Moving Boundary Model Research Articles

An inverse front tracking method for modeling solidification process in a smelting furnace

An inverse process based on the conjugate gradient and adjoint problem is developed for predicting the time-varying bank thickness during the solidification/melting process in a smelting furnace. The direct problem rest on a single-phase moving boundary model to simulate the solid bank and refractory brick, simultaneously. The time-varying heat flux at solid/liquid interface, initial bank thickness and time-varying heat transfer coefficient at outer surface of the furnace are considered as the unknowns. Unlike the methods developed so far based on the enthalpy model, the current method does not require any prior information regarding the thermophysical properties of the liquid-phase and complex physical phenomena that occur in it. This improves the uniqueness of the solution that is inherent in the ill-posed inverse methods. To avoid the so-called “inverse crime”, a two-phase enthalpy method is used to generate the simulated measurement. These measurements are used in the present single-phase method for reconstruction of bank history. The model has shown good performance for non-intrusive temperature obtained from the outer surface of the furnace. The inverse model has been validated through an experiment conducted in a metallurgical reactor. A reasonable agreement between the estimated and measured molten salt bank indicates the existence and convergence of the inverse solution.

Switching criteria analysis for a condenser moving boundary model

The switching moving boundary (SMB) scheme is widely used for numerical simulation of heat exchangers, especially in vapour compression refrigeration system. The method divides the heat exchanger into up to three zones (superheated vapour, two-phase fluid and subcooled liquid), depending on the operating conditions and treats each as a lumped-parameter system. During transients the number of zones may vary, and suitable switching criteria and related threshold values must be given, for this change to occur. Also, variables for the zones momentarily phased out need to be tracked, to allow smooth operation of the model. In this work, a switching moving boundary model of a brazed plate condenser in counter-flow arrangement is studied to obtain some useful guidelines for the selection of the optimal switching thresholds. It is shown that these values influence both the accuracy and the numerical robustness of the model; moreover an appropriate selection of these parameters may allow the usage of a fixed-step solver, which is more suitable for real-time simulations.

The dynamic behaviour of ORC-based power units fed by exhaust gases of internal combustion engines in mobile applications

Exhaust gases Waste Heat Recovery (WHR) in Internal Combustion Engines (ICEs) performed through ORC-based Power Units (ORC-bPU) ensures a reduction of fuel consumption and consequently CO2 emissions. Nevertheless, high fluctuations of hot source push the ORC-bPU to work frequently in severe off-design conditions. Hence, a deep knowledge of the unit dynamic behaviour is fundamental to develop control and operating strategies allowing to achieve a successful recovery. Dynamic response assessment of ORC-bPUs has been treated in literature but making mainly reference to theoretical approaches or to variations of input variables without considering the matching to the engine and the necessary constraints which are present in a real mobile application. Moreover, Moving Boundary (MB) models are generally used as theoretical tools to support the dynamic analysis focusing the attention on Heat Recovery Vapor Generator (HRVG) which rules the plant dynamic response. In MB models, boundary conditions at the HRVG exit are mainly fixed by the expander and by the remaining circuit. To date, the attention was focused on the presence as expander of dynamic machines (turbine), deserving an evident lower attention to volumetric expanders nonetheless their higher suitability for low-medium scale ORC applications (few kWs). To fill these knowledge gaps, a novel approach is pursued in the present paper. The dynamic response of an ORC-bPU was experimentally observed for a step change of torque and revolution speed of an ICE directly connected to the recovery unit. The variation of engine operating conditions produced an unsteady variation of the temperature and flow rate of the exhaust gas feeding the unit. The dynamics of the engine and the connecting pipes is considered as well as all the typical constraints of a real situation. Results show HRVG and exhaust pipe ruling the dynamic behaviour of the unit, leading to long time constant and raising time of gas temperature of 150 s and 300 s respectively. These results show that the unit almost always works in transient conditions being engine torque and speed variations very fast. Nevertheless, thanks to the self-regulation capacity and the robustness of the scroll expander, the unit reacts in a satisfactory way. A further novelty of the present study concerns the integration of the widely used Moving Boundary (MB) approach with Permeability theory which considers the presence of a volumetric expander and all the ither downstream components, finding a match not available in literature between the HRVG and a volumetric expander and pump. The results of the new Permeability-Moving Boundary model (P-MB) was compared with those of a more comprehensive mathematical model. The comparisons show a comparable accuracy and a significantly lower computational time achieved with P-MB. Hence, P-MB could be implemented on board to set up control strategies enhancing the recovery tuned by a model-based approach.

