CHAPTER 5
EXCAVATION-INDUCED RESPONSE OF THE FRANCES XAVIER WARDE SCHOOL

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The primary responses of the Warde School to the adjacent excavation were settlement of the shallow spread and continuous wall footings and tilting of the foundation walls. The optical survey data indicated that no lateral movement occurred at the ground level of the building. Consequently, slip must have occurred between the bottom of foundations and the ground. The building settled vertically and its walls tilted, but it did not translate in response to the excavation–induced ground movements. These primary responses produced distortions in the infill walls of the school

5.1 SETTLEMENT RESPONSE

Figure 5-1 presents the settlement data at points along the west side and north side of the Warde School. Settlement points W10 and W8 are located along the west side and are adjacent to the Inclinometer 1 and Inclinometer 2 locations, respectively. Settlement point W13 is located along the north side of the school and is adjacent to the Inclinometer 5. A general overview of the settlement responses to the excavation can be seen from comparing increases in settlement to excavation activities. The figure shows that the building response matched the soil response. Settlement points W8 and W13 showed approximately 8 mm to 9 mm of movement, respectively, in response to installation of the secant pile wall. After the wall installation, the movements were relatively small until the excavation was advanced below the clay crust on Day 73. The excavation along the west side of the Warde School was completed on Day 116, after which time the movement developed more slowly as a result of creep. The movements increased at the settlement locations once the chipping of the east secant pile wall was completed on Day 140. Figure 4-2 also shows that settlement point W13 was clearly affected by the excavation along State Street. The excavation along Chicago Avenue was not advanced into the soft clay layer until Day 170. From the figure, it can be seen that approximately half the total amount of settlement observed at W13 had already occurred at that time. From Day 170 to Day 208, which was the period of excavation along Chicago Avenue, the settlement at point W13 increased from 22 mm to 29 mm. There were no further settlements at settlement point W13 after Day 208.

5.1.1 Settlement Contours

Settlement contours were developed for the Warde School using settlement data from points located on the exterior walls and interior columns of the school. The location of these points can be seen in the inset of the Warde School located in Figure 5-1. In the inset, W is used to denote wall points, C is used for column points and R is used for roof points. Figure 5-2 presents the settlement response of the Warde School at the end of wall installation (5-2a), after the excavation had reached final grade (5-2b), and after backfill was completed (5-2c).

By comparing the contour of zero settlement for each of the construction stages, it is observed that the extent of the settlements behind the support wall developed mainly while installing the 19.3 m deep secant pile wall. Note that the small settlements that occurred in the northeast portion of the school developed as a result of relocating utilities along Chicago Avenue. The extent of movements can be defined in terms of the ratio of distance from wall to depth of wall of approximately 1. Several of the methods currently used to estimate settlement distribution behind excavation support walls (Hsieh and Ou, 1998; Clough and O’Rourke, 1990; and Peck, 1969) normalize the extent of settlement with the depth of excavation. However, Figure 5-2 shows that while the magnitudes of movements increased significantly during excavation and support stage, the extent of the movements did not. Thus, for the case where significant movements develop during wall installation, perhaps a more reasonable approach is to normalize the extent of settlement by wall depth as opposed to the excavation depth. Additional case studies should be evaluated to see how general is this response.

In further evaluating the settlement response of the school, it is helpful to evaluate the settlement response on days corresponding to (i) Day 73 – first observation of interior cracking; (ii) Day 131 – representing conditions when the State Street excavation was to final grade, and (iii) Day 365 – a time when all movements had stopped.
Figures 5-3, 5-4, and 5-5 presents 2D and 3D settlement contours on Day 73, Day 131, and Day 365, respectively. These figures show that the general patterns of the settlement contours were established as of Day 73 and remained similar throughout the project. The 3D portions of the figures show the settlement response at the foundation level of the building.

From Figure 5-3, it is seen that the settlement contours were slightly asymmetrical. This is due to the location of the excavation with respect to the Warde School. The approximate wall location given on the figure shows that the southern limits of the excavation along State Street only extended to the midway point of the south portion of the school. Also, the contour patterns observed on Day 73 were solely in response to excavation along State Street because no significant excavation had began on Chicago Avenue at this time. As a result of the location of the excavation and the governing excavation activities, the contours formed a bowl shaped pattern that was centered north of the building’s center. The bowl tilts fairly uniformly towards the west and is approximately symmetrical between columns C2 and C6 (see inset of Figure 5-1). The back end of the bowl was located approximately 10 m to 15 m from the western face of the school. This distance corresponds to the location of the north-south hallway of the school. The inset of Figure 5-1 shows that the east wall of the north-south hallway consists of columns C2, C4, C6, and C8, and the west wall consists of columns C1, C3, C5, and C7. The west wall of the hallway was located at about the 4 mm contour in Figure 5-3. Overall the north side of the school showed a uniform taper on Day 73, progressing from about 1 mm on the east end of the school to about 6 mm on the west end. During this same period, the settlement at the central portion of the school’s west face was approximately equal to 10 mm. The north and south segments of the west wall both sloped toward the middle, whereas the entire wall tilted slightly to the north.

Figure 5-4 gives the settlement contours at the end of excavation along State Street on Day 131. The figure shows that the bowl shaped pattern became asymmetrical in response to increased settlement towards the north end of the school. The center of the settlement trough moved further north and the school began showing a pronounced tilt toward the northwest. It is observed that although the general shape of the contours was no longer symmetrical, the eastern extent of the trough area remained relatively similar to what was observed for Day 73. The contours gradually slope toward the west up to the north-south hallway location and afterwards become dramatically steeper. On Figure 5-4, the west wall of the north-south hallway was located at the 10 mm contour.

