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3 CHAPTER 1 Background CANDE, an acronym derived from Culvert ANalysis and firms, manufacturers, universities, and research institutions in DEsign, is a finite element program developed especially for the United States and abroad who have used the program to the structural design, analysis, and evaluation of buried struc- design culvert installations, understand soil-structure behav- tures including culverts made of corrugated metal, reinforced ior, interpret experimental results, and design new products. concrete, and plastic as well as other soil-structure interaction The popularity of CANDE is, in part, due to the rigorous problems such as underground storage facilities and storm adherence to the principle of good mechanics and to the trust- water chambers. CANDE was first introduced in 1976 under worthiness of the program, earned over years of testing (5). the sponsorship of the FHWA (1, 2). Over the years, FHWA Equally important to its popularity is the availability of has sponsored upgrades to the program culminating in 1989 CANDE's source code and documentation of the program- with the CANDE-89 program (3, 4), which offers the follow- ming architecture. Accessibility to the source code is an ing analytical features: extremely important feature for researchers who often want to test new theories and models as part of their research effort. Plane strain geometry--a 2-D finite element representation Often, these research studies lead to new additions to the pro- of the soil and structure under quasi-static vehicular load- gram that will ultimately become available to the entire culvert ing conditions and based on small deformation theory. community. Incremental construction--the capability to simulate the physical process of placing and compacting soil layers, one CANDE Upgrade--AASHTO lift at a time, below, alongside, and above the culvert as the installation is constructed. In May 2005, TRB/NCHRP negotiated a contract with Interface elements--the ability to simulate the frictional Michael Baker Jr., Inc. to modernize and upgrade CANDE-89 sliding, separation, and re-bonding of two bodies origi- under the sponsorship of AASHTO. The project known as the nally in contact. Typically these elements are used between CANDE Upgrade Project, designated as NCHRP Project 15-28, the culvert and soil and between trench soil and in situ soil. is the funding source for the enhancements that have been in- Soil elements and models--soil elements are high-order con- corporated into CANDE-2007 presented in this report. tinuum elements with a suite of soil models ranging from The CANDE Upgrade Project targeted the following three linear elastic to highly nonlinear. The so-called Duncan and areas for enhancement: Duncan/Selig soil models are very representative of the non- linear soil behavior in most culvert installations. Pre- and post-processing with modern computer technol- Beam elements and pipe models--a culvert (or structure) ogy, is represented by a connected sequence of short beam- New analysis capabilities and architecture for multiple column elements that trace the culvert's periphery. The structures, and material models of beam elements distinguish between Update design criteria for all culvert types to include LRFD different pipe types. Each material model includes design methodology. criteria, which provide measures of safety against potential modes of failure. Pre- and Post-Processing Over the years, CANDE has enjoyed a great deal of popular- Previous versions of CANDE were in batch-mode input ity in the culvert community including state DOTs, consulting (i.e., ASCII text input file/output file). The input was provided

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4 via documented input instructions and an ASCII text editor Design Criteria and LRFD Methodology without dedicated GUI software to aid the user in data prepa- ration. Similarly, output data was written to an ASCII text The original CANDE program was based on the concept of output file without any post-processing capability to graphi- working-stress design methodology. Accordingly, the previ- cally display results. ous versions of CANDE reported safety factors against various CANDE-2007 is now equipped with a Windows-based, modes of failure (design criteria) that have been traditionally menu-driven format for interactive data input and real-time associated with the type of culvert being considered. In recent control of data output along with a context-sensitive help sys- years, AASHTO (6) has adopted the reliability-based LRFD tem and numerous graphical plotting options. methodology. Rather than using safety factors, the LRFD methodology uses load factors and resistance factors to achieve a safe design. New Analysis Capabilities As part of the CANDE Upgrade Project, a complete and The architecture developed for CANDE-2007 allows the compatible set of design criteria, applicable to both working- use of multiple pipe groups (previous versions of CANDE stress and LRFD methodologies, was identified for the permitted a single pipe group), thereby allowing an analy- common culvert materials: corrugated metal, reinforced con- sis of several culverts placed side-by-side, or a retrofit crete, and thermoplastic pipe. These design criteria are now design (e.g., a plastic pipe inserted inside a corrugated incorporated in the corresponding pipe subroutines of the steel pipe). CANDE-2007 analysis subsystem. The user now has the op- In addition to the small deformation theory utilized in the tion to choose either service load (working-stress evaluation original version of CANDE, CANDE-2007 has been updated of the design criteria) or factored loading (LRFD evaluation to include a Lagrange formulation that provides an accurate of the design criteria). and robust algorithm for predicting large deformations along Many other improvements have been incorporated into with methodology for predicting buckling capacity at the end CANDE-2007 that are not mentioned above but are discussed of each load step. in detail in the CANDE-2007 User Manual and Guideline and CANDE has also been updated to include an automated the CANDE-2007 Solution Methods and Formulations docu- bandwidth minimizer, thus relieving the user of the require- ments. It should be noted, however, that all the capabilities ment of assigning node numbers in a judicious manner to and options that existed in the CANDE-89 version have been manually reduce the bandwidth of the system matrix. retained.