Hyperbolic Parameters Research Articles

Macro-element modelling for lateral response of monopiles with local scour hole via hyperbolic hardening relation

Monopile is a popular choice in the foundation supporting offshore wind turbines (OWTs), with local scour significantly impacting their lateral responses. Macro-element model, which encapsulates the response between the monopile and the surrounding seabed soils into a force-displacement relation, has been extensively developed to describe offshore foundations. However, such kind of models specifically targeting monopiles subjected to lateral loading in local scour remain underdeveloped. This work proposes a macro-element model with a succinct hyperbolic hardening relation for laterally loaded monopiles in local scour conditions, using the evolutionary polynomial regression (EPR) machine learning technique for easy and optimal design. First, the finite element model is verified and extended to generate force-displacement responses considering the monopile geometries, soil characteristics, and local scour geometries. These results are then utilised to determine the optimal hyperbolic hardening relation of the macro-element model. Next, the EPR technique is employed to determine the relationship between the hyperbolic hardening relation parameters and the influencing factors. Finally, the macro-element model is successfully evaluated by comparing with measurements from centrifuge tests and numerical solutions by finite element analysis, demonstrating its applicability in practical design and the ability to reproduce FEA results with a significant reduction in computational cost.

Permanent deformation prediction model for freeze–thaw coarse–fine mixture of geomaterials with varying fine content: Influence of loading frequency

The impact of cyclic loading frequency (fcyc) on the permanent deformation (εp) of freeze–thaw coarse–fine mixture of geomaterials (FTCF) has been extensively investigated. In this work, long-term cyclic triaxial tests were conducted on FTCF specimens with varying fcyc and deviatoric stress (qcyc) with different numbers of freeze–thaw cycles (NFT), in order to investigate εp under freeze–thaw cycling. This study systematically analysed and discussed the effects of fcyc and qcyc on εp of FTCF samples with different fine particle contents (FC). A rate-dependent multistage load-prediction model for εp was proposed and evaluated. The results showed that the freeze–thaw cyclic had a less significant impact on εp when compared to the dynamic triaxial loading. The speed and piston effects of the FTCF under dynamic loads were mutually restricting, with their combined impact closely related to the loading frequency. A higher deformation resistance for a coarse-grained skeleton is attained with the effective filling of fine particle clusters in the pores of skeleton. A function was proposed to describe the relationship between the hyperbolic model parameters and fcyc, qcyc, as well as FC. This function could be used to estimate the hyperbolic model parameters under different dynamic stresses and material states. An equivalent stress-state parameter was introduced to consider the effect of the loading frequency, enabling the exploration of dynamic loading's influence on the equivalent vibration number (Neq). A comparison between the predicted results and the test data showed that the proposed model could accurately reproduce the cumulative behaviour of the εp of FTCF under different fcyc and qcyc.

Uncertainty analysis for drilled shaft axial behavior using CYCU/DrilledShaft/143

Drilled shaft axial capacities and their uncertainties were evaluated in this paper. A large load test database of drilled shafts labeled as CYCU/DrilledShaft/143 was compiled for this evaluation. All load tests were performed in the field under drained and undrained soil conditions. The database was made available at ISSMGE TC304 database sharing platform 304 dB. Drained and undrained analyses were conducted separately. These load test data were first analyzed using representative interpretation criteria to determine their “capacities”. The results of each of the interpretation criteria were next normalized by a standard interpretation criterion and a predicted capacity to establish the relationships between these various interpretation criteria and to characterize model factors, respectively. The analyses of 143 drilled shafts indicated that L1 and DeBeer interpreted loads can be recommended for the serviceability limit state design. The criteria van der Veen, 4%B, Terzaghi and Peck, slope–tangent, L2, and Fuller and Hoy yielded values that are at the transition region of the load–displacement curve, in which the “ultimate” capacity can be reasonably estimated. The Chin method is not conservative, because it produced a value larger than all of the above interpreted “ultimate” capacities with displacements exceeding 60 mm on the average and beyond the range of the measured load–displacement curve. The scatter in the load–displacement curves is studied by applying different normalization schemes and fitting the normalized curves to a hyperbolic model. The hyperbolic model (curve fitting) parameters are generally negatively correlated. Statistics of these hyperbolic model parameters are shown to be comparable to values reported in previous studies. This hyperbolic model is widely used for reliability-based design at the serviceability limit state. Hence, the statistics of the hyperbolic model parameters presented in this study are useful.

