Numerical modeling of fluid‐driven fractures in cohesive poroelastoplastic continuum

In this article, we investigate the main parameters that influence the propagation of a fluid‐driven fracture in a poroelastoplastic continuum. These parameters include the cohesive zone, the stress anisotropy, and the pore pressure field. The fracture is driven in a permeable porous domain that corresponds to weak formation by pumping of an incompressible viscous fluid at the fracture inlet under plane strain conditions. Rock deformation is modeled with the Mohr–Coulomb yield criterion with associative flow rule. Fluid flow in the fracture is modeled by the lubrication theory. The movement of the pore fluid in the surrounding medium is assumed to obey the Darcy law and is of the same nature as the fracturing fluid. The cohesive zone approach is used as the fracture propagation criterion. The problem is modeled numerically with the finite element method to obtain the solution for the fracture length, the fracture opening, and the propagation pressure as a function of the time and distance from the pumping inlet. It is demonstrated that the plastic yielding that is associated with the rock dilation in an elastoplastic saturated porous continuum is significantly affected by the cohesive zone characteristics, the stress anisotropy, and the pore pressure field. These influences result in larger fracture profiles and propagation pressures due to the larger plastic zones that are developing during the fracture propagation. Furthermore, it is also found that the diffusion process that is a major mechanism in hydraulic fracture operations influences further the obtained results on the fracture dimensions, plastic yielding, and fluid pressures. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions. Copyright © 2012 John Wiley & Sons, Ltd.     

Influence of size on the constitutive equations of concrete or rock dowels

The numerical fracture analysis of non‐homogeneous rock or concrete dowels subjected to shear and compression is described in detail. The method of analysis allows the consideration of scale and rate effects due to material non‐homogeneity and fracture. The proposed approach is verified by comparing numerical predictions with experimental results reported in the literature for a series of small rock samples, since experimental evidence for large bodies is not yet available (2007). Results generated by Monte Carlo simulation using the so‐called discrete element method to model the dowels suggest that a simple three parameters law can be used to predict the relationship between tangential stress at the base and lateral distortion. It is observed that the larger the size of the cubes, the smaller both the peak tangential stress and the rupture distortion. Size effects are also evaluated in samples with vertical restraint. The influence of loading rate is likewise numerically assessed for two sample sizes. The effect is compatible with experimental evidence available for concrete using small samples. Copyright © 2008 John Wiley & Sons, Ltd.     

Using a H∞ filter assimilation procedure to estimate root zone soil water content

Root zone soil water content impacts plant water availability, land energy and water balances. Because of unknown hydrological model error, observation errors and the statistical characteristics of the errors, the widely used Kalman filter (KF) and its extensions are challenged to retrieve the root zone soil water content using the surface soil water content. If the soil hydraulic parameters are poorly estimated, the KF and its extensions fail to accurately estimate the root zone soil water. The H‐infinity filter (HF) represents a robust version of the KF. The HF is widely used in data assimilation and is superior to the KF, especially when the performance of the model is not well understood. The objective of this study is to study the impact of uncertain soil hydraulic parameters, initial soil moisture content and observation period on the ability of HF assimilation to predict in situ soil water content. In this article, we study seven cases. The results show that the soil hydraulic parameters hold a critical role in the course of assimilation. When the soil hydraulic parameters are poorly estimated, an accurate estimation of root soil water content cannot be retrieved by the HF assimilation approach. When the estimated soil hydraulic parameters are similar to actual values, the soil water content at various depths can be accurately retrieved by the HF assimilation. The HF assimilation is not very sensitive to the initial soil water content, and the impact of the initial soil water content on the assimilation scheme can be eliminated after about 5–7 days. The observation interval is important for soil water profile distribution retrieval with the HF, and the shorter the observation interval, the shorter the time required to achieve actual soil water content. However, the retrieval results are not very accurate at a depth of 100 cm. Also it is complex to determine the weighting coefficient and the error attenuation parameter in the HF assimilation. In this article, the trial‐and‐error method was used to determine the weighting coefficient and the error attenuation parameter. After the first establishment of limited range of the parameters, ‘the best parameter set’ was selected from the range of values. For the soil conditions investigated, the HF assimilation results are better than the open‐loop results. Copyright © 2010 John Wiley & Sons, Ltd.     

On the hydraulic intake shape factor for a circular opening located at an impervious boundary: Influence of inclined stratification

In this paper, we develop an exact closed form solution for a circular entry point located at the interface between an impermeable material and a stratified porous medium, where the principal plane of hydraulic isotropy is inclined to the interface. Copyright © 2010 John Wiley & Sons, Ltd.     

