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PROGRESS REPORT (DMS-9313013)

Measurement, Modeling and Prediction for Infrastructural Systems

Alan F. Karr, Eric I. Pas, Jerome Sacks, Principal Investigators

May 27, 1998

Contents

1. Travel Demand
2. Intelligent Transportations Systems
3. Materials Science and Deterioration of Concrete
4. Other Items
5. References

1. Travel Demand.

Research has comprised multiple, complementary approaches to generating the activities and modeling the choices that create the demand for travel.

1.1 Activity Synthesis

Household Classification using Multivariate Regression Trees. C language code for the multivariate regression tree algorithm (The multivariate tree algorithm works exactly like the ordinary regression tree except that deviance is defined by a weighted sum of residuals for a multivariate rather than univariate response.) was implemented [42]. The purpose is to create classes of households defined by their demographic characteristics such that the classes are as homogeneous as possible with respect to multivariate measures of household activity patterns such as total time spent in each of several different activity categories. The scale of the data - 15 dependent variables, a potential 24 independent variables, and approximately 4,000 cases - required replacement of previous S-PLUS code.

Activity--Travel Patterns for TRANSIMS. In collaboration with researchers from the Los Alamos National Laboratory (LANL), methods are being developed and implemented to synthesize one day's activities for an entire (simulated) population for Portland, OR. (To be used as input to TRANSIMS, a detailed simulation currently under development at LANL.) The approach combines resampling activities from a 1994/95 survey of approximately 4500 households with spatial interaction models for activity locations.

Resampling is employed because conventional parametric activity choice models do not adequately capture household interaction. Each simulated household is matched (on the basis of demographic characteristics) with a survey household, which provides a skeletal pattern for the simulated household. New locations for the simulated household's activities are then generated using its location and spatial interaction models.

Given a skeletal plan calling for d activities (with known types a₁, ...,a_d and modes m₁, ..., m_d.) starting at location z₀ and ending at location z_d+1, the spatial interaction model generates their locations z₁, ..., z_d according to a continuous distribution of the form

f(z, m|a, t, z₀, z_d+1) = exp[c(z₀, z₁,m_{1, t}1, A) +g_a₁(z₁) + ...+ c(z_d, z_d+1, m_d+1, t_d+1, A)],

where c(z_k, z_k+1, m_k+1, t_k+1, A) is a cost function for travel from z_k to z_k+1 by mode m_k+1 at time of day t_k+1. The parameters are A estimated from data.

The attractiveness functions g_{a_k}(z_k) are estimated using a nonparametric model; Figure 1 illustrates for work locations.

Figure 1: Attractiveness function for Work Locations.

P. Speckman (Statistics, Missouri), D. Sun (Statistics, Missouri) and K. Vaughn (Metropolitan Transportation Commission, Oakland, CA) are the principals for this research, assisted by graduate student T. Bengston.

Synthetic Travel Pattern Generator (STPG). An analytical framework for the generation of synthetic daily activity-travel patterns has been developed, and its components estimated from empirical data [22, 23, 24, 25]. An initial implementation performs trip generation, trip distribution, and mode choice (That is, all parts of the conventional "four-step" process except network assignment. for the entire daily travel pattern of an individual, along a continuous time-of-day axis.

While promising for demand forecasting and policy analysis, as well as for the generation of synthetic travel pattern data, STPG overpredicts the frequencies of work, other, and home trips. This is believed to be due to inadequate representation of work schedules and future dependencies in behavior, and is being addressed.

R. Kitamura (Civil Engineering, California, Davis) has led this work, which also involved graduate student C. Chen.

Other Items. Additional threads of research on travel demand included:

Interdependencies. Models were developed that incorporate the interdependency of activity patterns of family members into the modeling framework [29]. Approaches included fuzzy clustering algorithms to establish the prominent activity pattern types and measures of distance between individual activity patterns and pattern types; and modeling activity-based travel as a component in a complex system of co-evolving agents.