Pattern formation and travelling waves in a multiphase moving boundary model of tumour growth.

We employ the multiphase, moving boundary model of Byrne et al. (2003, Appl. Math. Lett., 16, 567-573) that describes the evolution of a motile, viscous tumour cell phase and an inviscid extracellular liquid phase. This model comprises two partial differential equations that govern the cell volume fraction and the cell velocity, together with a moving boundary condition for the tumour edge, and here we characterize and analyse its travelling-wave and pattern-forming behaviour. Numerical simulations of the model indicate that patterned solutions can be obtained, which correspond to multiple regions of high cell density separated by regions of low cell density. In other parameter regimes, solutions of the model can develop into a forward- or backward-moving travelling wave, corresponding to tumour growth or extinction, respectively. A travelling-wave analysis allows us to find the corresponding wave speed, as well as criteria for the growth or extinction of the tumour. Furthermore, a stability analysis of these travelling-wave solutions provides us with criteria for the occurrence of patterned solutions. Finally, we discuss how the initial cell distribution, as well as parameters related to cellular motion and cell-liquid drag, control the qualitative features of patterned solutions.

Experimental Validation of Switched Moving Boundary Modeling of Phase Change Thermal Energy Storage Systems

Abstract Thermal Energy Storage (TES) devices use Phase Change Materials (PCMs) to store and release thermal energy. Control-oriented models are needed to predict the behavior of TES devices and experimental validation is necessary to demonstrate the predictive capabilities of these models. This paper presents an experimental validation of a switched Moving Boundary (MB) approach for modeling TES devices, where the dynamics of the device are captured with fewer states than traditional models. A graph-based modeling approach is used to model heat flow, while the moving boundary captures the time-varying liquid and solid regions of the TES. The model uses a Finite State Machine (FSM) to switch between four modes of operation based on the State-of-Charge (SOC) of the TES. Results show that the switched MB approach has similar accuracy and lower computational cost compared to traditional modeling approaches when predicting the SOC of an experimental TES device.

Abstract 18625: Mechano-Transcriptomic Interaction Mediates Spatial Variations in Early Vascular Fibrosis

Background: The spatiotemporal variations of wall shear stress (WSS) modulate vascular genomics and function. Despite the advances in imaging modalities and computational modeling, the link between local hemodynamics and genetic pathways underlying atherosclerosis development remains elusive. We hypothesized that differential WSS patterns in the aorta modulate fibroblast gene expression in response to high fat diet (HFD) leading to vascular stiffness. Methods: We performed ultrasound-based 4-D+time moving boundary computational fluid dynamics (CFD) on the aorta of Ldlr -/- mice fed a normal diet (ND) or HFD during 4 weeks. B-mode images (Vevo 3100) of the aortic arch were used to reconstruct a 3-D model of the lumen structure by revolving the vessel wall around the centerline in the aorta and the branches. Computational domain reconstruction was followed by image registration to generate a moving boundary model. WSS contours and velocity profiles were acquired by solving Navier-Stokes equations using svFSI code. The longitudinal strains along the outer curvature of the aortic arch over several cardiac cycles were measured, and the changes were compared with the effects of HFD. Mouse aortas were processed for single cell RNA sequencing and analyzed using the Scanpy package. Results and Conclusion: Our analysis of transcriptomics profiles revealed increased Acta2 and Postn expression in the myofibroblast subclusters, suggesting myofibroblast differentiation in response to HFD in the aortic arch. This was confirmed and localized to the lesser curvature of the aortic arch through Periostin immunostaining. We found that the increase in Postn and Acta2 is associated with reduced arterial strain or increased arterial stiffness measured in the aortic arch. In parallel, CFD analysis demonstrated that an elevated WSS along the outer curvature vs. low WSS and disturbed flow along the inner curvature in early diastole results in differential gene expression to regulate myofibroblast differentiation and modulates vascular stiffness.

