A constitutive model for mechanical and chemo‐mechanical compaction in sedimentary basins and finite element analysis

Compaction and associated fluid flow are fundamental processes in sedimentary basin deformation. Purely mechanical compaction originates mainly from pore fluid expulsion and rearrangement of solid particles during burial, while chemo‐mechanical compaction results from Intergranular Pressure‐Solution (IPS) and represents a major mechanism of deformation in sedimentary basins during diagenesis. The aim of the present contribution is to provide a comprehensive 3D framework for constitutive and numerical modeling of purely mechanical and chemo‐mechanical compaction in sedimentary basins. Extending the concepts that have been previously proposed for the modeling of purely mechanical compaction in finite poroplasticity, deformation by IPS is addressed herein by means of additional viscoplastic terms in the state equations of the porous material. The finite element model integrates the poroplastic and poroviscoplastic components of deformation at large strains. The corresponding implementation allows for numerical simulation of sediments accretion/erosion periods by progressive activation/deactivation of the gravity forces within a fictitious closed material system. Validation of the numerical approach is assessed by means of comparison with closed‐form solutions derived in the context of a simplified compaction model. The last part of the paper presents the results of numerical basin simulation performed in one dimensional setting, demonstrating the ability of the modeling to capture the main features in elastoplastic and viscoplastic compaction. Copyright © 2016 John Wiley & Sons, Ltd.     

A constitutive and numerical model for mechanical compaction in sedimentary basins

The aim of the paper is to provide new elements concerning the constitutive behavior of sedimentary rocks and the numerical aspects for basin simulators. A comprehensive model for mechanical compaction of sedimentary basins is developed within finite poroplasticity setting. Particular concern is paid to the effects of large porosity changes on the poromechanical properties of the sediment material. A simplified micromechanics-based approach is used to account for the stiffness increase and hardening induced by large plastic strains.A key challenge for numerical assessment of sedimentary basin evolution is to integrate multiple coupled processes in the context of open material systems. To this end, a numerical approach inspired from the ‘deactivation/reactivation’ method used for the simulation of excavation process and lining placement in tunnel engineering, has been developed. Periods of sediments accretion are simulated by progressive activation of the gravity forces within a fictitious closed system. Fundamental components of the constitutive model developed before (hydromechanical coupling, dependence of poroelastic properties on large plasticity, impact of irreversible porosity changes on the hardening rule, evolution of permeability with porosity) are included into our finite element code.Illustrative examples of basin simulation are performed in the one-dimensional case. Various aspects of the constitutive model are investigated. Their influence on the corresponding basin response is analyzed in terms of compaction law, porosity and fluid pressure profiles.     

Formulation of reference solutions for compaction process in sedimentary basins

This paper is devoted to the development of semianalytical solutions for the deformation induced by gravitational compaction in sedimentary basins. Formulated within the framework of coupled plasticity–viscoplasticity at large strains, the modeling dedicates special emphasis to the effects of material densification associated with large irreversible porosity changes on the stiffness and hardening of the sediment material. At material level, the purely mechanical compaction taking place in the upper layers of the basin is handled in the context of finite elastoplasticity, whereas the viscoplastic component of behavior is intended to address creep-like deformation resulting from chemo-mechanical that prevails at deeper layers. Semianalytical solutions describing the evolution of mechanical state of the sedimentary basin along both the accretion and postaccretion periods are presented in the simplified oedometric setting. These solutions can be viewed as reference solutions for verification and benchmarks of basin simulators. The proposed approach may reveal suitable for parametric analyses because it requires only standard mathematics-based software for PDE system resolution. The numerical illustrations provide a quantitative comparison between the derived solutions and finite element predictions from an appropriate basin simulator, thus showing the ability of the approach to accurately capture essential features of basin deformation.     

TWO-PHASE OIL MIGRATION IN COMPACTING SEDIMENTARY BASINS MODELLED BY THE FINITE ELEMENT METHOD

The upstream-weighted finite element method with lumped mass matrix is applied to the modelling of oil migration in compacting sedimentary basins. An implicit formulation is made in Lagrangian co-ordinates of a pressure, saturation and a temperature equation, which is based on immiscible two-phase flow of oil and water. The formulation accounts for the compaction of the sediments, the generation of oil from solid organic material (kerogen), the eventual pore space generated by kerogen breakdown, and the density variations of the fluids which may set up thermal convection. The model is validated by comparison with results from a one-dimensional (1D) fractional flow-based migration model. A 2D case example showing oil expulsion from source rocks, and the filling of a trap is presented. The mass balance of the model is easily checked because all oil in the basin originates from breakdown of kerogen. Compared with other alternatives, the simple upstream-weighted finite element method is suggested as a possible first choice for a numerical method for the modelling of oil migration in compacting sedimentary basins. It easily deals with the complex geometry of a basin, it yields reasonably good results, is simple to implement, and the same implementation applies to all spatial dimensions. © 1997 by John Wiley & Sons, Ltd.     