Variable Definitions. Methods were developed to assess the extent to which empirical definitions of activities and activity patterns influence the significance of explanatory socio-demographic variables in choice models.

1.2. Bayesian Methodology

The research on activity location models depends strongly on nonparametric estimates of spatial interaction distributions. Because the models developed to date do not readily incorporate additional information such as time of day and household demographics, Bayesian alternatives are being investigated. Approaches include

Bayesian nonparametric and semiparametric regression and density estimators and Bayesian hierarchical models [41]. The key contribution is use of conditional autoregressive models (CAR) and their generalizations for synthetic random effects to capture spatial variability and as prior distributions in nonparametric regression and density estimation.
Bayesian hierarchical linear mixed models in which the fixed effects have a vague prior such as a constant prior, the random effects follow a class of proper or improper CAR (1) models, and the variance components follow a class of noninformative priors [44, 45].
Generalized linear mixed models, which include as a special case the binomial logistic and Poisson log-linear models commonly used in disease mapping [43].

Speckman and Sun are conducting this research.

1.3. Choice Models

Several paths were pursued, including:

Detailed representations for workers' activity-travel patterns [10, 13]; for household stop generation, stop and car allocation to adult household members and the generation of daily travel pattern [6]; for presence/absence of non-work-stop-making during the evening commute, [8, 10]; for effects of level-of-service [9]; and for leisure activities [11].
A joint unordered-ordered discrete choice system to model the evening commute [7].
Continued development of the paired combinatorial logit model and comparison to nested logit models [26, 27, 28, 53].
Models relating residential location and tolls [17].

This work is being led by C. Bhat (Civil Engineering, Texas at Austin) and F. Koppelman (Civil Engineering, Northwestern), and also involves graduate students R. Misra (Texas at Austin), V. Pulugurta (Texas at Austin) and C. Wen (Northwestern).

1.4. Planned Work for Year 5.

Activity Synthesis. A necessary first step is to finish converting existing S-PLUS programs to C. (This accomplishes not only more rapid execution but also portability and modularity; the latter allows easy incorporation of new features,) Thereafter, new models will be developed for locations for additional categories of activities so that there are at least three models, one for work and school, one for household maintenance and one for recreation. We also will develop models for generating random start and end times for activities and assignment of travel mode.

STPG. To resolve the problems described above, we will construct models of work starting and ending times, and their flexibility; define prisms for each worker based on work schedules; develop models of activity engagement in the respective prisms; and simulate activity and travel by generating activity types, locations, durations and travel modes within each prism. Other possible improvements include: coherent treatment of the work/school base in a series of destination choices; integration of mode and destination choices in a series of home-based and non-home-based trips; representation of space-time constraints in the activity type, duration and destination choice components; representation of pertinent coupling constraints; and incorporation of accessibility and other measures for increased policy sensitivity.

Bayesian Models for Spatial Interaction. The nonparametric models used to date cannot easily include additional covariates such as time of day and household demographic variables. One path to be explored is Bayesian nonparametric regression and density estimation via generalized linear mixed models. An alternative is a Bayesian multinomial logistic model. Gibbs sampling will be used to compute the Bayesian estimators.

Choice Models. Principal tasks planned for the next year are:

Develop and apply methods to compute multi-dimensional integrals in mixed logit models to order to permit flexible substitution pattern specifications across alternatives as well to accommodate heterogeneity across individuals in responsiveness to alternative attributes.
Examine the effect of non-sampling error (measurement error and non-response error) on travel model parameter estimates.
Continuing research on representations for daily activity-travel patterns.
Formulate and apply discrete choice models (for one- and multi-dimensional choice contexts) that compare differing model formulation.

2. Intelligent Transportation Systems (ITS)

Research over the past year has focused on a number of traffic-related issues: freeway breakdown, validation of a regional-level model of traffic flow and mode/route choice, estimation of travel times in multiple settings, incident detection, evaluation of signalization plans and estimation of emissions from traffic data.