Survival, extinction, and interface stability in a two-phase moving boundary model of biological invasion

We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two adjacent populations: each population undergoes linear diffusion and logistic growth, and the boundary between the two populations evolves according to a two-phase Stefan condition. This mathematical model describes situations where one population invades into regions occupied by the other population, such as the spreading of a malignant tumour into surrounding tissues. Full time-dependent numerical solutions are obtained using a level-set numerical method. We use these numerical solutions to explore several properties of the model including: (i) survival and extinction of one population initially surrounded by the other; and (ii) linear stability of the moving front boundary in the context of a travelling wave solution subjected to transverse perturbations. Overall, we show that many features of the well-studied one-phase single population analogue of this model can be very different in the more realistic two-phase setting. These results are important because realistic examples of biological invasion involve interactions between multiple populations and so great care should be taken when extrapolating predictions from a one-phase single population model to cases for which multiple populations are present. Open source Julia-based software is available on GitHub to replicate all results in this study.

Modeling Strategies for Crude Oil-Induced Fouling in Heat Exchangers: A Review

Semi-empirical fouling models have proven more effective in predicting the fouling behavior of crude oils in heat exchangers. These models have aided refineries in optimizing operating conditions to minimize or eliminate fouling in preheat exchangers. Despite their complexity, the models continue to improve in approximating real behavior by taking into account previously neglected aspects. This paper summarizes these findings from various studies along with highlighting different factors which were considered to enhance the predictability of the models. A critical analysis is presented to emphasize that activation energy in the deposition term varies depending on the physical processes involved and may not conform to the precise definition of activation energy. Two primary modeling approaches for crude oil fouling have emerged, i.e., deterministic and threshold models. Threshold models have gained more attention due to their fewer adjustable parameters. The stability or compatibility of crude oils has a substantial impact on asphaltene deposition, which is a major contributor to fouling. However, incorporating this factor into fouling models has received little attention. The inclusion of parameters for inorganic fraction and ageing has increased predictability by accurately estimating the fouling thickness. The use of CFD to analyze fouling mechanisms is promising, particularly for complex geometries. The dynamic and moving boundary modeling approach has potential to broaden the applicability of fouling models.

A Peridynamic Approach for the Evaluation of Metal Ablation under High燭emperature

In this paper, the evaluations of metal ablation processes under high temperature, i.e., the Al plate ablated by a laser and a heat carrier and the reactor pressure vessel ablated by a core melt, are studied by a novel peridynamic method. Above all, the peridynamic formulation for the heat conduction problem is obtained by Taylor’s expansion technique. Then, a simple and efficient moving boundary model in the peridynamic framework is proposed to handle the variable geometries, in which the ablated states of material points are described by an additional scalar field. Next, due to the automatic non-interpenetration properties of peridynamic method, a contact algorithm is established to determine the contact relationship between the ablated system and the additional heat carrier. In addition, the corresponding computational procedure is listed in detail. Finally, several numerical examples are carried out and the results verify the validity and accuracy of the present method.

Pattern formation and front stability for a moving-boundary model of biological invasion and recession

We investigate pattern formation in a two-dimensional (2D) Fisher–Stefan model, which involves solving the Fisher–KPP equation on a compactly-supported region with a moving boundary. The boundary evolves analogously to the classical one-phase Stefan problem, such that boundary speed is proportional to the local population density gradient. By combining the Fisher–KPP and classical Stefan theory, the Fisher–Stefan model alleviates two limitations of the Fisher–KPP equation for biological populations. Unlike the Fisher–KPP equation, solutions to the Fisher–Stefan model have compact support, explicitly defining the region occupied by the population. Furthermore, the Fisher–Stefan model admits travelling wave solutions with non-negative density for all wave speeds c∈(−∞,∞), and can thus model both population invasion and population recession. In this work, we investigate whether the 2D Fisher–Stefan model predicts pattern formation, by analysing the linear stability of planar travelling wave solutions to sinusoidal transverse perturbations. Planar fronts of the Fisher–KPP equation are linearly stable. Similarly, we demonstrate that invading planar fronts (c>0) of the Fisher–Stefan model are linearly stable to perturbations of all wave numbers. However, our analysis demonstrates that receding planar fronts (c<0) of the Fisher–Stefan model are linearly unstable for all wave numbers. This is analogous to unstable solutions for planar solidification in the classical Stefan problem. Introducing a surface tension regularisation stabilises receding fronts for short-wavelength perturbations, giving rise to a range of unstable modes and a most unstable wave number. We supplement linear stability analysis with level-set numerical solutions that corroborate theoretical results. Overall, front instability in the Fisher–Stefan model suggests a new mechanism for pattern formation in receding biological populations.

