of Traffic-Induced Vibrations in a Cable-Stayed Bridge. Part II: Numerical Modeling and Stochastic Simulation

This paper describes the development of a numerical model to simulate the dynamic response of the bridge–vehicle system of Salgueiro Maia cable-stayed bridge, using the results from an extensive experimental investigation to calibrate this model. Further, a set of stochastic Monte Carlo simulations of the bridge–vehicle dynamic response is also presented, with the purpose of evaluating dynamic amplification factors, taking into account the randomness of different factors associated to characteristics of the pavement, of the vehicles and of the traffic flow.     

Stochastic Modeling of Snow Loads Using a Filtered Poisson Process

The Bernoulli pulse process has been used in the past for modeling snow loads. However, it is not an appropriate model for heavy snow-load areas as the snow accumulation cannot be simulated, which may lead to an underconservative assessment of buildings in such areas. In this study, a filtered Poisson process (FPP) is investigated and demonstrated to be an effective stochastic model capable of simulating snow loads with or without accumulation. Weather records obtained from the National Climatic Data Center are used to calibrate the simulated ground snow-load records using the FPP model. A genetic algorithm is employed to determine the parameters of the FPP model. Illustrated by three selected sites in the United States, the annual maximum and daily ground snow-load characteristics are well captured by the FPP model. Potential applications of the model in reliability analysis and risk assessment are discussed.     

Techniques for Numerical Simulations of Concrete Slabs for Demolishing by Blasting

The subject of this article is the numerical simulation of concrete under explosive loading using a meshbased and a meshfree discretization technique. The presented techniques are verified by experimental data. Experimental evidence suggests that the complete stress–strain history relation must be considered as a basis for constitutive modeling if concrete is subjected to high loading rates. These dynamic phenomena cause a retardation of damage activation which must be taken into account when constitutive modeling is pursued on mesolevel instead of microlevel. By including a dynamic relaxation formulation within the framework of a general three-dimensional coupled continuum damage-plasticity law, it is shown that the solution of the wave propagation problem in materials with strain-softening becomes independent of mesh size. As the simulation of concrete under contact detonation causes severe numerical problems because of the large deformations, special numerical spatial discretization techniques have to be used. In this article we compare the results of a concrete slab under contact detonation using the finite element method code LS-DYNA with an arbitrary Lagrangian Eulerian coupling and the results obtained by a MLSPH code developed at our institute with experimental data. The same constitutive model for concrete and the same equation of state for the explosive is implemented in the two codes. The results of the different numerical simulations and the experimental data agree with each other well.     

Extension of Weighted Integral Stochastic Finite Element Method to the Analysis of Semi-Infinite Domain

In this study, one of the nonstatistical stochastic methods, i.e., the weighted integral method, is extended to analyze the semi-infinite domain. In the semi-infinite domain the region of uncertainties is vast when compared with that of the ordinary finite domain. Accordingly, the response variability in this domain has more significance than that in the ordinary finite domain. In modeling the semi-infinite domain, the coupled use of the infinite element is adopted. The results obtained using the proposed weighted integral method is compared with those obtained by Monte Carlo simulation. It is shown that the results of proposed method and those by the Monte Carlo simulation are in good agreement with each other showing the adequacy of the proposed method. In addition, the improvement in the response statistics, when the infinite domain is included in the model, is also attained, which shows the importance of the inclusion of far field in the analysis.     

Simulation Model for Level Furrows. II: Description, Validation, and Application

In a companion paper, experimental evidence was elaborated to confirm that in particular circumstances the performance of level-furrow irrigation can exceed that of level-basin irrigation. The application of a single furrow simulation model to an irrigation event in a level-furrow field resulted in large estimation errors. To overcome them, the development and validation of a numerical model of level-furrow irrigation is reported in this work. The model is based on the interconnection of a number of one-dimensional channels. The individual channels are connected using confluence or bifurcation points. Furrow infiltration is modelled through a Kostiakov infiltration equation including the furrow discharge as an independent variable. The proposed model is validated using the experimental level furrow evaluation presented in the companion paper. Finally, the model is applied to explore the conditions in which level furrow irrigation can outperform level basin irrigation. The proposed model stands as a valuable tool in the design and management of level furrow irrigation systems.     