Using FEM-AI Technique to Predict the Behavior of Strip Footing Rested on Undrained Clay Layer Improved with Replacement and Geo-Grid

The objective of this research is to predict how strip footings behave when rested on an undrained clay layer enhanced using a top replacement layer with and without a geo-grid. The study was conducted in several stages, including collecting load-settlement curves from "Finite Element Method" (FEM) models with different clay strengths, replacement thicknesses, and axial stiffnesses of the geo-grid. These curves were then idealized using a hyperbolic model, and the idealized hyperbolic parameters were predicted using three different AI techniques. According to the numerical results, the ultimate bearing pressure of pure clay models was found to be five times the undrained strength of the clay. These findings align with most established empirical bearing capacity formulas for undrained clays. The results also suggest that the initial modulus of the subgrade reaction is solely influenced by replacement thickness. Additionally, the enhancement in subgrade reaction due to the replacement layer decreases with increasing clay strength. However, the percentage of improvement decreased with higher clay strength. Moreover, the impact of the geo-grid was significant for settlement beyond 50mm, and it was more impactful in soft clay than in stiff clay. Finally, the research proposed predictive models employing the "Genetic Programming" (GP), "Artificial Neural Networks" (ANN), and "Evolutionary Polynomial Regression" (EPR) techniques, and these models exhibited an accuracy of about 88%. Doi: 10.28991/CEJ-2023-09-05-014 Full Text: PDF

Behavior of strip footing rested on undrained clay using consistency limits-based constitutive law

The behavior of undrained clay was extensively studied by many earlier researchers. A lot of constitutive models were developed to describe the behavior of undrained clay based on its mechanical properties. The aim of this research is to present an innovative constitutive model for undrained clay based on its consistency limits and water content. The main concept of this model is to estimate the mechanical properties of clay using earlier correlations with consistency limits, then implement the estimated mechanical properties in a hyperbolic model and calibrate the hyperbolic parameters to match the failure criteria of the undrained clay. To verify the validity of the developed constitutive model, it was applied on a standard problem which is a strip footing rested on undrained clay layer, the results confirmed the ability of the model to simulate the nonlinear behavior of undrained clay up to ultimate condition. The main advantage of this constitutive model is the ability to capture the reduction of mechanical properties of clay with the increase in its water content, which makes it ideal to study the impact of seepage on shallow foundation.

Post-construction safety assessment of a high concrete face rockfill dam

The most important issue regarding the safety and performance of concrete face rockfill dams (CFRDs) is to determine stresses and deformations. However, predictions of crest settlements of CFRDs are usually performed using empirical relationships. In recent years, CFRDs have been constructed much higher and at more complicated topographical and geological dam sites, so numerical analysis is required to evaluate the stress and deformations in the entire dam body. Also, assessing long-term rockfill behaviour and the concrete face membrane crack potential are important for post-construction dam safety. This study evaluates post-construction deformations and crest settlements of a high CFRD under two different loading cases, considering the non-linear elasto-plastic behaviour of the rockfill structure. As a constitutive model, the Duncan–Chang hyperbolic stress–strain model was applied in finite-element simulations considering the failure criterion is isotropic and hardening. Calibration of the rockfill's hyperbolic parameters was performed by comparing the calculated displacements with actual settlement measurements. Computed crest settlements were also compared with those of some CFRDs given in the literature. Calculated crest settlement and other deformations are in good agreement with the rockfill settlement measurements and in acceptable ranges, and do not threaten the dam's safety.