前陆盆地异常流体压力: 地质作用及其增压效率

在前陆盆地形成过程中,强烈挤压构造应力场和特殊的盆-山关系造成极为复杂的沉积环境和构造形变,多种地质作用都可能对地层内异常流体压力的产生及演化起到十分重要的作用。通过对准噶尔盆地南缘地区中段的地质条件及压力分布的分析,利用数值盆地模型方法,模拟分析了在前陆盆地构造挤压和盆地沉降过程中压实作用、断裂开启、褶皱、剥蚀等地质过程对流体压力的作用和影响,定量讨论了压力异常的成因机制及其效率。模拟分析结果表明,构造应力在水平方向上派生的侧向压实作用、强烈的褶皱作用及伴随的快速沉积-剥蚀作用等是前陆盆地中特有的增压作用,都可造成较高压力异常。准噶尔盆地南缘中新生界地层中广泛分布的高异常压力是新生代以来,特别是第四纪以来,在快速的压实作用、构造挤压作用所形成的高地层压力背景下,叠加了近期因断裂活动和背斜构造快速形成所引起的他源高压而形成的。     

The geometry of fan‐deltas and related turbidites in narrow linear basins

The sediment distribution in three narrow, linear basins, two modern and one ancient, in Greece and Italy, was studied and related to changes in basin configuration. The basins are the Plio‐Quaternary Patras–Corinth graben, the Pliocene–Quaternary Reggio–Scilla graben and the middle Tertiary Mesohellenic piggy‐back basin. These basins were formed at different times and under different geodynamic conditions, but in each case, the tectonic evolution produced a narrow area in the basin where the water depth decreased dramatically, forming a strait with a sill. This strait divided the basin into major and minor sub‐basins, and the strait has a similar impact on sedimentary environments in all three basins, even though different depositional environments were formed along the initial basin axis. Predictions for the development of depositional environments in the two modern basins, especially in their straits, are based on the studied ancient basin. In the straits, powerful tidal flows will transport finer sediments to sub‐basins and trapezoidal‐type fan‐deltas will gradually fill up and choke the strait through time. In sub‐basins, according to basin depth, either deltaic (in the shallow minor sub‐basin) or turbiditic (in the deep major sub‐basin) deposits may accumulate. Moreover, an extensive shelf is likely to develop between the strait and major sub‐basin. This shelf will be cross‐cut by canyons and characterized by thin fine‐ to coarse‐grained deposits. These sediment models could be applied to analogous basin geometries around the world. Copyright © 2003 John Wiley & Sons, Ltd.     

Three‐dimensional analysis of the seismic behaviour of micropiles used in the reinforcement of saturated soil

This paper includes a numerical study of the behaviour of micropiles used for the reinforcement of saturated soil. Analysis is carried out using the (u–p) formulation (displacement for the solid phase and pore‐pressure for the fluid phase) implemented in a three‐dimensional finite element program. The soil behaviour is described by means of a cyclic elastoplastic constitutive relation which was developed within the framework of the bounding surface concept. The paper is composed of three parts. The first one is concerned with a presentation of the numerical model; the second includes analysis of the seismic behaviour of a single micropile; the last part deals with the group effect under seismic loading. Copyright © 2001 John Wiley & Sons, Ltd.     

Sequence Stratigraphic Modeling of Sedimentary Basin: Conceptual Model and Application to Erlian and Yinggehai Basins, China

INTRODUCTIONQuantitativebasinmodelinghasbecomeoneofthefrontiersinsedimentarybasinanalySis.Alargevarietyofnumericalmodelsconcerningbasinformation,basinfillingprocess,thermalhistory,hydrocarbongenerationandaCCUmulationhavebeenformulatedoverthelastdecadetondAnctheprocessesandevollltionofsedimentarybasins(Mckenzie,1978,signeretal.,1990;Ungereretal.,1990).Thebasinmodeling,utilizingcomputersimulationtechnique,isapowerfultoolforbasinanalySisandhasincreasinglybeenintegratedintoconventionalbasi…     