2.1. Freeway Breakdown

An important issue for management of freeways is recognizing incipient congestion. Methods have been developed [19] to predict the onset of freeway breakdown, which occurs when, in heavy traffic and without an external cause (such as an accident or lane closure), flows and speeds drop rapidly and dramatically.

The methods were developed using a unique, 200 MB data set assembled by NISS: in real time and over the Internet, counts and occupancies were obtained from more than 170 single loop detector stations on a 10-mile stretch of I-5 in northern and north suburban Seattle, WA. Data were collected for weekday morning and afternoon peak periods, amounting to ten hours per day, over two months. Data quality was a significant issue: forty per cent of the readings had to be discarded.

Statistical models using classification trees were used to construct prediction algorithms that detect roughly sixty percent of breakdowns up to ten minutes before they begin, with false alarm rates of five percent. Since the data are available in real time and the prediction models can be evaluated very quickly, these results could be used to trigger strategies (For example, ramp metering to restrict access.) aimed to prevent breakdown. Predictions are improved usefully but not dramatically when the spatial spread of congestion is modeled. (That is, when data from downstream detectors are used to predict congestion at a given location. Data aggregated to a one-minute level are more useful, albeit not dramatically, than five-minute data.

Karr and N. Rouphail (Civil Engineering, North Carolina State University [NCSU]) have led this effort, which also involved NISS postdoctoral fellows T. Graves and V. Thakuriah (now at University of Illinois at Chicago).

2.2. Regional-Level Network Model Validation

The objective is to estimate and validate a regional travel forecasting model at the level of detail used by transportation planning organizations to forecast traffic, ridership and vehicle emissions. Successful validation will provide professionals with a sound basis for using state-of-the-art models in place of traditional methods.

The setting is the Chicago region, which requires a model with approximately 1800 zones, 4 trip purposes, and 2 modes (auto and an integrated transit mode). Primary model outputs are travel choices on a typical weekday pertaining to origin-destination, mode, route and time period of travel by trip purpose in an integrated manner. The model is solved using an algorithm based on the work of S. P. Evans; the central issues are scale and the embedding of a logit model for mode and departure time choice within a network equilibrium model. The network model determines travel times, which affect travel costs, which affect travelers' choices. Parameters of the logit model are estimated using maximum likelihood methods utilizing the Chicago Area Transportation Study (CATS) 1990 home interview survey, estimates of trip origins and destinations by trip purpose, and associated transportation networks.

A new computer code in the C language was designed and implemented, and tested for a model with one trip purpose. Currently, the code is being extended to accommodate multiple trip purposes. The parameter estimation procedure has been redesigned and tested with a smaller version of the target model, and is being added to the code.

The memory requirements and execution time requirements of the new code are being analyzed. Effects of alternative convergence levels at four points in the solution and estimation procedure were examined; as a result, execution time has been reduced substantially.

Sacks and D. Boyce (Civil and Materials Engineering, University of Illinois at Chicago [UIC]) have led this research; other participants are R. Buck (Mathematics and Statistics, Western Michigan), P. Nelson (Computer Science, UIC), M. Tatineni (UIC postdoc) and graduate students at the UIC.

2.3. Travel Time Estimation.

Two long-term efforts on estimation of travel times were completed; a new line of inquiry was initiated.

Freeways. Work on new methods to estimate travel time distributions from single loop detectors is complete, and is reported in [33]. Critical steps were to limit the support of the estimated distribution and dynamically to use the "naive" speed estimate (count divided by the product of occupancy and a nominal vehicle length) to center the estimated distribution.

A new line of investigation focuses on stochastic models for freeway travel based on individual vehicle features (e.g., arrival time, speed, lane, length, height, and color) collected in a spatially sparse but temporally dense fashion; the motivating example of such data is a network of video cameras stationed at approximately one mile intervals and sampling at about five Hz. (Double loop detectors are another source of such data.)