Hyperbolic Representation of Lateral Force–Displacement Relationship for Underground Installed Pipe

Extreme natural hazards such as earthquakes, landslides, and liquefaction create permanent ground deformation (PGD). With the recognition that PGD often causes the most serious local damage in underground structures such as buried pipelines and mining facilities, research and engineering practices for underground structures have focused on soil–structure interaction under PGD. In this study, an underground pipeline was investigated due to its simple geometry. Geotechnical data collection and analysis were used as a study method. Of key importance is the soil–pipe interaction with respect to PGD below the subsurface. This response is typically highlighted by a force vs. displacement relationship and is primarily a function of soil unit weight, depth from surface to the pipe centerline, and the pipe diameter. The non-linear force vs. displacement relationship for transverse horizontal force on a pipe subjected to lateral ground movement, can be represented by a hyperbola. The nonlinear hyperbola can then be turned into a linear line by transforming the axis. This paper investigates a wide range of soil characteristics and summarizes representative hyperbolic parameters for dry medium, dense, and very dense sand for lateral ground movement. The approach is convenient for modeling the soil–pipe interaction and is critical for addressing the complexities of soil and pipe performance, consistent with real-world soil–pipe behavior. The ideas and data analysis techniques presented in this study may be fine-tuned and applied to more complex problems including mining and could ultimately contribute to the management of geotechnical risks.

Two Mechanisms Drive Changes in Boreal Peatland Photosynthesis Following Long-Term Water Level Drawdown: Species Turnover and Altered Photosynthetic Capacity

Climate change and the related increases in evapotranspiration threaten to make northern peatlands drier. The carbon sink function in peatlands is based on the delicate balance between the photosynthesis and decomposition. However, little is known about how existing and invading plant species will photosynthesize under drier conditions. The aim of this study is to quantify the long-term consequences of climate change-induced drying for peatland photosynthesis in the level of individual species and vegetation community. We measured the species-level photosynthesis of vascular plants and mosses characteristic for the three peatland types (rich fen, poor fen, bog) within a 16-year water level drawdown (WLD) experiment. Measurements were made in the laboratory from mesocosms collected from the field within the same day. We applied nonlinear mixed-effects models to test the impact of WLD on hyperbolic photosynthetic light response curve parameters. The model was then used to upscale photosynthesis to site-level. WLD impacted site-level photosynthesis through two mechanisms: species turnover and changes in species-level photosynthesis rate. The rich fen was the most sensitive and underwent major changes through both mechanisms; the vascular plant community shifted to woody plant dominance with higher rate of photosynthesis than the pre-treatment vegetation, and the rate of species-level photosynthesis increased significantly. The bog had a stable plant community with little change in photosynthesis, while the poor fen was an intermediate of the three peatland types. Our results suggest that vascular plants are the main drivers of site-level productivity changes, while mosses are more resistant to change. The change seems proportional to the availability of mineral nutrients, with higher nutrient status supporting vascular plant expansion.

Artificial neural network prediction models for Montney shale gas production profile based on reservoir and fracture network parameters

The prediction of shale gas production is necessary to evaluate the project's economical feasibility. Some studies suggested prediction models for predicting shale gas production. However, the model-based planar fracture assumption may not apply to a naturally fractured shale gas reservoir which induces a complex fracture network. This paper proposes three ANN architectures for predicting the peak production and Arps's hyperbolic decline parameters (Di and b) of a shale gas well in the Montney formation with an existing natural fracture system. A production profile can be reconstructed using the Arps' hyperbolic decline model and the predicted parameters. The ANN architectures were developed based on 370 simulation data of the reservoir, hydraulic fracture design parameters, and the fracture network properties, including fracture spacing and fracture conductivity, which remarkably affect shale gas production. The testing results, using another set of 92 simulation data, confirmed the high correlation between the input and objective functions with R2 > 0.86. Moreover, good agreement was observed between the measured and predicted cumulative gas production at one-, five-, ten-, fifteen-, and twenty-years of production with R2 > 0.94, and percentage errors were lower than 15.6%. This suggests that the shale gas production can be predicted efficiently and reliably using the Arps' hyperbolic model and the predicted parameters. The estimated production profiles can be used to continuously update the field development plans and calculate the project's NPV. Furthermore, the proposed method is applicable for predicting the production of newly produced reservoirs with limited production history.