Structure and tectonic history of the foreland basins of southernmost South America

The common elements and differences of the neighboring Austral (Magallanes), Malvinas and South Malvinas (South Falkland) sedimentary basins are described and analyzed. The tectonic history of these basins involves Triassic to Jurassic crustal stretching, an ensuing Early Cretaceous thermal subsidence in the retroarc, followed by a Late Cretaceous–Paleogene compressional phase, and a Neogene to present-day deactivation of the fold–thrust belt dominated by wrench deformation. A concomitant Late Cretaceous onset of the foreland phase in the three basins and an integrated history during the Late Cretaceous–Cenozoic are proposed. The main lower Paleocene–lower Eocene initial foredeep depocenters were bounding the basement domain and are now deformed into the thin-skinned fold–thrust belts. A few extensional depocenters developed in the Austral and Malvinas basins during late Paleocene–early Eocene times due to a temporary extensional regime resulting from an acceleration in the separation rate between South America and Antarctica preceding the initial opening of the Drake Passage. These extensional depocenters were superimposed to the previous distal foredeep depocenter, postdating the initiation of the foredeep phase and the onset of compressional deformation. Another pervasive set of normal faults of Paleocene to Recent age that can be recognized throughout the basins are interpreted to be a consequence of flexural bending of the lithosphere, in agreement with a previous study from South Malvinas basin. Contractional deformation was replaced by transpressive kinematics during the Oligocene due to a major tectonic plate reorganization. Presently, while the South Malvinas basin is dominated by the transpressive uplift of its active margin with minor sediment supply, the westward basins undergo localized development of pull-apart depocenters and transpressional uplift of previous structures. The effective elastic thickness of the lithosphere for different sections of each basin is calculated using a dynamic finite element numerical model that simulates the lithospheric response to advancing tectonic load with active sedimentation.     

The Danube River inception: Evidence for a 4 Ma continental‐scale river born from segmented ParaTethys basins

Before reaching the Black Sea, the Danube River passes through a string of Para‐Tethyan (Vienna, Pannonian and western and eastern Dacian) basins. The key question is, when and how did the Danube River become a continental‐scale river with a drainage similar to present? New data presented here show that the Late Miocene deepwater strata in the Black Sea have a significant sediment source and depositional style change at about 4 Ma. However, the presence of active Miocene basins within the Danube catchment raises questions about the timing of Danube River inception and whether the upstream palaeogeography would have allowed or disallowed delivery of large sediment volumes to the deepwater Black Sea. Stratigraphic analyses in the Pannonian and Dacian basins reveal a phase of coeval sedimentary fill of the basins along the Danube at about 4 Ma. This multi‐basin observation points to a concurrent basin‐fill model rather than the basin fill‐and‐spill or Messinian‐type lowstand models previously proposed for Danube inception.     

沉积泥砂非线性大变形固结沉降计算模型

沉积形成的水底黏性泥砂自重固结过程表现出显著非线性大变形固结特征,应采用大变形固结理论进行泥砂沉积固结计算。基于软黏土一维非线性大应变固结理论,应用有效应力、渗透系数与孔隙比间扩展幂次函数固结本构关系,由达西定律、有效应力原理、连续介质方程等建立大变形固结控制方程,根据固结单元孔隙水渗流、单元变形与泥砂沉积层固结沉降耦合关系形成黏性泥砂大变形自重固结数值模型。泥砂自重作为固结荷载,数值模型假定沉积泥砂各向同性且固结沉降应变、孔隙水渗流仅发生于竖直方向,为一维单向沉积固结过程;采用泥砂沉降柱试验确定泥砂非线性扩展幂次函数关系参数。模型应用中,划分竖向固结单元,由沉积泥砂固结本构关系确定各固结单元有效应力及超孔隙水应力,通过超孔隙水应力时间维度上的消散过程及各固结参数间的耦合关系计算泥砂固结沉降。数值模型计算结果表明,沉积黏性泥砂自重固结初期表现为有效应力调整过程,初始有效应力与孔隙比根据固结本构关系匹配调整为扩展幂次函数关系;沉积泥砂应变与应力固结度存在20%左右误差,泥砂固结沉降发展快于超孔隙水应力消散过程,证明沉积泥砂固结沉降变形的发展与超孔隙水应力消散并非同步耦合。计算模型应用于室内沉降柱试验模拟淤积黏性泥砂自重固结沉降预测中,模型输出与试验结果符合良好。     