A primary issue is to match vehicles at successive detectors. The approach being pursued treats the unknown matches as missing data, and uses an EM algorithm to estimate parameters in the model corresponding to quantities of interest. The estimation step of the EM algorithm is approximated by running Markov Chains over the state space of possible matches, whose transition probabilities depend on the relative likelihood of the candidate state to the current state as specified by the model at the vehicle level.

This component of the project is housed at the University of California, Berkeley (UCB). Participants are P. Bickel (Statistics, UCB), J. Rice (Statistics, UCB), Y. Ritov (Statistics, Hebrew National), K. Petty (NISS postdoc, based at UCB), assisted by graduate students J. Kwon and M. Ostland, and with the cooperation of P. Varaiya (California PATH project) and S. Russell (California PATH project).

Arterial Streets. Research on the prediction of travel times on signalized arterials has also been completed [20]. The models are based on multiple data sources: probe vehicles, video records of the traffic exiting from an intersection and of the traffic signal, and single loop detectors.

A key finding is that a vehicle's travel time on a link depends most critically on the time that the vehicle enters the link relative to the cycle of the downstream traffic signal. Figure \ref{fig.dundee} illustrates. Knowledge of the number of vehicles exiting the link before the probe but in the same signal cycle removes much of the remaining variation in travel times.

Given these data, neither detector counts nor occupancies improved predictions. This research was performed by Karr, Graves and Thakuriah.

Figure 2: Travel Time as a Function of Relative Entry Time.

2.4. Incident Detection

Rapid, error-free detection of incidents (For example, accidents and vehicle breakdowns.) is essential to safe, efficient operation of freeways.

A decision theoretic approach is being developed, based on the dollar cost of operating the detection algorithm is calculated. The total cost for running the incident detection algorithm at each set of thresholds is the sum of the cost to dispatch aid (Ordinarily, a tow truck, whose cost is assumed to be fixed and independent of whether there was actually an incident.) and the cost of the delay resulting from the incident. (Which is reduced by rapid response to the incident.) The algorithm is trained and tested using data on actual incidents. A software infrastructure has been developed that allows tuning and investigation of a number of algorithms.

The methodology also allows meaningful comparisons between incident detection algorithms and incident management scheme that lack an inherent performance curve, such as operating a roving tow truck system.

Participants are Bickel, Rice, Ritov and Petty.

2.5. Evaluation of Signalization Plans

The goal of this component of the project is to develop a strategy for credible evaluation of traffic signalization plans -sensors, control algorithms and data sources - for urban areas. Such methodology is needed in particular to evaluate proposed systems for dynamic control of traffic signals. Specifically, research is focusing on suitability of the CORSIM model (Developed under auspices of the Federal Highway Administration [FHWA].) as the evaluation testbed.

The principal accomplishment to date has been to calibrate CORSIM in detail for a small network in the central business district (CBD) of Chicago. The calibration was based on video data recording traffic and pedestrian volumes, free flow speeds and queue discharge headways, as well as link travel times. The latter constitute the measure of system performance.

Never before has calibration in such detail been attempted: no non-default parameter values were used that were not measured. Some potentially severe shortcomings of CORSIM were identified: neither long-term events nor clearing of intersections by turning vehicles when the signal changes to red appears to be handled properly. However, the effort was successful; next steps are described below.

Key participants are Karr, Rouphail, Sacks, Sen, Thakuriah, E. Miller-Hooks (NISS postdoc), and graduate student T. Green (North Carolina at Chapel Hill).

2.6. Measurement of Vehicle Emissions

Leveraging funding from the Transportation Research Board (TRB), field experiments are being conducted to explore the feasibility of predicting emissions (of carbon monoxide and hydrocarbons) by vehicles from aggregated traffic data (counts and speeds).

