Finite Elements Analysis in Construction – An Application for Studying Foundation Response to Earth Backfill

Introduction

In current practice, structural engineers rely heavily on computer-based analysis techniques for most design problems.  Major commercial structural analysis programs typically employ the finite element method because it is relatively easy to generalize for modeling a wide range of structural configurations.  Although software developers have worked to make these programs more user friendly through the development of graphical user interfaces, finite element structural analysis is still a skill that must be developed and maintained through significant training and experience.  The user must also have the ability to interpret and evaluate the output to avoid using incorrect results caused by improper model development.  Although analysis software should not be used as a black box on which inexperienced individuals base critical decisions because “the computer must be right,” applications using advanced techniques are feasible that would provide useful information to a technically competent constructor.

Construction professionals are responsible for the structural performance of temporary structures and the partially completed structure.  They derive the technical skills to design and evaluate structures through consultation with the design engineer, the use of specialty subcontractors, and experienced superintendents.  Graduates of accredited construction management programs are also required to have some instruction in structural design and analysis.  These courses usually build on prerequisites from physics and engineering, but most construction management graduates only expect to develop a level of understanding adequate to communicate effectively with the structural engineer (Arumala, 2002, Opfer and Gambatese, 1999).

The constructor must understand the response of structural components to loads imposed during construction and recognize cases where an engineer should be consulted.  The construction supervisor may have gained competence through experience in the design and erection of specific temporary structural systems using the manufacturer’s guidelines or design tables; however, many structural design issues involving temporary structures or the partially completed primary structure will be beyond their proficiency.  There is an opportunity in the “gray area” between situations in which a licensed engineer is required by law and those where the constructor needs assistance to offer tools to improve the quality of structural decisions made on the construction site.

Finite-element-based structural analysis software is being developed to simplify the development of structural systems through user interfaces customized for specific applications and integrated design/analysis/redesign functions.  The “Design by Analysis” approach involves a graphical user interface that allows the user to quickly describe the structure by specifying a limited number of parameters (US Army Corps of Engineers, 2003A).  A finite element model is automatically generated based on these parameters, and the structure is analyzed to determine the response under all significant loads.  The program then checks the design against applicable codes and other requirements and modifies the structure based on those results.  The final result is translated into a solid model of the structure that can be used throughout the design and construction.

This approach, which combines a powerful analysis tool with a user-friendly interface, can provide useful information to the constructor, as well as the design engineer, to improve decisions on the construction site.  Design by Analysis software developed to design innovative navigation structures (US Army Corps of Engineers, 2003B).  was adapted to evaluate the response of a reinforced concrete mat foundation during backfill operations in order to determine when backfilling could begin and to what depth the backfill could be placed before completing the first floor.  The preprocessor is described in detail, and analysis results are presented to demonstrate the capabilities of this approach.

Design by Analysis

The Design by Analysis approach seeks to significantly increase the efficiency of the designer by automating much of the modeling and design process.  A custom program for a specific type of structure can be developed with a small set of essential modeling and analysis options to minimize the time required to create a new design.  With some assumptions about typical structural configurations, the design process can be highly automated so the structural model is generated from a minimal number of parameters (Slattery, 2002).

Approach

The typical reinforced concrete structure is composed of beams, slabs and the joints between these elements.  The beams and slabs are defined by their overall dimensions and the reinforcement.  The extent of the structural elements is determined by the functional requirements of the structure while the depth of beams, thickness of slabs and reinforcement is determined by the loads on the structure.

The essential parameters required to describe a simple rectangular structure are the length, width and height.  A more detailed description would include the spacing of beams and columns, floor heights, and the location and size of openings.  Design by Analysis software creates a complete model of a structure from these inputs.  Initial member sizes are provided by the user or assumed and then modified during analysis/redesign iterations to meet the design objectives.  Required reinforcement is determined to resist the shear, moment and thrust produced in each member by the most severe load case.

Finite Element Approach

Reinforced concrete structures are modeled using a combination of conventional shell elements for concrete slabs and solid superelements to produce an accurate three-dimensional model of joints between slabs.  Beam and column elements were not required in previous research but will be developed in future work.

Superelements

Figure 1 shows a typical superelement used to model the corner of a structure where two slabs meet.  The element is defined by five parameters – length, width, depth and the rise and run of the corner taper.  The element is divided into solid 8-node hexahedral and 6-node prism elements.  Static condensation (Weaver and Johnston, 1984) is then used to reduce this detailed, solid model to the six shell nodes shown.  These connect to six-degree-of-freedom nodes on the shell elements used to model the slab.  These operations are fully automated in the Design by Analysis program.  The user may change the refinement of the solid model used to generate the superelement.