Effect of Particle Size, Moisture Content and Density on the Hyperbolic Model Parameters for Non-cohesive Soil

Effect of Particle Size, Moisture Content and Density on the Hyperbolic Model Parameters for Non-cohesive Soil

Impact of curing time on UCS-electrical resistivity relation of cement grouted sands

As the curing process proceeds, both the strength and electrical resistivity (pmix) of cement-based (or cement-grouted) materials increase, leading to the nondestructive pmix measurement technique is very appealing in the assessment/monitoring of the quality of cement-grouted materials. However, the strength gain of cement-grouted sands with time differs from the increase in pmix with time. Thus, the relationship between unconfined compressive strength (UCS) and pmix can be affected by the curing time. This study evaluated the effect of curing time on the relationship between pmix and UCS of sands grouted with microcement. The ultimate goal of this study is to estimate UCS over time of cement-grouted sands based on pmix. Three silica sands with different median particle sizes were grouted with microcement at different water-to-cement ratios (wc) of 1.0, 1.5, and 2.0. Both unconfined compression test and electrical resistivity measurement test were conducted. Results demonstrate that curing time, particle size, and wc influenced both pmix and UCS of tested grouted sands in a similar manner; therefore, a direct relationship between pmix and UCS can be established. However, the complex impact of curing time on the relation between UCS and pmix and the nonlinear increase in UCS with time hinder the capture of adequate interplay between UCS, pmix, and curing time. Because a nonlinear increase in UCS with time can be represented by hyperbolic model, an estimation method for hyperbolic model parameters is newly suggested in this study based on pmix at early curing days.

Time delay compensation control using a Taylor series compound robust scheme for a semi‐active suspension with magneto rheological damper

AbstractTime delay significantly degrades the control performances of semi‐active magneto rheological damper. However, the robust control approaches combined with the Taylor series are difficult to perform time delay compensation because it has strict application conditions. In this study, two Taylor series compound robust control schemes are presented to address the robust control and time delay compensation problems for the semi‐active magneto rheological damper with time delay. The formulation of a quarter vehicle model with a magneto rheological damper is described by a hyperbolic tangent model. Given the mechanical characteristics, an experimental test was conducted to fit the hyperbolic tangent model parameters. As a prototype, the Taylor series‐H2/H∞ control approach is proposed through establishing a first‐order Taylor series‐delay equation in augmented state equation and using the H2/H∞ norms to constrain the predictive control force. Moreover, the Taylor series‐H2/H2 controller is proposed to reduce the conservatism and suppress the predictive control force amplification. Simulation results corroborate the efficacy of both control strategies. Specifically, compared with the Taylor series‐H2/H∞ control, the Taylor series‐H2/H2 control can obtain a better control effect for time delay compensation.

Constitutive Modelling of Short-Term Tensile Response of Geotextile Subjected to Mechanical and Abrasion Damages

This paper discusses simple constitutive models to represent the tensile response of a geotextile (GTX) and the influence of two endurance durability factors on that response: mechanical and abrasion damage, acting independently and sequentially. The damage was induced in laboratory under standard conditions. Two types of models were used: polynomial and hyperbolic. The polynomial models (order 4 and 6) approximated the short-term tensile experimental data very well (and better than the hyperbolic model), but its model parameters have no physical meaning. The hyperbolic model parameters did not always have the physical meaning reported in the literature. Correction factors were introduced successfully, to achieve that physical meaning. These correction factors were not materials constants and were affected by the damage induced, and by the type of aggregate used in the mechanical damage tests. Equations to estimate the model parameters of the damaged samples were proposed using the model parameters for the undamaged sample and its properties (tensile strength and corresponding correction factor), and the reduction factors allowing for damage for the initial stiffness (Ji) and tensile strength (Tmax).

