Evert C. Lawton

An iterative finite element-boundary element algorithm

A domain decomposition algorithm coupling the finite element and boundary element methods is presented in this paper. This algorithm is iterative in nature. It essentially involves subdivision of the problem domain into subregions being respectively modeled by the two methods, as well as restoration of the original problem with continuity and equilibrium being satisfied along the interface. An arbitrary displacement vector is first assigned to the interface of the boundary element subdomain. Then, the energy equivalent nodal forces of the solved interface tractions are treated as the boundary conditions for the finite element subdomain to solve for the interface displacements. The solution is achieved when these two sets of displacements converge. To speed up the rate at which the algorithm converges, a relaxation of the displacement data at the interface is employed for the next iteration. Strategies for static and dynamic choices of relaxed displacements are addressed, and the validity of the algorithm is verified by solving an example problem. Numerical solutions of the test problem obtained using the proposed algorithm are compared with solutions from the finite and boundary element methods.

Numerical Modeling of Geofoam Embankments

In 2001, the Utah Department of Transportation completed a 4-year

Performance of Geopier Reinforced Soil Foundations During Simulated Seismic Tests on I-15 Bridge Bents

1.4 billion I-15 reconstruction project in Salt Lake City, Utah. This project included widespread use of expanded polystyrene geofoam as lightweight embankment at important utility crossings and where close proximity to existing buildings necessitated minimizing consolidation settlement. This paper presents construction and long-term monitoring results for some of these embankments with numerical modeling of the field measurements. Fast Lagrangian Analysis of Continua, a finite-difference program, was used to estimate the complex stress distribution and the displacements (i.e., strain) that developed in select geofoam embankments. The writers used a bilinear elastic model to produce reasonable estimates of gap closure, block seating, and the subsequent elastic compression of the geofoam embankment at higher stress levels. Such estimations are important for modeling and designing geofoam embankments and potential connections with other systems. The calculation of the complex stress distribution and displacements that develops in a geofoam embankment has application to settlement, lateral earth pressure against retaining and buried walls, slope stability, and seismic design of geofoam embankments.

Estimation of Time Rate of Settlement for Multilayered Clays Undergoing Radial Drainage

Results are presented from full-scale tests on geopier foundations subjected to simulated seismic activity. The foundations were subjected to large cyclic lateral and uplift-compression loads as well as significant overturning moments produced by the horizontal forces. For the conditions of the tests, including large loads, poor subsurface soils, and no embedment of the foundations, the magnitudes of the maximum displacements and rotations were relatively small. Furthermore, the permanent displacements at the end of the tests were small. Overall the results indicate that geopier foundations are ductile and can sustain large displacements—such as those generated by earthquakes—without significant damage and can thereby maintain serviceability after an earthquake.

LABORATORY STUDY OF FEASIBILITY OF STABILIZING ZINC CLINKER AND ROAD MILLINGS TO PRODUCE LOW-PERMEABILITY PAVEMENT MATERIAL

This paper demonstrates how the finite difference technique can be used to estimate the time rate of settlement for soft, compressible clayey soils treated with prefabricated vertical drains at sites where primary consolidation settlement is occurring in a multilayered system at varying rates. Semiempirical methods based on surface settlement monitoring have typically been used to estimate the progression of primary consolidation settlement. However, interpretation of such methods can be problematic for multilayered soil profiles. For such sites, it is crucial to obtain a reasonable characterization of the foundation soils’ horizontal drainage properties and include these estimates in the time rate of settlement projections. Field monitoring of subsurface instrumentation is extremely valuable in providing additional information about the consolidation behavior of different layers. When subsurface field measurements are coupled with the proposed numerical method, far more reliable projections are obtained. This paper focuses on how to integrate field and laboratory data with projections of time rate of settlement obtained from semiempirical and finite difference methods to predict more accurately the time rate of consolidation behavior of multilayered foundation soils.

Comparison of Methodologies for Establishing Design Properties of Horizontal Drainage in Soft Cohesive Soils