Coupled Crop and Solid Set Sprinkler Simulation Model. II: Model Application

In this work, applications of the coupled solid set sprinkler irrigation and crop model AdorSim introduced in the companion paper are presented. The sprinkler irrigation model is based on ballistic theory, while the crop model is based on CropWat. AdorSim was used to evaluate the effect of sprinkler spacing on seasonal irrigation water use (WU) and crop yield. The most relevant results were related to the characterization of advanced irrigation scheduling strategies. The differences in crop yield and WU derived from irrigating at different times of the day were estimated for two locations strongly differing in wind speed. Irrigation guidelines were established in these locations to relate gross water use and water stress induced yield reductions. Simulations were also applied to estimate adequate wind speed thresholds for irrigation operation. In the experimental conditions, thresholds of 2.0–2.5?m?s?1 proved effective to control yield reductions and to minimize WU.     

Coupled Large Strain Consolidation and Solute Transport. II: Model Verification and Simulation Results

The results of numerical simulations for coupled large strain consolidation and solute transport, obtained using the CST1 model, are presented. CST1 accounts for advection, longitudinal and transverse dispersion, first-order decay reactions, and linear equilibrium sorption. Verification checks of CST1 show excellent agreement with analytical solutions for one-dimensional (1D) transport in rigid porous media, including various Peclet numbers and concentration boundary conditions. Similarly excellent agreement is observed for two-dimensional advection-dispersion transport in rigid media and 1D advection-dispersion transport in compressible media undergoing large strain consolidation. CST1 is then used to investigate consolidation-induced solute transport for a single composite liner system and a confined disposal facility for dredged contaminated sediments. In both cases, solute transport was found to be strongly affected by consolidation-induced advection both during and after the consolidation period. Consolidation has a lasting effect on solute migration because transient advective flows change the distribution of solute mass, which then becomes the initial condition for subsequent transport processes.     

Physically Based Coupled Model for Simulating 1D Surface–2D Subsurface Flow and Plant Water Uptake in Irrigation Furrows. II: Model Test and Evaluation

A physically based seasonal Furrow Irrigation Model was developed, which comprises three modules: The one-dimensional surface flow, the two-dimensional subsurface flow, and a crop model. The modeling principles of these modules, their simultaneous coupling, and the solution strategies were described in a companion paper (W?hling and Schmitz 2007). In the current contribution, we present the model testing with experimental data from five real-scale laboratory experiments [Hubert-Engels Laboratory (HEL)], two field experiments in Kharagpur, Eastern India (KGP), one literature data set [Flowell-wheel (FW)], and data from three irrigations during a corn growing season in Montpellier, Southern France [Lavalette experiments (LAT)]. The simulated irrigation advance times match well with the observations of the HEL, FW, and KGP experiments, which is confirmed by coefficients of determination R2 ≥ 0.99 and coefficients of efficiency Ce ≥ 0.7. Predicted recession times also match with the observations of the HEL runs, however, the values of R2 ≥ 0.9 and Ce ≥ 0.6 are lower for predicted recession times as compared to predicted advance times. In contrast to the other experiments in the study, advance times are underpredicted for the experiments in France. The established soil hydraulic parameters for this site lead to an underestimation of the actual initial infiltration capability of the soil. In the long-term simulation, however, the overall change in soil moisture storage is correctly predicted by the model and the calculated yield of 12.8?t?ha?1 is in very good agreement with the observations (12.7?t?ha?1). We evaluated the sensitivity of the input parameters with regards to predicted advance time and runoff in both a 26.4?m long furrow and a long 360?m long furrow. The analysis revealed that calculated runoff is four to five times more sensitive to the inlet flow rate than to infiltration parameters. Furrow geometry parameters are most sensitive to calculated advance times in the short furrow with low infiltration opportunity time, whereas the inflow rate and infiltration parameters are more sensitive to calculated advance times in the long furrow with larger infiltration opportunity time.     

