## 2 Concept Development  
### General Analysis of the Problem  
Before the development of the test setup, a specimen geometry had to be chosen. The majority of triaxial testing that has been conducted on concrete has used cylindrical specimens. However, applying tensile forces in more than one direction on a cylindrical specimen is extremely challenging without altering the specimen geometry in ways that create stress concentrations. Due to this difficulty and the need to reduce stress concentrations, cube specimens were chosen for this study. Cubes are ideal for triaxial testing since they provide flat faces in three orthogonal directions for load application. The next step was determining the specimen size. [PERSON] and [PERSON] selected 100 mm cubic specimens [12]. However, the use of a non-standard cube size would create issues with the repeatability of testing and with form construction. Therefore, the specimen size was set to 50 mm \(\times\) 50 mm \(\times\) 50 mm due to it being a standard size for compression testing of grouts and mortars. Moreover, since most UHPC mix designs use fibers that are 13 mm long, the 50 mm dimension was still at least three times the size of the largest constituent in the mix, thus meeting typical requirements for fiber-reinforced concrete test specimens. However, using this specimen size limits the fibers to a maximum length of 17 mm per ASTM C1609 [15]. Therefore, an attempt was made during the design of the triaxial test setup to provide the option of testing larger cube specimens. This consideration will create the opportunity for triaxial tension testing of specimens with longer fiber lengths. Lastly, the tensile force transfer method had to be determined. The application of tensile forces to brittle materials is inherently complicated by the required load transfer mechanisms. For example, in uniaxial testing, tension is applied to steel specimens through textured wedge grips that are designed to compress into the specimen as tension is applied [16]. This load transfer method is feasible due to the general malleability and ductility of steel. If this method were attempted with concrete, its brittle nature would not allow the wedge grip teeth to mold the surface without causing the concrete surface to fracture, thus losing grip strength. There have been numerous studies evaluating the best method for applying tensile forces to concrete specimens for uniaxial testing [17; 18; 19; 20; 21]. The most common method among these studies was applying tension through collars on dogbone specimens. The use of collars to apply the tensile forces would require casting projections with angled faces on each side of the cube specimen for the collar to react against. This method would cause complications in the specimen fabrication since it would require specialized formwork to cast the bell shapes on each face. Moreover, the projections from the cube face would inevitably create stress concentrations on the cube specimen, which are best avoided. [PERSON] was successful in transferring tensile forces through aluminum end caps that were directly epoxied to the ends of dogbone specimens [20]. While the specimen shape provided a larger area for epoxying the end caps than the center area, the epoxy used in that study was not the strongest available (tensile strength of 26.9 MPa), and using a stronger epoxy had the potential to mitigate the bond strength issues. The tapered design not only provided a larger area for epoxy; however, the distance between the epoxy surface and the test surface was far enough to avoid issues associated with confinement by the epoxy. While this is beneficial for determining tensile strength, the bevels required for changes in diameter will inherently create areas of stress concentration, which could potentially cause pre-mature failure. [PERSON] and [PERSON] attempted to reduce the effects of confinement by using brush heads for load transfer.