A new moving-boundary algorithm to predict heat transfer rate of counter-flow water-cooled transcritical CO2 gas cooler

A new moving-boundary model was proposed for predicting steady-state heat transfer rate of water-cooled transcritical CO2 gas cooler. The new model aims to separate the CO2 gas cooler into up to three zones depending on the local thermal capacitance rate, which is significantly different from the moving-boundary models used in subcritical region, which is based on fluid phase. The experimental data from the literature were used for model validation, and the results show that the prediction accuracy of the new moving-boundary model is comparable to that of the finite volume method. The deviations between predicted and measured heating capacities are within ±5%, and the predicted CO2 outlet temperatures are within ±4°C. The averaged computation time of the model is 22% of that of the finite volume model for the 45 data points in the present study. The proposed new model is suitable for steady-state simulation of transcritical CO2 water-cooled gas cooler, either standalone or integrated into overall CO2 heat pump water heater systems.

(Invited) Battphase – a Convergent, Non-Oscillatory, Efficient Algorithm and Code for Predicting Shape Changes in Lithium Metal Batteries Using Phase-Field Models

Electrochemical models at different scales and varying levels of complexity have been used in the literature to study the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale (phase-field approaches), and multiscale models.1-5 Thermodynamics-based equations have been used to study phase changes in lithium batteries using phase-field approaches. However, grid convergence studies and the effect of additional parameters needed to simulate these models are not well-documented in the literature. In this talk, using a motivating example of a moving boundary model in one- and two-dimensions, we show how one can properly formulate phase-field models using the immersed interface/domain approach, implement robust and efficient algorithms for the same and analyze the results (Figure 1). An open-access code with no restrictions is provided as well. The talk concludes with some thoughts on the computational efficiency of phase-field models for simulating dendritic growth. Acknowledgements The authors would like to express gratitude to Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the DOE through the Advanced Battery Material Research (BMR) Program (Battery500 consortium). This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Supported by the Laboratory Directed Research and Development program at Sandia National Laboratories, a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. VS acknowledges interactions with Dr. Srikanth Vedantam from IIT Madras, India and Dr. Daniel Wheeler from National Institute of Standards and Technology for early discussions on phase-field and level-set methods. VS also acknowledges Richard Braatz from Massachusetts Institute of Technology for pointing out the poor results from standard algorithms because of the convective nature of the models.

Immersed Interface and Diffuse-Domain Approach for Current-Potential Distributions and Electrodeposition Problems

Several numerical approaches are being developed to solve the moving boundary models which predict the morphological evolution of the electrode surface during electrodeposition. Despite these significant research efforts over a broad range of materials, scales, and purposes, the prediction of the shape evolution of the electrodes over time is still a challenging problem. One needs to solve these moving boundary problems, as the potential and current distributions within the cell get affected by the geometry.1-2 In this work, we will demonstrate a recently developed numerical framework based on the diffused domain approach using phase-field models for two classical example, Hull cell and copper deposition in trenches.3 The original model equation was carefully reformulated as a diffuse-domain/immerse domain approach for steady state current-potential distribution problems.4-5 Then the shape change problem is cast as a transient phase-field problem to predict the shape changes of the electrode during electrodeposition. A comparative analysis has also been performed for the efficiency, accuracy, speed, and convergence of the present solutions for the Hull cell with other available numerical and even analytical methods. It can be stated that the present phase-field model is robust and efficient for predicting the shape changes of the electrode over time without oscillations. Acknowledgments This research was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the US Department of Energy (DoE) through the Advanced Battery Materials Research Program (Battery500 Consortium) References V. R. Subramanian, and R. E. White, J. Electrochem. Soc, 149(10) C498 (2002).R. Alkire, T. Bergh, and R. L. Sani, J. Electrochem. Soc., 125, 1981 (1978).T. Jang, L. Mishra, S. A. Roberts, A. Subramaniam, M. Uppaluri, M. P. Gururajan, J. Zhang, and V. R. Subramanian, “BattPhase – A convergent, non-oscillatory, efficient algorithm and code for predicting shape changes in lithium metal batteries using phase-field models – 1. Secondary Current Distribution,” ECSarXiv (2022), doi:10.1149/osf.io/k2vu6C. S. Peskin, Acta Numer., 11, 479 (2003).X. Li, J. Lowengrub, A. Ratz and A. Voigt, Commun. Math. Sci., 7, 81 (2009).