Linking Nonlinear System Identification with Nonlinear Dynamic Simulation under OpenSees: Some Justifications and Implementations

This study seeks to bridge the gap between nonlinear system identification and nonlinear dynamic finite-element analysis. Motivated by the needs in earthquake simulation, it is first investigated under which conditions and to what degree the prediction of maximum lateral drift and base shear requires accurate nonlinear hysteretic moment-rotation joint models. A series of simulations is carried out using a simple but typical steel frame under two different earthquake ground motion time histories scaled up to various levels. As one of the two major classes of models in nonlinear system identification, nonparametric models are proposed to be implemented into OpenSees. A methodology with details is provided to effectively implement feedforward neural networks with one hidden layer as a new one-dimensional nonlinear smooth material model directly from a MATLAB environment to OpenSees. The same methodology can be applied to benefit the implementation of other parametric and nonparametric models with linear parameterization. Numerical examples are provided. Challenges are discussed and future work is identified.     

Optimal Layout of Sewer Systems: A Deterministic versus a Stochastic Model

The optimization of a new or partially existing urban drainage system may be modeled as a subproblems sequence of layout and optimal design within the discrete search space. The design optimization, incorporating the optimal selection of the pumping stations, intermediate manholes, pipe sections, and installation depths, for a general system fixed layout in plan, is a high level sequential decision problem which may be efficiently solved deterministically through a multilevel dynamic programming model. The optimal general layout may be selected in a deterministic way by means of a simple economical comparison of all plan solutions having optimized designs, for small to medium sized systems (if the specific restrictions of the applications are appropriately exploited) in practicable computer time. For larger dimension networks, where it is clearly impossible to achieve plan optimization with full enumeration (which is a NP complete), stochastic search models can be used. For the subproblem layout, an effective enumeration model is presented; the results of a stochastic model proposed previously, using simulated annealing for an application example, are compared and discussed in detail.     

Life-Cycle Cost Analysis using Deterministic and Stochastic Methods: Conflicting Results

Life-cycle cost analysis is an essential approach to differentiating alternative rehabilitation strategies for steel bridge paint systems. An economic analysis (EA), which is a deterministic method, and the Markov decision process (MDP), which is a stochastic method, were used to carry out the life-cycle cost analysis. These analyses were applied to data from two state Departments of Transportation. The deterioration curves for steel bridge paint condition rating against age were constructed. Different rehabilitation scenarios were proposed for steel bridge paint. The EA and the MDP were used to analyze and differentiate among the proposed rehabilitation scenarios. The results of the EA were different from those of MDP for the two data sets. MDP favored the “do nothing” scenario until the end of paint life and then a complete repainting. EA indicated that the scenario “do spot repairs at state 3 of the paint life” and repeat that until the end of the bridge life was superior. The results were analyzed to determine the reason for the conflict.     

Global and Local Nonlinear System Responses under Narrowband Random Excitations. II: Prediction, Simulation, and Comparison

The response behavior of the single-degree-of-freedom (SDOF) nonlinear structural system subjected to narrowband stochastic excitations studied in Part I is investigated via simulations to verify the stochastic system characteristics assumed in the development of the semianalytical method. In addition, to demonstrate the accuracy of the method, predicted response–amplitude probability distributions are presented and compared to simulation results. Numerical simulations are conducted by directly integrating the SDOF system with the narrowband excitation modeled by the 1971 Shinozuka formulation. It is observed that the proposed semianalytical method is capable of accurately characterizing the stochastic response behavior of the nonlinear system by predicting the response–amplitude probability distribution and capturing the trends of variations in the response–amplitude statistical properties. In both the primary and the subharmonic resonance regions, good agreements between the response–amplitude probability distributions predicted by the semianalytical method and obtained from simulation results are observed both qualitatively and quantitatively. In addition, trends of the variations in the probability masses associated with the modes with variations in excitation parameters (bandwidth and variance) are captured.     