The experiment employs roadside infrared sensors to measure emissions of individual vehicles and the Mobilizer video imaging and analysis system to assemble detailed traffic data. Significant calibration and drift problems with the infrared sensors have been encountered, and are currently being addressed.

Those involved are C. Frey (Civil Engineering, NCSU), C. Gu (visiting NISS from Purdue), Karr, Rouphail, and graduate students from NCSU.

2.7. Additional Topics

Other ITS-related research has addressed:

Route choice and network flow models [16, 18, 30, 31, 36, 37, 46, 47, 48].
Additional issues associated with estimation of travel times [32, 38, 39, 40, 49, 50, 51].
General aspects of travel forecasting and urban transportation [14, 15].
Route guidance under real-time information.

2.8. Planned Work for Year 5

Regional-Level Model Validation. The principal thrusts will b

Fully to implement and test the solution algorithm and parameter estimation procedure for the large-scale model with multiple trip purposes described above.
To validate the model for the 1990 base year, and to subject the model parameters and other inputs to an uncertainty analysis to determine the sensitivity of the parameter estimates and output variables to the model inputs. Requisite data are in place, including the 1990 Census of Population and Housing, and highway and transit flows collected by CATS and the Regional Transportation Authority (RTA).

Ensuring widespread use of the model will require reducing computational requirements to the extent necessary to make it a practical option for professional practice, as well as preparing a model solution procedure using a software system in general use by professionals to evaluate further the practicality of the solution algorithm.

Regional Commodity Flows. The principal goal of this activity, which builds directly on the regional-level model validation, will be to relate regional economic activity (measured through establishment-level production and consumption data and commodity flow data from the Bureau of Transportation Statistics) to the infrastructure (rail, highway, waterway) over which goods flow. Products of the research include, for example, forecasts of traffic flows and analyses of economic consequences of changes in the transportation system.

The work will be directed by G. Hewings (Director, Regional Economics Applications Laboratory, Illinois at Urbana-Champaign and Economist, Federal Reserve Bank (FRB), Chicago), Boyce and Sacks, and will be centered in Chicago. One postdoctoral fellow and two research assistants are anticipated to be involved.

Travel Time Estimation. The model in 2.3 performs well on simulated data for the simple situation described there. Video data are anticipated to be available by the end of 1998. In addition to using these data, future work will focus on extending the model in both time and space. Hidden Markov models will be explored as approximations for the underlying state of the traffic system.

Incident Detection. Completion of the study of incident detection algorithms will include not only evaluating the current set of incident detection algorithms in the transportation literature but also developing new algorithms that account explicitly for historical data. Various dispatching routines will be explored as well.

Algorithm and Measurement Testbed. In cooperation with the California PATH project, a measurement testbed is being constructed to implement real-time algorithms for a variety of transportation problems. It will be used to evaluate regression-based travel time estimation algorithms, incident detection algorithms and other travel time prediction algorithms. Results of algorithms will be compared to video data.

Evaluation of Signalization Plans. Building on the CORSIM validation described in 2.5, the following items will be addressed:

Data-based validation of CORSIM for a 20-40 intersection network in the Chicago CBD.
For this network, detailed examination of the sensitivity of CORSIM to key inputs, including those identified in the initial validation. Techniques for design of numerical experiments in high-dimensional spaces will play a central role.
Identification of "benchmark" signalization plans and plausible alternatives, as well as measures of network performance.
Extensive runs of CORSIM, varying not only signalization plans, but also key inputs in a manner that replicates variability in real traffiic.

Measurement of Vehicle Emissions. Assuming that data of acceptable quality can be collected (see 2.6), the crucial issues are to assess loss of predictive capability when only restricted data are available, as well as the effects of two variables: vehicle type and the proportion of "cold start" vehicles. Extending previous work, we also plan to assemble, evaluate, and validate a new low-cost on-board emissions measurement (OBEM) system. This system will be used to investigate factors that affect the level and variability of on-road emissions, and ultimately, to devise and test strategies to design and conduct experiments that evaluate vehicle-based pollution prevention strategies. Among complications to be confronted are nonstandard design issues (for example, vehicle movements in "path space"), high dimensionality of the factors, uncontrollability of some factors and the need for detailed characterization of residual uncertainty.