BattPhase—A Convergent, Non-Oscillatory, Efficient Algorithm and Code for Predicting Shape Changes in Lithium Metal Batteries Using Phase-Field Models: Part I. Secondary Current Distribution

Electrochemical models at different scales and varying levels of complexity have been used in the literature to study the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale (phase-field approaches), and multiscale models. Thermodynamics-based equations have been used to study phase changes in lithium batteries using phase-field approaches. However, grid convergence studies and the effect of additional parameters needed to simulate these models are not well-documented in the literature. In this paper, using a motivating example of a moving boundary model in one- and two-dimensions, we show how one can formulate phase-field models, implement algorithms for the same and analyze the results. An open-access code with no restrictions is provided as well. The article concludes with some thoughts on the computational efficiency of phase-field models for simulating dendritic growth.

Travelling-Wave and Asymptotic Analysis of a Multiphase Moving Boundary Model for Engineered Tissue Growth

We derive a multiphase, moving boundary model to represent the development of tissue in vitro in a porous tissue engineering scaffold. We consider a cell, extra-cellular liquid and a rigid scaffold phase, and adopt Darcy’s law to relate the velocity of the cell and liquid phases to their respective pressures. Cell–cell and cell–scaffold interactions which can drive cellular motion are accounted for by utilising relevant constitutive assumptions for the pressure in the cell phase. We reduce the model to a nonlinear reaction–diffusion equation for the cell phase, coupled to a moving boundary condition for the tissue edge, the diffusivity being dependent on the cell and scaffold volume fractions, cell and liquid viscosities and parameters that relate to cellular motion. Numerical simulations reveal that the reduced model admits three regimes for the evolution of the tissue edge at large time: linear, logarithmic and stationary. Employing travelling-wave and asymptotic analysis, we characterise these regimes in terms of parameters related to cellular production and motion. The results of our investigation allow us to suggest optimal values for the governing parameters, so as to stimulate tissue growth in an engineering scaffold.

A thermal network model for hydrocarbon heat pump systems: A coupling analysis of configuration, working condition, and refrigeration distribution

The ambition of zero emission neighborhood has been set out to operate the building components with zero life cycle greenhouse gas emissions. Hydrocarbon heat pumps as the building components with nearly zero greenhouse gas emissions are faced with the problem of simultaneously reducing refrigerant charges and maintaining competitive capacities. These must be resolved by formulating an effective modeling tool for detailed design and optimization. To develop a resistance–capacitance network model, interdisciplinary knowledge (including graph theory, heat and mass transfer, local moving boundary modeling, and algebraic multigrid) is integrated. The model simultaneously considers heat exchanger circuitries with a high detail level and component behaviors at a holistic system level. Based on experimental validation, the model’s error is ∼ 10%. In an R290 heat pump case study, the coupling mechanism of the system’s configuration, working conditions, and refrigerant distribution are analyzed. Results indicate that the refrigerant charge can be reduced by 11.6% at the expense of a 4.2% reduction in the coefficient of performance, by varying the compressor displacement alone. In response to the variation in the system’s refrigerant, 46.8%, 7.85%, and 44.2% of the total amount of refrigerants are allocated to the condenser, evaporator, and compressor, respectively. The distribution of the refrigerant quality in the heat exchanger is also visualized to indicate the direction of refrigerant reduction.