Age-coherent extensions of the Lee–Carter model

Age coherence describes the property that forecast mortality rates across ages will not diverge in the long run. Although intuitively and biologically reasonable, this property is lost when the seminal Lee–Carter (LC) model and almost all its existing extensions are employed. In this paper, we propose two effective extensions of the LC model, allowing for the geometric (LC-G) and hyperbolic (LC-H) decayed relative speed of mortality decline at each age, over the out-of-sample forecasting steps. Those approaches are based on the original in-sample estimates of LC, which are easy to obtain. An inversed Epanechnikov kernel is employed to model the geometric and hyperbolic parameters across ages, and unknown parameters are selected via a data-driven method. With little added computational cost to LC, our approaches incorporate the dynamic and rotating relative speeds of mortality decline over ages, recognize the growing difficulty of such declines at older ages, provide age-coherent forecasts of mortality rates in the long run, and is easily extensible to multi-population cases. Using a large sample of 15 countries, we demonstrate that LC-G and LC-H, as well as their multi-population counterparties, consistently improve the forecasting accuracy of the competing LC model and its single- and multi-population extensions.Feng, L., Shi, Y., & Chang, L. (2021). Forecasting mortality with a hyperbolic spatial temporal VAR model. International Journal of Forecasting, 37(1), 255–273.

Predicting the Performance of Undeveloped Multi-Fractured Marcellus Gas Wells Using an Analytical Flow-Cell Model (FCM)

The objective of the present study is to predict how changes in the fracture treatment design parameters will affect the production performance of new gas wells in a target zone of the Marcellus shale. A recently developed analytical flow-cell model can estimate future production for new wells with different completion designs. The flow-cell model predictions were benchmarked using historic data of 11 wells and 6 different completion designs. First, a type well was generated and used with the flow-cell model to predict the performance of the later infill wells—with variable completion designs—based off the performance of earlier wells. The flow-cell model takes into account known hyperbolic forecast parameters (qi, Di, and b-factor) and fracture parameters (height, half-length, and spacing) of a type well. Next, the flow-cell model generates the hyperbolic decline parameters for an offset well based on the selected changes in the fracture treatment design parameters. Using a numerical simulator, the flow-cell model was verified as an accurate modeling technique for forecasting the production performance of horizontal, multi-fractured, gas wells.

Piezo-photo-thermoelasticity transport process for hyperbolic two-temperature theory of semiconductor material

A general solution for propagating waves in a generalized piezo-photo-thermoelastic medium for the one-dimensional (1D) problem under the hyperbolic two-temperature theory is investigated. The governing equations of the elastic waves, carrier density (plasma wave), quasi-static electric field, heat conduction equation, hyperbolic two temperature coefficient and constitutive relationships for the peizo-thermoelastic medium are obtained using Laplace transformation method in 1D. On the interface adjacent to the vacuum, mechanical stress loads, thermal and plasma boundary conditions are applied to obtain the main basic physical quantities in the Laplace domain. The inversion of Laplace transform by a numerical method is applied to obtain the complete solutions in the Laplace time domain for the main physical fields in this phenomenon. The effects on the force stress, displacement component, temperature distribution and carrier density of the thermoelastic, thermoelectric and hyperbolic two-temperature parameters by the applied force were graphically discussed.

FRACTAL CHARACTERIZATION AND MECHANICAL BEHAVIOR OF PILE–SOIL INTERFACE SUBJECTED TO SULFURIC ACID

This study aimed to investigate the different performance of pile–soil interfaces when the concrete was subjected to sulfuric acid corrosion. A series of large-scale direct shear tests were carried out to study the influence of sulfuric acid corrosion on the interface between soil and concrete pile. Concrete specimens immersed in sulfuric acid solution for different durations (0, 31, 93 and 154 days) were used to simulate the concrete pile surface roughness under sulfuric acid environment, which would be more realistic than the artificially roughened surfaces. Sand was used to simulate the soil. Geometric models of concrete specimens attacked by sulfuric acid were captured using a 3D laser scanning technology, and fractal dimension was adopted to evaluate the surface characterization of concrete subjected to sulfuric acid. The shear stress–displacement curves of the interface between sand and corroded concrete were measured. The shear strength parameters and the Clough–Duncan hyperbolic model parameters were obtained. The relationship between friction angle and fractal dimension was established. The results of the tests showed that with the increase of the corrosion duration, the concrete surface became rougher, the fractal dimensions of concrete surface, the sand-corroded concrete interface friction angle, and the shear displacement at peak stress became larger. A nonlinear relationship was found between the fractal dimension and interface friction angle. The results could provide a reference to diagnose, evaluate, and analyze the interface behavior between sulfuric acid corroded concrete materials and soil.