Cohesive‐frictional model for bond and splitting action of prestressing wire

This paper presents a numerical procedure for bond between indented wires and concrete, and the coupled splitting process of the surrounding concrete. The bond model is an interface, non‐associative, plasticity model. It is coupled with a cohesive fracture model for concrete to take into account the splitting of such concrete. Bond between steel and concrete is fundamental for the transmission of stresses between both materials in precast prestressed concrete. Indented wires are used to improve the bond in these structural elements. The radial component of the prestressing force, increased by Poisson's effect, may split the surrounding concrete, decreasing the wire confinement and diminishing the bonding. The combined action of the bond and the splitting is studied with the proposed model. The results of the numerical model are compared with the results of a series of tests, such as those which showed splitting induced by the bond between wire and concrete. Tests with different steel indentation depths were performed. The numerical procedure accurately reproduces the experimental records and improves knowledge of this complex process. Copyright © 2010 John Wiley & Sons, Ltd.     

A mass‐balance approach to estimate in‐stream processes in a large river

A mass‐balance approach was used to estimate in‐stream processes related to inorganic nitrogen species (NH₄⁺, NO₂^? and NO₃^?) in a large river characterized by highly variable hydrological conditions, the Garonne River (south‐west France). Studies were conducted in two consecutive reaches of 30 km located downstream of the Toulouse agglomeration (population 760 000, seventh order), impacted by modification of discharge regime and high nitrogen concentrations. The mass‐balance was calculated by two methods: the first is based on a variable residence time (VRT) simulated by a one‐dimensional (1‐D) hydraulic model; the second is a based on a calculation using constant residence time (CRT) evaluated according to hydrographic peaks. In the context of the study, removal of dissolved inorganic nitrogen (DIN) for a reach of 30 km is underestimated by 11% with the CRT method. In sub‐reaches, the discrepancy between the two methods led to a 50% overestimation of DIN removal in the upper reach (13 km) and a 43% underestimation in the lower reach (17 km) using the CRT method. The study highlights the importance of residence time determination when using modelling approaches in the assessment of whole stream processes in short‐duration mass‐balance for a large river under variable hydrological conditions. Copyright © 2007 John Wiley & Sons, Ltd.     

The soil hydrologic response to forest regrowth: a case study from southwestern Amazonia

As a large and dynamic land‐use category, tropical secondary forests may affect climate, soils, and hydrology in a manner different from primary forests or agricultural areas. We investigated the saturated hydraulic conductivity K_sat of a Kandiudult under different land uses in Rondonia, Brazil. We measured K_sat at four depths (12·5, 20, 30 and 50 cm) under (a) primary forest, (b) a former banana–cacao plantation (SF1), and (c) an abandoned pasture (SF2). At 12·5 cm, all three land uses differ significantly (α = 0·1), but not at the 20 and 30 cm depths. At 50 cm, K_sat was significantly greater in the former pasture than in other land uses. Lateral subsurface flow is expected during intense rainfall (about 30 times per year) at 30 cm depth in SF1 and at 50 cm depth in the forest, whereas the relatively low permeability at shallow 12·5 cm in the SF2 may result not only in lateral subsurface flow, but also saturation overland flow. For modelling purposes, recovering systems seem to have K_sat values distinct from primary forest at shallow depths, whereas at deeper layers (>20 cm) they may be considered similar to forests. Copyright © 2002 John Wiley & Sons, Ltd.     

Analysis of a deformable fracture in permeable material

The response of deformable fractures to changes in fluid pressure controls phenomena ranging from the flow of fluids near wells to the propagation of hydraulic fractures. We developed an analysis designed to simulate fluid flows in the vicinity of asperity‐supported fractures at rest, or fully open fractures that might be propagating. Transitions between at‐rest and propagating fractures can also be simulated. This is accomplished by defining contact aperture as the aperture when asperities on a closing fracture first make contact. Locations on a fracture where the aperture is less than the contact aperture are loaded by both fluid pressure and effective stress, whereas locations where the aperture exceeds the contact aperture are loaded only by fluid pressure. Fluid pressure and effective stress on the fracture are determined as functions of time by solving equations of continuity in the fracture and matrix, and by matching the global displacements of the fracture walls to the local deformation of asperities. The resulting analysis is implemented in a numerical code that can simulate well tests or hydraulic fracturing operations. Aperture changes during hydraulic well tests can be measured in the field, and the results predicted using this analysis are similar to field observations. The hydraulic fracturing process can be simulated from the inflation of a pre‐existing crack, to the propagation of a fracture, and the closure of the fracture to rest on asperities or proppant. Two‐dimensional, multi‐phase fluid flow in the matrix is included to provide details that are obscured by simplifications of the leakoff process (Carter‐type assumptions) used in many hydraulic fracture models. Execution times are relatively short, so it is practical to implement this code with parameter estimation algorithms to facilitate interpretation of field data. Copyright © 2006 John Wiley & Sons, Ltd.