Numerical Study of Finite Element Method Based Solutions for Propagation of Wetting Fronts in Unsaturated Soil

The accurate prediction of the propagation of a wetting front in an unsaturated soil subjected to surficial infiltration is of practical importance to many geotechnical and geoenvironmental problems. The finite element method is the most common solution technique as the hydraulic soil properties are highly nonlinear. Two important issues are often found to create difficulties in such analyses. First, numerical oscillations are usually observed in the calculated pore pressures at the wetting front. Second, when a reasonable mesh size and time step are used, the elevation of the wetting front may be seriously overpredicted. This paper is focused on the second issue. The under-relaxation (UR) technique used in the iterative process within each time step is found to have a serious impact on rate of convergence with refinement in mesh size and time step. Two different techniques are typically used; the first evaluates the hydraulic conductivity using an average of heads calculated from the preceding time node and the most recent iteration of the current time node (UR1), and the second evaluates the hydraulic conductivity using the average of heads calculated from the two most recent iterations of the current time nodes (UR2). The study shows that UR1, which is adopted in programs such as SEEP/W, ensures that the solution converges rapidly to a stable solution within a time step, but may converge to the wrong wetting front at a given elapsed time unless a sufficiently refined mesh is used. UR2 converges much more slowly within a time step, but the error in the wetting front is smaller than that generated by UR1.     

Block preconditioners for symmetric indefinite linear systems

This paper presents a systematic theoretical and numerical evaluation of three common block preconditioners in a Krylov subspace method for solving symmetric indefinite linear systems. The focus is on large‐scale real world problems where block approximations are a practical necessity. The main illustration is the performance of the block diagonal, constrained, and lower triangular preconditioners over a range of block approximations for the symmetric indefinite system arising from large‐scale finite element discretization of Biot's consolidation equations. This system of equations is of fundamental importance to geomechanics. Numerical studies show that simple diagonal approximations to the (1,1) block K and inexpensive approximations to the Schur complement matrix S may not always produce the most spectacular time savings when K is explicitly available, but is able to deliver reasonably good results on a consistent basis. In addition, the block diagonal preconditioner with a negative (2,2) block appears to be reasonably competitive when compared to the more complicated ones. These observation are expected to remain valid for coefficient matrices whereby the (1,1) block is sparse, diagonally significant (a notion weaker than diagonal dominance), moderately well‐conditioned, and has a much larger block size than the (2,2) block. Copyright © 2004 John Wiley & Sons, Ltd.     

Block constrained versus generalized Jacobi preconditioners for iterative solution of large-scale Biot’s FEM equations

Generalized Jacobi (GJ) diagonal preconditioner coupled with symmetric quasi-minimal residual (SQMR) method has been demonstrated to be efficient for solving the 2 × 2 block linear system of equations arising from discretized Biot’s consolidation equations. However, one may further improve the performance by employing a more sophisticated non-diagonal preconditioner. This paper proposes to employ a block constrained preconditioner P_c that uses the same 2 × 2 block matrix but its (1, 1) block is replaced by a diagonal approximation. Numerical results on a series of 3-D footing problems show that the SQMR method preconditioned by P_c is about 55% more efficient time-wise than the counterpart preconditioned by GJ when the problem size increases to about 180,000 degrees of freedom. Over the range of problem sizes studied, the P_c-preconditioned SQMR method incurs about 20% more memory than the GJ-preconditioned counterpart. The paper also addresses crucial computational and storage issues in constructing and storing P_c efficiently to achieve superior performance over GJ on the commonly available PC platforms.     

Unsaturated Soil Seepage Analysis Using a Rational Transformation Method with Under-Relaxation

The finite-element method provides a convenient and effective means for solving problems of seepage in unsaturated soils. However, convergence difficulties exist in numerical simulations of unsaturated flow analyses because of the high nonlinearity of the soil hydraulic properties. This technical note presents a combination approach consisting of a rational function transformation method and a common under-relaxation technique to solve the h-based form of Richards equation. Numerical studies show that this combined method can use a larger time step and corresponding oscillation-free mesh size to produce acceptable results and also converge to a stable solution quickly in each time step.     

Some Observations on the Performance of the Signal Matching Technique in Assessment of Pile Integrity

The pulse-echo method is commonly used to assess pile integrity in a nondestructive way. One of the strategies for detecting relative variation in pile impedance is to analyze the wave reflections from the anomalies based on the 1-D stress wave theory. In current practice, however, several difficulties remain to be resolved in interpreting the wave patterns. Firstly, due to possible three-dimensional (3-D) behavior near the source and dispersion behavior far from the source, 1-D stress wave theory is not always applicable in analyzing the reflections from the anomalies. Secondly, reflections can be produced continuously along the shaft due to the pile-soil interaction, so that the reflection patterns are highly correlated to those from the pile body in complex layered soil profiles, and thus it is generally difficult to distinguish whether the reflections are produced by pile anomalies or by the changes in the soil profiles. In this paper, actual wave characteristics are analyzed based on numerical simulations and guided wave theory, the conditions for 1-D approximation are suggested, and the a method for uncoupling the soil resistance and the pile impedance effects is presented. The evaluation of pile integrity can be improved with help of the 1-D based signal matching technique. The technique is applied to experiments conducted on model piles, test piles for accreditation of pile inspectors, and routine in-situ piles. The results show that 1-D stress wave theory is approximately applicable in analyzing the reflections from deep anomalies under certain limited conditions, and the soil resistance and the pile impedance effects can be effectively uncoupled by relating the pile-soil interaction to the pile radius and the properties of the surrounding soils.     