Development of hot deformation rheological model as exemplified by 1424 and V-1461 aluminum-lithium alloys

The article proposes a variant of the rheological model of hot deformation – the law of hyperbolic sine, which, in contrast to the standard one, takes into account not only the strain rate and process temperature, but also the strain ratio. Material constants included in the law of hyperbolic sine are replaced by polynomial functions of the strain ratio with coefficients calculated using the corresponding method developed. The paper describes applications of the rheological model proposed in low-density aluminum-lithium alloys 1424 of the Al–Mg–Li–Zn system and V-1461 of the Al–Cu–Li–Zn system, for which flow curves in the temperature range 400–480 °C and strain rate range 1–60 s–1 up to a strain ratio of 0.6 are defined by physical simulation at the Gleeble 3800 unit. The influence of the initial material state was also investigated – samples were taken from both the ingot and hot-rolled plates. Constants were determined for the rheological model of hot deformation including the Zener–Hollomon parameter and the law of hyperbolic sine for the entire range of stresses and strains. After approximating the dependences of the model parameters on true strains with a 4th degree polynomial law, a rheological model was created that describes the alloy behavior in the temperature-rate range under study. The features of changes in hyperbolic sine law parameters depending on the strain ratio were established. It was shown that, in general, parameters for the cast material are higher than for the rolled one. A comparison between the standard and proposed models showed that the use of the standard model over the entire strain interval leads to too high flow stress values (up to 12 %).

Superpotential method for chiral cosmological models connected with modified gravity

We consider the Chiral Cosmological Models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs admitting exact solutions is developed. New classes of exact solutions in the two-component CCM connected with an $f(R)$ gravity model with an additional scalar field have been constructed. We construct new cosmological solutions for a diagonal metric of the target space, including modified power-law solutions. In particular, we propose the reconstruction procedure based on the superpotential method and present examples of kinetic part reconstruction for periodic and hyperbolic Hubble parameters. We also focus on a cyclic type of Universe dubbed the Quasi-Steady State (QSS) model, with the aim of constructing single- and double-field potentials for one and the same behaviour of the Hubble parameter using the developed superpotential method for the CCM. The realization of this task includes a new set of solutions for a CCM with a scale factor characterized by the QSS theory. We also propose a method for reducing the two-field CCM to the single scalar field model.

Probing the roots of Arps hyperbolic relation and assessing variable-drive mechanisms for improved DCA

This paper explores the relationship between the natural form of pressure buildup/falloff response to Arps hyperbolic formula in conventional reservoir systems. The primary motivation stems from the fact that semianalytical proof exists for obtaining average-reservoir pressure from either pressure buildup or falloff response with the rectangular hyperbola method (RHM), whereas the Arps hyperbolic relation is anchored in empiricism. Despite its origin, the hyperbolic relationship has served the industry very well in performance predictions under diverse reservoir-drive mechanisms since its inception in 1945. Most reserves estimation in conventional reservoirs is anchored in Arps decline-curve analysis (DCA) to meet regulatory guidelines.We show that the Arps hyperbolic parameters b and D can be estimated from the RHM, thereby giving credence to its basis. Note that the RH method is a semianalytical proof of pressure-buildup/falloff relation. We also show that Arps hyperbolic parameter b is tied to the energy support available for production and can be estimated using a type curve instead of the parameter-regression approach. Besides, we point out that well shut-in periods need to be collapsed to obtain valid b and D parameters; otherwise, optimistic b values are estimated, leading to performance overprediction. Synthetic examples verified the approach presented here, and several field examples with diverse b-factors validated the overall methodology as espoused here.