3. Materials Science and Deterioration of Concrete

This work has been overseen by Karr and S. Shah, Director, Center for Advanced Cement Based Materials (ACBM), Northwestern University (NU). Other participants are B. Ankenman (Industrial Engineering and Management Sciences, NU), D. Daley (Statistics, Australian National), T. Igusa (Civil Engineering, NU), C. Aldea (postdoc, ACBM), J. Picka (postdoc, NISS, based at ACBM), K. Wang (postdoc, ACBM) and graduate students S. Jaiswal and H. Liu.

3.1. Experiments and Models for Permeability

A multi-year program of experimentation and data analysis to develop models for chloride permeability of concrete is nearly complete. Results are reported in [3, 21]; additional papers will report on details of the image analysis and stereological measurements, as well as final statistical models. A typical model [3] for concrete with "gapped" natural aggregate is

log(Initial current) = -1.3208 + 1.51 VF + 1.56 AP + 2.03 WC - 1.93 WC AP - 0.92 VF AP

where VF is the volume fraction of aggregate, AP is the proportion of large aggregate and WC is the water-to-cement ratio. (The principal materials variable.) In this equation, the sample size is n = 66, the (multiple-) r² is 0.91, and all coefficients significant at p < .01.

In part, the interpretation of is straightforward: the dominant VF effect is dilution, the main AP effect is detouring, and the WC effect is as expected. There are also more subtle issues: the AP-VF interaction appears to be weak "percolation" effect, while the AP-WC interaction is simply puzzling: AP matters only for small values of WC.

3.2. Permeability of Cracked Concrete

Consistent with the original aims of the project, research on permeability of cracked samples of concrete is being carried out in order to understand the feedback between permeability and deterioration. An initial study is reported in [53].

Research over the past year has focused on factors that may influence the relationship between damage and permeability. These include thickness of the sample, material composition (paste, mortar, normal strength concrete and high strength concrete), and the average width of the induced crack (ranging from 50 to 400 microns). Key steps in the experimental protocol were:

Cracks of designed widths were induced in the concrete specimens using a feedback controlled splitting test. See Figure 3.
Chloride permeability of the cracked samples was evaluated using rapid chloride permeability test (RCPT), using ASTM C 1202-94. See the left panel in Figure 4.
Water permeability was evaluated by a low-pressure water permeability test (WPT), which is appropriate for infrastructure. See the right panel in Figure 4.

Results to date [1, 2] indicate that the water permeability is significantly more sensitive than conductivity (Used here in place of "chloride permeability" to help avoid confusion.) with respect to the crack widths used in this study. Among the materials tested, only for high strength concrete is conductivity sensitive with respect to cracking. Material type and crack parameters affect water permeability significantly, however. The water permeability of cracked specimens decreased significantly with time, and the rate of decrease in the permeability coefficient was found to depend on the size of the initial crack opening. Possible explanations are autogenous healing of cracks and self-sealing of uncracked material; these are being investigated.

Figure 3: Apparatus for Feedback Controlled Splitting Test.

Figure 4: Permeability Testing Equipment. Left: Chloride permeability. Right: Water permeability.

3.3. Experimental Designs

In contrast to early phases of the work, in which the experimental design criterion that was most influential was the need to efficiently cover a large multi-dimensional factor space with a limited number of observations, (For which optimal space-filling experimental designs were employed.} in later stages the primary criterion has become the estimation of certain effects and variances. In particular, it is important to estimate not only the effects of the compositional variables such as water-to-cement ratio and maximum aggregate size, but also the variation effects due to mixing multiple batches of concrete (batch-to-batch variance) and casting multiple test cylinders (cylinder-to-cylinder variance) of the same composition.