Reduced membrane fouling in a novel bio-entrapped membrane reactor for treatment of food and beverage processing wastewater

A novel Bio-Entrapped Membrane Reactor (BEMR) packed with bio-ball carriers was constructed and investigated for organics removal and membrane fouling by soluble microbial products (SMP). An objective was to evaluate the stability of the filtration process in membrane bioreactors through backwashing and chemical cleaning. The novel BEMR was compared to a conventional membrane bioreactor (CMBR) on performance, with both treating identical wastewater from a food and beverage processing plant. The new reactor has a longer sludge retention time (SRT) and lower mixed liquor suspended solids (MLSS) content than does the conventional. Three different hydraulic retention times (HRTs) of 6, 9, and 12 h were studied. The results show faster rise of the transmembrane pressure (TMP) with decreasing hydraulic retention time (HRT) in both reactors, where most significant membrane fouling was associated with high SMP (consisting of carbohydrate and protein) contents that were prevalent at the shortest HRT of 6 h. Membrane fouling was improved in the new reactor, which led to a longer membrane service period with the new reactor. Rapid membrane fouling was attributed to increased production of biomass and SMP, as in the conventional reactor. SMP of 10-100 kDa from both MBRs were predominant with more than 70% of the SMP <100 kDa. Protein was the major component of SMP rather than carbohydrate in both reactors. The new reactor sustained operation at constant permeate flux that required seven times less frequent chemical cleaning than did the conventional reactor. The new BEMR offers effective organics removal while reducing membrane fouling.     

A review of synthesis and morphology of SrTiO3 for energy and other applications

With the increasing demand and depleting trend of commercial energies, it has forced the researchers all over the world to accelerate research and development in the area of renewable energy. Currently, unique and interesting features of binary compounds have gained more attention by researchers, and it became a favourite research topic among various groups of researchers around this world. It was noticed that strontium titanate (SrTiO₃) consists of several extraordinary properties that can apply for miscellaneous applications especially for energy storage, fuel cells, as well as to generate hydrogen fuel via photocatalysis process. Besides that, it was noticed that SrTiO₃ can be synthesised in different pathways. The method of preparation and amount of precursors can affect the surface properties of SrTiO₃. Thus, this article presents a critical review on how SrTiO₃ synthesis methods affect its surface morphology and the applications of SrTiO₃ in various fields.     

Observations on Limit Equilibrium–Based Slope Reliability Problems with Inclined Weak Seams

This study addresses the complexity of slope reliability problems based on limit equilibrium methods (LEMs). The main focus is on the existence of multiple failure modes that poses difficulty to many LEM-based slope reliability methods. In particular, when weak seams are present, the failure modes associated with those seams may be difficult to detect. A systematic way of searching the failure modes is proposed, and its robustness over slopes with or without weak seams is demonstrated. It is found that in the presence of weak seams, assuming circular slip surfaces may cause underestimation of slope failure probability. The conclusion of the study promotes the use of finite elements as the stability method for reliability evaluation because it is not necessary to search for failure surfaces in finite-element stability analysis.     

Effects of the Source on Wave Propagation in Pile Integrity Testing

One-dimensional stress wave theory is widely used to analyze quantitatively the reflections in low-strain integrity testing of piles. However, a point or disk loading produces body and Rayleigh waves near the pile top. The multireflections of these waves from the lateral surface of a pile are present in the wave field near the pile top. Effects of three-dimensional waves on the near field responses are obvious. These effects can be interpreted erroneously by an inexperienced user as “noises” or “pile anomalies.” To investigate wave propagation in the longitudinal direction, the behavior of the waves in the far field (some distance below the pile top) is studied by theoretical analysis of the longitudinal modes in free cylinders and numerical simulations. The wave pattern at the pile top is analyzed based on the response of an elastic half-space to a harmonic disk loading. The results show that when the ratio of the characteristic length of an impact pulse to the cylinder radius is large enough, the components of Rayleigh waves in the wave field at the pile top are diminished; the waves in the far field behave approximately as plane waves; the responses at positions between 1/2R and 3/4R from the pile axis are less affected by the multireflections. The results from numerical simulations support the practical recommendation to use a ratio of characteristic wavelength to pile radius larger than four. Under this condition, the reflections from the far field (say deeper than two pile diameters) can be analyzed from the responses at receiver positions about 0.6R from the pile axis based on one-dimensional stress wave theory.     

Efficient Evaluation of Reliability for Slopes with Circular Slip Surfaces Using Importance Sampling

Evaluating the reliability of a slope is a challenging task because the possible slip surface is not known beforehand. Approximate methods via the first-order reliability method provide efficient ways of evaluating failure probability of the “most probable” failure surface. The tradeoff is that the failure probability estimates may be biased towards the unconservative side. The Monte Carlo simulation (MCS) is a viable unbiased way of estimating the failure probability of a slope, but MCS is inefficient for problems with small failure probabilities. This study proposes a novel way based on the importance sampling technique of estimating slope reliability that is unbiased and yet is much more efficient than MCS. In particular, the critical issue of the specification of the importance sampling probability density function will be addressed in detail. Three examples of slope reliability will be used to demonstrate the performance of the new method.