|Typical shear deformation and diagonal cracking in a masonry wall due to in-plane loading.|
It is very common for seismic loading to induce "X" cracking in masonry structures, resulting from in-plane loading in alternate directions, as shown in the photo below:
|An example of diagonal shear cracking due to cyclic in-plane seismic loading. [EERC 1995]|
At Pompeii, there has not been a systematic survey of the walls to document cracking that may be due to in-plane loading, although anecdotal accounts indicate that it is not widespread. There is one instance of diagonal cracking at the southeast corner of the Macellum, shown in the photo below:
|An example of diagonal cracking at Pompeii. (Courtesy of John J. Dobbins)|
There are several explanations for this crack, which will be explored in detail later. Since it is a single crack rather than an "X" crack, it is probably not due to seismic loading, but is more likely the result of foundation settlement, which can also induce shear deformations, or pyroclastic flow, which would induce uni-directional loading rather than cyclic loading. The direction of the crack is consistent with the direction of loading that would be induced by pyroclastic flow; the photo is looking westward, with Vesuvius to the northwest, toward the right.
|A typical out-of-plane failure, where forces perpendicular to the wall have caused it to collapse outward. Note the characteristic scooping shape as the line of failure moves upward near the transverse support at the corner. [EERC 1995]|
For walls carrying heavy gravity loads it is possible for out-of-plane loading to induce compression failure of the masonry material, for this factor to be significant, the compression stress due to gravity needs to be approximately 25 percent of the material failure stress. Assuming a material density of 23.5 kN/m3 (150 lb/f3) and a failure stress of 6,900 kPa (1,000 psi) a free-standing masonry wall would need to be 73 m (240 ft) tall to reach 25 percent of the failure stress. This stress level will be found only in the lower stories of multi-story buildings, or in walls carrying long-span heavy roofs. At Pompeii, most of the buildings are one and two story, and carry relatively light roofs, so the primary concern for out-of-plane failure is stability rather than material failure in compression.
Out-of-plane failure may also result from pyroclastic flow. The image below shows the ruins of St. Pierre after the 1902 eruption, where the characteristic scooping pattern of failure is clearly visible in the walls parallel to the plane of the photograph; these walls were perpendicular to the direction of the flow.
|St. Pierre after the 1902 volcanic eruptions. The photo is looking north; note the characteristic scooping pattern of failure in the east-west walls. [La Croix 1904, pl XIX]|
Evidence of out-of-plane failure and repair is common in the walls of Pompeii. The following discussion examines two areas of the Macellum where there is such evidence: the north wall, and the southeast corner. The plan of Macellum shown below uses symbols to show the viewpoints of photographs used in the discussion.
|A plan of the Macellum, with symbols indicating photograph viewpoints. (Adapted from Dobbins [1994a])|
The images below show an area on the north wall of the Macellum where the different materials of the wall indicate the repair of an out-of-plane failure; the second image highlights the scooping line of failure. Archaeological examination of the materials in this area shows that the repair is ancient, indicating that the damage most likely resulted from the 62 A.D. earthquake [Dobbins 1994, pp. 673-4]
|An example of out-of-plane failure and repair at Pompeii. The yellow line in the lower image indicates the line of failure. Archaeological evidence shows that the repair in this location is ancient, indicating that the failure is most likely due to the earthquake of 62 A.D. (Courtesy of John J. Dobbins)|
The images below show the southeast corner of the Macellum, viewed from the exterior, showing clear evidence of out-of-plane failure. In this case, archaeological investigation of the materials and methods does not conclusively resolve the question of whether the repair is ancient or modern.
|Evidence of out-of-plane failure at the southeast corner of the Macellum It is uncertain whether the repair is ancient or modern. (Courtesy of John J. Dobbins)|
The boundary conditions (e.g. the nature of the supports at the edges of a wall) strongly influence out-of-plane behavior, defining two basic types of structural response: one-way span, where the spanning action works primarily in one direction; and two-way span. The distinction can be seen in the annotated image below. The failure line is characterized by a long horizontal section in the middle, with scooping portions at the ends. The horizontal portion characterizes one-way spanning action, where the vertical span of the wall creates tension stresses on a horizontal plane. The scooping diagonal portion characterizes two-way spanning action, resulting from the support of the horizontal foundation and the vertical intersecting walls.
|An annotated version of the image of earthquake damage shown above. The region of one-way span is characterized by a horizontal line of failure resulting from the stresses induced by the vertical span between the ground and the roof structure. The region of two way span is characterized by a scooping or diagonal line of failure resulting from the supporting action of the foundation and the intersecting wall. [EERC 1995]|
In this photo, in the near portion of two-way span, it is clear that the end wall of the building is providing the structural support; however it is not apparent what is providing this support at the far end. Most likely, there is an internal intersecting wall that is not visible in the photo.
The investigation requires the simulation of out-of-plane behavior, particularly two-way behavior. The following discussion reviews the research literature on this topic to assess available methods.
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