含天然气水合物沉积物分解过程的有限元模拟

温度和压力的变化会引起含天然气水合物沉积物的分解,其过程伴随着相态转换、孔隙水压力和气压力耗散、热传导、骨架变形等过程的相互耦合作用。基于多孔介质理论建立了描述含天然气水合物沉积物分解过程的数学模型,考虑了水合物分解产生的水、气流动、水合物相变和分解动力学过程、热传导、骨架变形等过程的耦合作用。基于有限元法,建立了模拟水合物分解过程的数值模型,并编制了计算机分析程序。通过对降压法和升温法开采过程的数值模拟,揭示了在水合物分解过程中沉积物储层的变形、压力、温度等因素的变化规律。结果表明：降压法和升温法都会导致储层变形以及产生超孔隙压力,但两种方法作用效果不同;同时,水合物分解过程包含渗流及热传导作用。     

A constitutive model for the dynamic and high‐pressure behaviour of a propellant‐like material: Part II: Model development and applications

This paper presents the second part of a work that aims at developing a mechanical model for the behaviour of propellant‐like materials under high confining pressure and strain rate. The model is to be employed to determine the temperature rise due to mechanical dissipation during a dynamic penetration event. Using the kinematical and thermodynamic background derived in the first part, a viscoelastic–viscoplastic–compaction model is put forward and identified. Viscoelasticity and compaction refer to the elastomeric nature of the material, while viscoplasticity, including implicit damage through dilatancy, reflects its granular nature. Some numerical exercises are performed, in view of determining the major model forces and weaknesses, and of assessing the numerical algorithm robustness. A penetration event is preliminarily simulated, and a temperature rise field predicted. Necessary model improvements are finally discussed, together with several ways of research for a longer term approach. Copyright © 2001 John Wiley & Sons, Ltd.     

A finite element formulation in Lagrangian co-ordinates for heat and fluid flow in compacting sedimentary basins

This article presents a numerical model of heat and fluid flow in compacting sedimentary basins formulated in Lagrangian co-ordinates. The Lagrangian co-ordinates are the sediment particle positions of the completely compacted basin. A finite element formulation of excess water pressure and temperature in these Lagrangian co-ordinates is presented, in addition to an equivalent formulation in the real co-ordinates. The later formulation is also Lagrangian of nature, since the elements of the grid in the real co-ordinates always frame the same sediment particles. In other words, it is the Lagrangian grid mapped to the real space. This is done in an iterative loop which solves for excess water pressure, and then updates the real co-ordinates of the sediment particles. By comparing the two finite element formulations it is concluded that the one in real space is the simplest, most efficient and most precise. The model is validated by comparison with two dimensionless one-dimensional solutions, one analytical for the linear case, and one numerical for the non-linear case. Both these one-dimensional solutions are obtained on the unit interval, where the moving top boundary caused by continuous sedimentation is incorporated.     

二维沉积层序计算机模拟研究

本项研究建立了综合性的二维沉积层序模拟系统SSMS。该模拟系统由盆地的沉降过程模拟与盆地充填过程模拟两个子系统构成。盆地的沉降模拟结合了反演的沉降回剥和盆地形成的正演模型;盆地充填过程模拟综合考虑了盆地沉降、重力均衡作用、海（湖）平面升降、沉积物供给、侵蚀作用、沉积物分布和压实等因素。结合实例分析表明,该模拟系统可用于定量分析盆地构造、海（湖）平面、沉积物供给等变化对沉积层序的形成过程、几何形态及其沉积体系分布的控制作用,检验地质模型和进行预测。     

Developing constitutive models from EPR‐based self‐learning finite element analysis

A constitutive model that captures the material behavior under a wide range of loading conditions is essential for simulating complex boundary value problems. In recent years, some attempts have been made to develop constitutive models for finite element analysis using self‐learning simulation (SelfSim). Self‐learning simulation is an inverse analysis technique that extracts material behavior from some boundary measurements (eg, load and displacement). In the heart of the self‐learning framework is a neural network which is used to train and develop a constitutive model that represents the material behavior. It is generally known that neural networks suffer from a number of drawbacks. This paper utilizes evolutionary polynomial regression (EPR) in the framework of SelfSim within an automation process which is coded in Matlab environment. EPR is a hybrid data mining technique that uses a combination of a genetic algorithm and the least square method to search for mathematical equations to represent the behavior of a system. Two strategies of material modeling have been considered in the SelfSim‐based finite element analysis. These include a total stress‐strain strategy applied to analysis of a truss structure using synthetic measurement data and an incremental stress‐strain strategy applied to simulation of triaxial tests using experimental data. The results show that effective and accurate constitutive models can be developed from the proposed EPR‐based self‐learning finite element method. The EPR‐based self‐learning FEM can provide accurate predictions to engineering problems. The main advantages of using EPR over neural network are highlighted.     