An international mining company has funded research to develop a lowpermeability pavement material by stabilizing on-site waste materials (zinc clinker and road millings) at a zinc processing plant in the mid-western United States. The need for development of this material has arisen from concerns of the state environmental protection agency (EPA) that rain is leaching zinc from stockpiles of clinker, thereby contaminating the surface soils, drainage ditches, and groundwater on the site. The desired engineering properties of the stabilized material are as follows: (a) the material must have sufficiently low permeability to act as an “impermeable” liner, (b) the material must bind the zinc to the clinker so that it does not leach out, and (c) the material must be stiff and strong enough to serve as a pavement base course and wearing surface. Laboratory tests were conducted with various stabilized combinations of asphaltic road millings, zinc clinker, and local clay from a zinc processing plant in the midwestern United States to determine whether a lowpermeability pavement material could be produced. Two methods of stabilization were studied: (a) one with portland cement and (b) one with a combination of three cold-mix additives (a binder, a stabilizer, and a sealant). The primary types of laboratory tests conducted were unconfined compression tests with cement-stabilized materials, Marshall stability tests with cold-mix-stabilized materials, and leachate-permeability tests with both types of stabilized materials. A design mixture was produced by the addition to the waste materials of the three proprietary coldmix additives (a binder, a stabilizer, and a sealant) and a local clay that meets all three requirements in tests with laboratory-prepared specimens. Field tests are needed to verify that these attributes can be produced by full-scale construction techniques. In addition, laboratory and field tests are needed to determine the durabilities of these stability materials for the repetitive traffic loads and environmental conditions to which pavement systems are subjected.

Using a Rowe Cell to Establish Horizontal Drainage Properties of Soft Soils

Estimating the rate of settlement for foundation soils treated with vertical drains requires an understanding of the horizontal drainage behavior of the soil, because the time of consolidation settlement may be critical to the overall construction schedule and sequencing. This paper provides a case study comparison of the results of methodologies associated with obtaining design parameters for horizontal drainage for use with vertical drain design, including backcalculation of field settlement data, cone penetrometer testing for pore pressure dissipation, and laboratory Rowe cell testing, by means of the soft, cohesive Lake Bonneville soil deposits in Salt Lake City, Utah. Each of these methodologies has an inherent set of strengths and limitations that should be considered when vertical drains are being designed or time of consolidation settlement is being estimated. Backcalculation of field performance data is effective in identifying true in situ settlement behavior but is not always feasible. Rowe cel...

A Review of Shear Stress Sign Convention in Interpreting Mohr's Circle Using the Pole of Planes Method

When estimating the time-rate of settlement for foundation soils treated with vertical drains, understanding the horizontal drainage behavior of the soil is important because the time of consolidation settlement may be critical to the overall construction schedule and sequencing. This paper explains the process for obtaining the horizontal properties of soft soils in the laboratory using a Rowe cell, a laboratory device that directly measures the horizontal drainage of soft soil samples through a radial consolidation test. The Rowe cell further allows for back-saturation of test specimens and the ability to replicate in situ lateral stress conditions with an applied cell pressure. This paper summarizes how challenges associated with specimen preparation, test setup and procedure, and data analysis and interpretation can be overcome. Finally, this paper demonstrates that this is a viable method that should be considered more often for obtaining horizontal drainage design parameters.

Field tests and numerical analyses of subgrade soil reinforced with grids of stabilized granular columns

The pole of planes method is a popular technique for interpreting Mohr’s circle to determine the stresses (normal and shear) on planes of differing rotations in 2-D space. A survey of undergraduate textbooks on soil mechanics shows differing viewpoints on the sign convention for interpreting the shear stresses. This paper makes a rigorous evaluation of the consequences of using a clockwise (CW) or counterclockwise (CCW) positive sign convention for the proper interpretation of Mohr’s circle of stresses using the pole of planes method. In either sign convention case, the shear stress axis is considered positive upwards while the normal stress axis is considered positive to the right. It was found that if the shear stresses acting on an element are considered CW positive, the resulting stresses found on a rotated plane do not satisfy static equilibrium. However, the stresses determined using a CCW positive sign convention do satisfy static equilibrium. Hence, when interpreting Mohr’s circle with the Pole method, the use of compression positive normal stresses must also use a CCW (right-hand rule) sign convention for shear stresses.

Bearing Capacity of Reinforced Sand Subgrades

Field tests and numerical analyses conducted to establish the feasibility of reinforcing soft, loose, or otherwise inadequate subgrade soils with a grid of small-diameter, stabilized, vertical granular columns to support traditional pavement systems are described. This technique may prove to be cost-effective if it is used to improve subgrade soils so that the subbase or base courses can be reduced in thickness or eliminated. Field plate bearing tests were carried out on unreinforced cohesionless silty sand and on the same soil reinforced with vertical reinforcing columns constructed of four materials: crushed granitic gneiss, silica sand, cement-stabilized native soil, and cement-stabilized silica sand. The field tests indicated that the columns made of the two cement-stabilized materials substantially increased the subgrade modulus of the native soil. In contrast, the two unstabilized columnar reinforcing materials produced no substantial improvement in stiffness. The field tests were modeled by using a...