Comparison with Experiment

The Yokel Studies

The testing configuration for the Yokel Studies Yokel 1971, figure 5.1, p. 8]

A Statically Loaded Solid Block Wall

One of the Yokel tests included a panel composed of solid 8-inch concrete blocks with a 25 Kip vertical surcharge. The light load and solid masonry construction are similar to conditions at ancient masonry construction, and were selected for verification.

The figure below shows a deformed finite element model of the test panel. The vertical support at the bottom of the wall is modelled with springs to model the flexibility of the 0.5 in fiberboard. The interface elements at the base of the wall have a low coefficient of friction to account for sliding of the fiberboard. The horizontal loading bars are modelled as displacement boundary conditions. The vertical loading is modelled as concentrated forces on each node at the top of the wall so that the forces maintain the vertical direction even when the top of the wall rotates. The lateral pressure is modelled as a distributed load on the element faces.

The deformed shape at failure predicted by the block-interface model for test 3-3 of Yokel 1971]. The red triangles indicate displacement boundary conditions, and the white spirals at the bottom of the wall indicate spring elements used to model the flexibility of the 0.5 fiberboard underlying the wall assembly. Displacement magnification factor = 10.

A detail of the image from above, showing the pattern of cracking in the analytic model. Note the small cracks forming above and below the primary crack. Displacement magnification factor = 10.

A photograph of a solid block wall at failure. This wall was subjected to a much larger vertical compression load (150 Kips) than that of the model above (25 kips), and so shows signs of compression failure, but the pattern of tension cracking at one bed joint is similar in the analytic model and the experiment. Yokel 1971, p. 19, figure 6.13, test 3-6]

Several variations of the finite element model were explored in comparison with the experimental results. The key variables were the following:

• The number of laminations: The mesh subdivided the wall into a series of vertical layers called laminations. The model shown above includes 6 laminations. The study examined models with 4, 6, and 8 laminations.

• The number of element layers per course: The mesh also subdivides the wall into horizontal layers called courses. A course is bounded by interface elements top and bottom, and corresponds to a row of blocks in the actual wall. Courses may be further subdivided into horizontal groups called element layers, where there are no horizontal interface elements between the solid elements. The study examined models with 1, 3 and 5 element layers per course.

The figure below illustrates the organization of laminations, courses and element layers, using the deformed shape of a model with six laminations, and two element layers per course.

A model using six laminations (the vertical layers) and two element layers per course, where a course is a horizontal group between interface elements. Magnification factor = 50.

The figure below compares the load-displacement characteristics of various models with Yokel's experimental results. The curves reveal the following trends.

• The model with 4 laminations severely overestimates the elastic stiffness and underestimates the displacement capacity.

• The model with 6 laminations and 1 element layer per course is better than the 4-lamination model, but still tends to overestimate elastic stiffness. An 8-lamination model (not shown on the figure) has a load-displacement curve nearly identical to that of the 6-lamination model.

• The model with 6 laminations and 3 element layers per course does a much better job in the elastic range. It is clear that the 1-layer model overestimates the flexural stiffness of the courses. In the inelastic range, however, the 1-layer and 3-layer models take the same path at a displacement of approximate 0.18 inches, indicating that the behavior in this range is dominated by cracking rather than block flexure.

• The model with five element layers per course is close to the curve for the 3-layer model, but its displacement at maximum load is 0.38 in, rather than 0.18 in for the 3-layer model. This is much closer to the experimental result.

• Although the five layer model estimates the displacement capacity much better than the other models, all of the models predict the maximum load capacity within about 5 percent.

Load-displacement curves comparing the experimental and analytic results. The analytic model overestimates the stiffness and underestimates the strength and displacement capacity, although the general pattern is similar. (Experimental curve is derived from data in figure 8.19 p. 44, and table 6.2, p. 10 Yokel 1971]

A Statically Loaded Solid Brick Wall

The deformed shape at failure predicted by the block-interface model for test 6-3 of Yokel [1971]. The white spirals at the bottom of the wall indicate spring elements used to model the flexibility of the 0.5 fiberboard underlying the wall assembly. Displacement magnification factor = 10.

A photograph from Yokel [1976], with the caption: "Typical failure of brick walls with low vertical compressive loads." (fig. 6.14, p. 20)

Two variations of this model were developed, one with 4 laminations and 1 element layer per course, and another with 4 laminations and 2 element layers per course. The figure below compares the published load-displacement curve from the experiment with those of the analytic models.

Load-displacement curves comparing the experimental and analytic results. The analytic model overestimates the stiffness and strength, but underestimates displacement capacity. (Experimental curve derived from figure 8.21, p. 47 and table 6.4. p. 11 [Yokel 1971]

The figure reveals the following points:

• As with the concrete block comparison, the analytic models tend to overestimate stiffness in the elastic range, and underestimate the displacement at maximum strength. Using more element layers per course gives better agreement in the elastic range.
• Unlike the concrete block models, there is a notable difference in strength between analytic models: The 2-layer model is clearly weaker, and much closer to the experimental results, than the one-layer model.