A unified approach to mechanical compaction,pressure solution,mineral reactions and the temperature distribution in hydrocarbon basins

In modelling sediment compaction and mineral reactions, the rheological behaviour of sediments is typically considered as poroelastic or purely viscous. In fact, compaction due to pressure solution and mechanical processes in porous media is far more complicated. A generalised model of viscoelastic compaction and the smectite to illite mineral reaction in hydrocarbon basins is presented. A one-step dehydration model of the mineral reaction is assumed. The obtained non-linear governing equations are solved numerically and different combinations of physical parameters are used to simulate realistic situations in typical sedimentary basins. Comparison of numerical simulations with real data has shown very good agreement with respect to both the porosity profile and the mineral reaction.     

Solute transfer during consolidation based on a solid‐fluid‐solute coupling model

The migration of contaminant through soil is usually modeled using the advection‐dispersion equation and assumes that the porous media is stationary without introducing a constitutive equation to represent soil structure. Consequently, time‐dependent deformation induced by soil consolidation or physical remediation is not considered, despite the need to consider these variables during planning for the remediation of contaminated ground, the prediction of contaminated groundwater movement, and the design of engineered landfills. This study focuses on the numerical modeling of solute transfer during consolidation as a first step to resolve some of these issues. We combine a coupling theory‐based mass conservation law for soil‐fluid‐solute phases with finite element modeling to simulate solute transfer during deformation and groundwater convection. We also assessed the sensitivity of solute transfer to the initial boundary conditions. The modeling shows the migration of solute toward the ground surface as a result of ground settlement and the dissipation of excess pore water pressure. The form of solute transport is dependent on the ground conditions, including factors such as the loading schedule, contamination depth, and water content. The results indicate that an understanding of the interaction between coupling phases is essential in predicting solute transfer in ground deformation and could provide an appropriate approach to ground management for soil remediation.     

Data assimilation using the particle filter for identifying the elasto‐plastic material properties of geomaterials

A computational method, incorporating the finite element model (FEM) into data assimilation using the particle filter, is presented for identifying elasto‐plastic material properties based on sequential measurements under the known changing traction boundary conditions to overcome some difficulties in identifying the parameters for elasto‐plastic problems from which the existing inverse analysis strategies have suffered. A soil–water coupled problem, which uses the elasto‐plastic constitutive model, is dealt with as the geotechnical application. Measured data on the settlement and the pore pressure are obtained from a synthetic FEM computation as the forward problem under the known parameters to be identified for both the element tests and the ground behavior during the embankment construction sequence. Parameter identification for elasto‐plastic problems, such as soil behavior, should be made by considering the measurements of deformation and/or pore pressure step by step from the initial stage of construction and throughout the deformation history under the changing traction boundary conditions because of the embankment or the excavation because the ground behavior is highly dependent on the loading history. Thus, it appears that sequential data assimilation techniques, such as the particle filter, are the preferable tools that can provide estimates of the state variables, that is, deformation, pore pressure, and unknown parameters, for the constitutive model in geotechnical practice. The present paper discusses the priority of the particle filter in its application to initial/boundary value problems for elasto‐plastic materials and demonstrates a couple of numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.     

Load‐displacement and bearing capacity of foundations on granular soils using a multi‐surface kinematic constitutive soil model

A finite element approach based on an advanced multi‐surface kinematic constitutive model is used to evaluate the bearing capacity of footings resting on granular soils. Unlike simple elastic‐perfectly plastic models, often applied to granular foundation problems, the present model realistically accounts for stress dependency of the friction angle, strain softening–hardening and non‐associativity. After the model and its implementation into a finite element code are briefly discussed, the numerical difficulty due to the singularity at the footing edge is addressed. The bearing capacity factor N_γ is then calculated for different granular materials. The effect of footing size, shape, relative density and roughness on the ultimate bearing capacity are studied and the computed results compare very favourably with the general experimental trends. In addition, it is shown that the finite element solution can clearly represent counteracting mechanisms of progressive failure which have an important effect on the bearing capacity of granular foundations. Copyright © 2006 John Wiley & Sons, Ltd.