"Split factorial'" designs were developed that allow estimation of both types of effects.The basic idea is that an experiment is split (conceptually) into two halves. In the first, multiple batches of concrete from each recipe are made and a single cylinder from each is tested, while in the second, a single batch of concrete is made for each recipe and multiple cylinders are cast and tested. Figure 5 illustrates

Figure 5. Spilt Factorial Design.

Data from the first half are used to estimate the batch-to-batch variance, those from the second half to estimate the cylinder-to-cylinder variance, and data from both halves to estimate the fixed effects. The technique (which is broadly applicable) and its properties are described in [4].

3.4. Numerical Models

The time-consuming nature of the experimentation and the near-impossibility of obtaining reliable measurements of the three-dimensional structure of specimens have led to initiation of a strong effort on numerical models for permeability. Such models have two principal components:

A model to simulate the structure of the concrete; and
A model to simulate diffusivity given the structure.

The latter exist; the former do not.

Current efforts to develop simulation models for concrete structure focus on random set models for materials consisting of at least two phases, one of which is impermeable to chloride ions. Such models are typically based on germ-grain models, but grains (representing the chloride-impermeable aggregate) are not allowed to interpenetrate. This forces complicated dependence relationship onto the positions of the grains, which in turn renders useless many of the methods used in the study of Boolean models.

Instead, models are being pursued that connect the local phenomena of non-interpenetrability and the dependence that this induces with the bulk properties of the material, such as random set moments and transport properties. (In structure, they are similar to those used in the study of ideal gases in statistical physics.) Few useful statistics have been developed for the analysis of such models, but several are being investigated and results have been formulated concerning their estimation, building on [34, 35].

Two additional classes of models for concrete permeability are being developed:

Equivalent medium models, in which two- and three-phase media are replaced by a one-phase continuum. These models are accurate only in the dilute limit, where the volume fraction of aggregate is small. Nevertheless, they provide insight into the effects of the interfacial transition zone (ITZ) on permeability.
Three-dimensional numerical representations of concrete, for which the diffusion equation is solved for the two- and three-phase media using the appropriate field constants and boundary conditions for the aggregate, ITZ and cement. Whereas spherical harmonics have been used in the past for infinite, periodic arrays, finite-element techniques are used in this effort.

3.5. Planned Work for Year 5

The thrust of the research will be to develop insight usable in the design phase of a structure or in the repairs of cracks formed in existing construction.

Permeability of Cracked Concrete. To develop deeper understanding of the effects of cracking in permeability, additional measurements will be made of:

Porosity, using mercury intrusion porosimetry (MIP); and
3D structure of the cracks, using video microscopy and image analysis.

Using the latter data, a fracture mechanics model will be developed to predict the two-dimensional crack pattern, and compared with the experimental results. A new set of experiments will investigate permeability of cracked fiber-reinforced cement-based materials, which show strong promise of improved durability.

Permeability under Loading. Because all structures are loaded during use, a new direction of the research will be to develop permeability tests of cracked concrete under loading. An experimental setup - itself a major contribution - is being designed and developed. The data it yields will allow new insight into relationships among structure, deterioration and permeability.

Numerical Experiments. Work will continue to model permeability numerically in realizations of the two- and three-phase random-set models. Principal activities will be to:

Simulate structures replicating physical characteristics (e.g., high volume fraction realistic size distribution of aggregate) of concrete. Random close packings will be simulated in order to develop further models, and the sensitivity of these models to small changes in algorithms will be investigated.
Develop descriptive statistics for these models.
Identify characteristics of the structure that affect diffusivity.
Devise estimators of these characteristics from the kinds of data available in practice, and develop properties of the estimators.
Assess fit and robustness of models.

4. Other Items

4.1. Project Leadership

Eric I. Pas of Duke University, a principal investigator on the project, died on November 21, 1997. To fill in part the gap caused by his death, Nagui M. Rouphail, Professor of Civil Engineering at North Carolina State University, has been appointed a principal investigator. Rouphail's expertise on traffic engineering and intelligent transportation systems will contribute significantly to the continued success of the project.