Autoparametric Resonance in a Pedestrian Steel Arch Bridge: Solferino Bridge, Paris

Autoparametric resonance is treated as the reason of arising excessive lateral vibrations in the steel arch bridge (the Solferino Bridge). To explain this phenomenon, a physical model (a double pendulum) is proposed. Its behavior, as a rule, depends on dynamic characteristics of a bridge rather than on its type. The response of a two degree-of-freedom system with quadratic nonlinearities in the presence of two-to-one autoparametric resonance is investigated. The perturbation method of multiple time scales is used to construct first-order nonlinear differential equations and to determine steady state solutions and their stability. Bifurcation analysis is performed to determine a critical (threshold) value in the external load (control) parameter. The autoparametric resonance becomes possible if an excited torsional mode is near a primary resonance and an external load parameter caused by pedestrians is equal or higher than its critical value. When the increasing load parameter passes through the critical value (because a quantity of pedestrians on the bridge is increased), a jump phenomenon (or fast growth) is observed for the lateral mode, the torsional mode is saturated and has much smaller amplitudes. Field tests were held to understand a phenomenon of an excessive lateral movement, and to enforce the Solferino Bridge. Theoretical results of the present paper are compared with those experimental measurements. Swaying of pedestrian bridges can be treated as a two-step process. The first step (achievement of parametric resonance), described in this paper, is the condition for the beginning of the second step—the process of possible synchronization of applied forces and the interactions between them and the lateral and torsional modes of vibration.     

Physically Based Coupled Model for Simulating 1D Surface–2D Subsurface Flow and Plant Water Uptake in Irrigation Furrows. I: Model Development

Physically based modeling of the interacting water flow during a furrow irrigation season can contribute to both a sustainable irrigation management and an improvement of the furrow irrigation efficiency. This paper presents a process based seasonal furrow irrigation model which describes the interacting one-dimensional surface–two-dimensional subsurface flow and crop growth during a whole growing period. The irrigation advance model presented in a previous study is extended to all hydraulic phases of an irrigation event. It is based on an analytical solution of the zero-inertia surface flow equations and is iteratively coupled with the two-dimensional subsurface flow model HYDRUS-2. A conceptual crop growth model calculates daily evaporation, transpiration and leaf area index. The crop model and HYDRUS-2 are coupled via its common boundaries, namely (1) by the flux across the soil-atmosphere interface; and (2) by the flux from the root zone, which is associated with the plant water uptake. We assume the water stress is the only environmental factor reducing crop development and hence final crop yield. The model performance is evaluated with field experimental data in the companion paper, Part II: Model Test and Evaluation (W?hling and Mailhol 2007).     

Coupled Large Strain Consolidation and Solute Transport. I: Model Development

The development of a numerical model, CST1, for coupled large strain consolidation and solute transport in saturated porous media is presented. The consolidation algorithm is one-dimensional and includes the capabilities of a previous code, CS2, with the addition of time-dependent loading, unload/reload effects, and an externally-applied hydraulic gradient. The solute transport algorithm is two-dimensional and accounts for advection, longitudinal and transverse dispersion, first-order decay reactions, and linear equilibrium sorption. Solute transport is consistent with temporal and spatial variations of porosity and seepage velocity in the consolidating layer. The key to the transport model is the definition of two Lagrangian fields of elements that follow the motions of fluid and solid phases separately. This reduces numerical dispersion and simplifies transport calculations to that of dispersion mass flow between contiguous fluid elements. The effect of relative numerical resolution of fluid and solid elements on the accuracy of sorption/desorption is also discussed. This paper presents the theoretical and numerical development of the CST1 model. A companion paper presents verification checks of CST1 and the results of simulations that illustrate the significance of consolidation-induced solute transport for some interesting numeric examples.     

Peak Response of a Nonlinear Beam

A model for estimating the peak dynamic response distribution of a nonlinear beam, based on a special class of non-Gaussian stochastic processes, is proposed in this paper. It is shown that the stochastic response of a cantilever beam with geometrically nonlinear behavior can be accurately calibrated with translation processes. Different models to describe the significant bimodal features in the marginal probability density functions of the response time histories are proposed. Finally, two of these models are used to estimate the response peak value distributions and the results are compared. This comparison demonstrates the effects of inaccurate models for the parent response processes on the peaks estimation.