Analysis of Reinforced Concrete Slabs using Shell Elements

The preliminary results of a finite element analysis are the deflections and rotations of the nodes in the model.  These are then used to calculate other output quantities.  The design of concrete slabs is based primarily on the shear and moment.  Since these quantities vary throughout the slab, the designer could specify a varying thickness and reinforcement scheme throughout a slab.  However, any economy that may be gained by saving materials would be more than offset by forming and other construction costs.  Therefore, it is assumed that the thickness and reinforcement in a slab is constant and based on the worst case of shear, moment and thrust.

Since the finite element model was initially generated from a description of the slabs forming the structure, the Design by Analysis program can easily identify the shell elements in each slab and determine which governs the performance of the slab.  The maximum shear load is compared to the shear capacity of the slab given its thickness and the maximum positive and negative moments in both directions are compared to the capacity of the slab given the reinforcement on each face in each direction.

Analysis of a Mat Foundation during Backfilling

The Design by Analysis approach provides a powerful tool to make the finite element method available to construction professionals.  An application was developed to analyze the basement walls on a mat foundation during backfilling in order to demonstrate this approach.  The example problem will be a 40 foot by 60 foot building with 12 inch thick walls and #5 bars spaced at 12 inches in the vertical direction and #6 bars at 12 inches in the horizontal direction on each face of the wall.  The walls are 16 feet high and will be backfilled to a height of 10 feet with a well-drained granular fill.  The strength of the concrete is assumed to have reached 4000 psi.  A reinforced concrete floor slab will be placed at the top of the walls, but the constructor would like to determine whether or not the basement could be backfilled before placing the floor.  Figure 2 is a sketch of the structure.

Description of Structure

The input form shown in Fig. 3 prompts the user for the dimensions of the building and the wall thickness.  The user also specifies whether or not the floor slab is in place.  Reinforcement information for each wall is input in the form shown in Fig. 4.  The Cover dimension is expressing in inches and eighths of an inch.  The Hout button indicates that the horizontal reinforcement is on the outside nearest the surface of the wall.  This can be clicked tp change the caption to Vout indicating that the vertical reinforcement is on the outside.  The finite element model shown in Fig. 5 is then generated by selecting an option on the main menu.

Definition of Loads

 Information about the loads on the foundation is input using the form shown in Fig. 6.  The soil loads are modeled as a linearly-increasing pressure on the outside face of the walls.  The user must make decisions to determine the rate at which the pressure increases with depth (Fletcher and Smoots, 1974).  They may use the default, conservative case which models the soil as a fluid with a density equal to that of the soil or seek information to justify more realistic loads.  A help system may be included with the program to assist the user with selecting the correct model.

Results

 The results plot shown in Fig. 7 shows the safety factor in all regions of the model.  The safety factor is the design strength divided by the required strength given the imposed loads.  Safety factors are calculated at each point for both shear and flexural responses and the lowest value is reported.  The user must decide what safety factor is acceptable.  In this case the lowest safety factor is greater than three, which indicates that the proposed backfill operation is safe.

If the safety factor is near to or less than one, the user can repeat the analysis to investigate other options.  Possible courses of action include: 1) consulting a geotechnical engineer to determine whether their value for soil pressure was realistic, 2) determining the required concrete strength to develop an adequate safety factor and estimating if and when the concrete may reach this strength, 3) evaluating the structural response with the floor in place, or 4) modeling other backfill depths to determine whether a partial backfill at this time would be permitted.

Conclusions

Finite-element-based structural analysis methods may be used to aid the decision making process in construction.  Well-developed user interfaces are required so the occasional user can quickly obtain valid results.  A technically competent individual who understands the assumptions used in the analysis must still interpret these results.  The results must be used in the context of their experience and input from other sources involved in the construction.  As with any software used in the design and analysis of structures, the user must be aware that they are still ultimately responsible for the proper evaluation, interpretation and use of the results.

References

Arumala, J. (2002). Student-centered activities to enhance the study of structures. International Proceedings of the 38^th Annual Conference, Associated Schools of Construction, 1-8.

Fletcher, G.A. & Smoots V.A. (1974). Construction guide for soils and foundations. New York: John Wiley & Sons.

Opfer, N.D. & Gambatese J.A. (1999) Temporary construction structures coursework, Proceedings of the 35^th Annual Conference, Associated Schools of Construction, 231-239.

 Slattery, K.T. (2002). Automated design and analysis of marine structures during “in-the-wet” construction. International Proceedings of the 38^th Annual Conference, Associated Schools of Construction, 319-324.

US Army Corps of Engineers. (2003A). Design by analysis of innovative navigation structures, theoretical manual. (Technical Report TBD). Vicksburg, MS.

US Army Corps of Engineers. (2003B). Design by analysis of innovative navigation structures, user manual. (Technical Report TBD). Vicksburg, MS.

Weaver, W., Jr. & Johnston P.R. (1984). Finite elements for structural analysis. Englewood Cliffs, NJ: Prentice-Hall.