4.2. Postdoctoral and Student Support

Seven postdoctoral fellows and 23 graduate students, five of whom received Ph.D. degrees, were supported by the project.

4.3. Conference Presentations

Presentations of the research conducted under this project were given at the 1997 Summer Conference on New Developments and Applications of Experimental Design (Seattle, June, 1997); the 1997 Joint Statistics Meetings (Anaheim, CA, August, 1997); the 8th Meeting of the International Association for Travel Behavior Research (Austin, TX, September, 1997); the Symposium on Nonparametric Functional Estimation (Montreal, October, 1997); the 12th International EMME/2 Users' Group Conference (San Francisco, October, 1997); INFORMS national meetings (Dallas, October, 1997, and Montreal, April, 1998); the fifth International Conference on Brittle Matrix Composites (Warsaw, October, 1997); the Regional Science Association International (Buffalo, November, 1997); the Fifth International Conference on Structural Failure, Durability and Retrofitting (Singapore, November, 1997); the Materials Research Society Fall Meeting (Boston, December, 1997); the Workshop on Infrastructural Materials (San Diego, April, 1998); the 12th Engineering Mechanics Conference (San Diego, May, 1998); the International Conference on Reliability and Survival Analysis (DeKalb, IL, May, 1998); the Sixth Valencia International Meeting on Bayesian Analysis (Alcossebre, Spain, May, 1998); the 1998 Spring Research Conference (Santa Fe, NM, June, 1998); the International Workshop on Concrete Technology for a Sustainable Development in the 21st Century (Svolaer, Norway, June, 1998); and TRISTAN III (Triennial Symposium on Transportation Analysis) (San Juan, PR, June, 1998).

Nearly a dozen presentations were made at the 77th Annual Meeting of the Transportation Research Board (Washington, January, 1998). Several are scheduled for the 1998 Joint Statistical Meetings (Dallas, August, 1998).

References

[1] Aldea, C., Shah, S. P., and Karr, A. F. (1998a). Permeability of cracked concrete. Submitted to Materials and Structures.

[2] Aldea, C., Shah, S. P., and Karr, A. F. (1998b). Effect of cracking on water and chloride permeability of concrete. Submitted to Cement and Concrete Res.

[3] Ankenman, B. E., Igusa, T., Jaiswal, S., Karr, A. F., Picka, J. D., Shah, S. P, Styer, P., and Wang, K. (1998). Experimental studies of the chloride permeability of concrete. Submitted to Int. J. Cement and Concrete Res.

[4] Ankenman, B. E., Liu, H., Karr, A. F., and Picka, J. D. (1998). Experimental design for estimating a response surface and variance components. Submitted to Technometrics.

[5] Bhat, C. R. (1997). Incorporating observed and unobserved heterogeneity in urban work mode choice modeling. Submitted to Transp. Sci.

[6] Bhat, C. R. (1998a). An analysis of travel mode and departure time choice for urban shopping trips.Transp. Res. (to appear)

[7] Bhat, C. R. (1998b). Accommodating flexible substitution patterns in multidimensional choice modeling: formulation and empirical application to travel mode and departure time choice. Transp. Res. (to appear)

[8] Bhat, C. R. (1998c). A post-home arrival model of activity participation behavior. Transp. Res. (to appear)

[9] Bhat, C. R. (1998d). Accommodating variations in sensitivity to level-of-service variables in travel mode choice modeling. Transp. Res. (to appear)

[10] Bhat, C. R. (1998e). Modeling the commute activity-travel pattern of workers: formulation and empirical analysis. Submitted to Transp. Sci.

[11] Bhat, C.R., and Misra, R. (1998). Discretionary activity time allocation of individuals between in-home and out-of-home and between weekdays and weekends. Submitted to Transportation.

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