Modeling of the time evolution of the solidification front in ice cubes

The present work is aimed at putting forward a three-dimensional moving-boundary model to calculate the water solidification in ice trays subjected to operating conditions typically found in household appliances. To better understand the physical phenomena and validate the model, experiments were performed in a purpose-built closed-loop wind tunnel facility at -23 °C and air flow rate of 10 m³ h−1 using a single volume of 145 ml fed with distilled, mineral, and filtered tap water. The end of the solidification process was identified by monitoring the cooling curves with the aid of seven thermocouples placed within the ice cube. In the numerical front, the ice cube was modeled as a pyramid trunk and Stefan's formulation was applied to each of the domain boundaries so that the ice thickness could be calculated over time. Deviations within a ±10% error band were observed for all cases. A good agreement between the model predictions for the time evolution of the ice cube temperature and the experimental counterparts was also verified. In addition, literature data for the position of the solidification front and the remaining liquid fraction were fairly predicted by the model.

A moving-boundary model of reactive settling in wastewater treatment. Part 2: Numerical scheme

A numerical scheme is proposed for the simulation of reactive settling in sequencing batch reactors (SBRs) in wastewater treatment plants. Reactive settling is the process of sedimentation of flocculated particles (biomass; activated sludge) consisting of several material components that react with substrates dissolved in the fluid. An SBR is operated in cycles of consecutive fill, react, settle, draw, and idle stages, which means that the volume in the tank varies and the surface moves with time. The process is modelled by a system of spatially one-dimensional, nonlinear, strongly degenerate parabolic convection-diffusion-reaction equations. This system is coupled via conditions of mass conservation to transport equations on a half line whose origin is located at a moving boundary and that models the effluent pipe. A finite-difference scheme is proved to satisfy an invariant-region property (in particular, it is positivity preserving) if executed in a simple splitting way. Simulations are presented with a modified variant of the established activated sludge model no. 1 (ASM1).

Dynamic simulation model with virtual interfaces of supercritical working fluid heat exchanger based on moving boundary method

The supercritical cycle has a better variable-temperature match between the working fluid and heat source, potentially providing higher efficiency. Accurate simulation of the transient performance of supercritical heat exchangers is significant in advanced thermal system control. This paper proposes a dynamic model of supercritical heat exchangers based on the moving boundary method. The model redefines the concept of “interface” in the traditional moving boundary model. The new interfaces are determined by the thermophysical properties of the working fluid, called “virtual interfaces”. A control-volume separation method is proposed based on the virtual interface. Additionally, the specific enthalpy is selected as the switching criterion for the configuration of the control volumes, so the model can dynamically adjust the number of control volumes. The integrity check results show that the simulation accuracy is at least equivalent to the finite volume model with 20 control volumes; however, the time cost is approximately 1/5 of that of the finite volume model with the same precision. An experimental study on the convective heat transfer of supercritical n-decane in an electrically heated vertical tube was conducted. The maximum absolute error of the steady-state outlet temperature is ±1.5 K, and the relative error is ±3% under different pressures.

Centrifuge modelling of wave-induced seabed response in clay

This paper describes a programme of centrifuge tests investigating the behaviour of clayey seabed under wave loading using an in-flight wave loading system. Three model seabeds of kaolin clay capturing typical unconsolidated, normally consolidated and overconsolidated soil responses were considered, with each seabed experiencing several episodes of wave loading and resting. Data acquisition measures included pore pressure transducers, accelerometer, bender elements and T-bar penetrometers. The depth-wise distribution of excess pore pressure, soil strength and modulus, as well as the motion of the liquefied layer of the seabed, was monitored throughout to enable a thorough investigation into the liquefaction and reconsolidation features of the soil. For the unconsolidated and normally consolidated soils, remarkable development of residual pore pressure was observed, and there was evidence that the strength/modulus recovery cannot be achieved by the surficial soil within a prototype time of 15 days. Within a certain depth below this surficial layer, there was a drastic increase in undrained strength, and this phenomenon was carefully examined by a modified moving-boundary model. For the overconsolidated soil, the build-up of residual pore pressure was rather limited, but discernible amplification of oscillatory pore pressure amplitude was observed. Implications for practice in offshore engineering are discussed based on the experimental findings.