The excavation along Chicago Avenue was advanced below the first level bracing (elevation +2.1 m CCD) on Day 131. Figure 5-4 shows that a distinct break point in the slope along the north wall formed approximately 21 m from the west wall of the school. This break point appears to correspond to the zone of influence of the excavation activities along Chicago Avenue, which extended approximately 11 m north of the secant pile wall.

The lowest point on the contours on Day 131 was located at settlement point W10 (see Figure 5-1 inset). Although this was the location of the pit for Escalator #4, excavation activities for the escalator did not start until Day 162. The north and south segments along the west side of the school both showed increased total settlement on Day 131, but the differential settlement along the north segment was roughly 4 mm as compared to approximately 8 mm of differential settlement along the south segment.

Figure 5-5 shows that the 3-D effects became more pronounced as the excavation along Chicago Avenue was further advanced and completed. Settlement of the north wall of the school increased, and the northwest corner of the school settled approximately three times more than the southwest corner, thus producing greater overall building tilt towards the northwest. Again the distinction between the settlement contours gradually sloping towards the west and the point whereupon the contours steeply slope towards the west is the north-south hallway. In the figure, the west wall of the north-south hallway was located at the 14 mm contour.

All movement had stopped as of Day 365. Thus, Figure 5-5 shows the final settlement contours. The settlement trough had deepened, but did not widen in extent. An inflection point was observed along the south segment of the west wall. This inflection point approximately coincides with the southern extent of the excavation activities.

The settlement profile in Figure 5-5 suggests that the southeast corner of the excavation had the effect of reducing the total settlement by an amount proportionate to the distance from the corner. Several researchers (Lee et al., 1998; Ou and Shiau, 1998; and Ou et al., 1996) have investigated corner effects on the behavior of diaphragm walls. However, their work primarily pertained to corner effects on the lateral movements of the walls. No work was found in the literature pertaining to corner effects on the settlement response of building adjacent to support walls. Although settlement can be implied from lateral movements for no-volume-change conditions, there are several complicating factors, which preclude applying the lateral deformation results directly to building responses at corners of excavations. These factors include building type and configuration, and building orientation with respect to the excavation, depth of excavation, and extent of excavation. Additional research that considers these factors is required.

5.1.2 Zones of Sagging and Hogging

The contours presented in Figures 5-3, 5-4 and 5-5 show that the school experienced both hogging and sagging modes of deformation. These terms are defined in Figure 5-6. Sagging implies that the settlement profile is concave upward, whereas hogging indicates that the settlement profile is concave downward. The figure shows the building response idealized as an elastic deep beam in bending. The sagging mode produces tension along the bottom fiber and compression along the top fiber. The hogging mode produces tension along the top fiber and compression along the bottom. However, actual buildings differ from beam theory in that the surrounding soil at the foundation level provides lateral restraint in the sagging mode. This restraint can be idealized by assuming the neutral axis is at the bottom fiber, effectively limiting tension in the beam to direct tensile strains with no bending-induced tension. The hogging mode of deformation is not the reciprocal of the sagging mode. There is no external lateral restraint at the roof level for most buildings. Consequently, the neutral axis remains at the centroid of the building/beam model in the hogging deformation.

The upper half of the beam is in tension and the tensile strain resulting from bending increases with distance from the neutral axis. The definitions of the deflection ratio (sagging) and the deflection ratio (hogging) are included in Figure 5-6. These ratios are simply the deflection ratios in the sag and hog zones, respectively. The deflection ratio (sagging) is a measure of curvature of a member whose deformed shape is concaved up. The deflection ratio (hogging) is a measure of curvature of a member whose deformed shape is concaved down.

Figure 5-7 shows areas of the building where hogging and sagging occurred. These areas were defined based on the settlement profiles shown in Figure 5-3 and Figure 5-5. Figure 5-7a shows the sagging and hogging zones on Day 73 when damage was first observed in the Warde School. Figure 5-7b show the hogging and sagging zones on Day 116, which was when excavation was completed on the east side of State Street. Figure 5-7c gives these zones based on the post construction survey on Day 365. The figures show that the sagging mode of deformation developed within the central portion of the west side of the school. Hogging occurred elsewhere. The north-south extent of the sagging zone remained relatively constant between Day 73 and Day 365. After the excavation had bottomed out on Day 116, movements continued toward the excavation as a result of reducing the bending stiffness of the wall and creep of the soft clay. During this time, the east-west length of the sagging zone gradually increased until the maximum east-west extent of the sagging zone was approximately equal to the depth of the secant pile wall.

To illustrate further the deformation patterns throughout the building, several settlement profiles are plotted in Figure 5-8 and Figure 5-9. Figure 5-8 shows east-west settlement profiles taken along the north wall in an area of hogging (5-8a) and through the Inclinometer 1 location in the region of sagging (5-8b). Sagging was limited to an average distance of about 12 m from the west edge of the building, the location of the west wall of the north-south hallway. The deflection ratios were computed from the profiles taken through the interior of the building, in the east-west direction (5-8b). The sag zone included settlement points W11, W10, and C1. The hog zone started at point C1 and included points C2 and W19. Table 5-1 shows the deflection ratios for each of the construction days given in Figure 5-8b. The deflection ratios (hogging) were negligible until some time near Day 108 and did not approach the initial deflection ratio (sagging) value until after the escalator base slab was poured.

Figure 5-9 shows north-south settlement profiles taken along the west wall of the building (5-9a) and along the west most interior column line (5-9b). The figure also shows that the interior of the building experience a sagging mode of deformation, while the ends experienced hogging. Hogging was particularly pronounced along the north wall where the effects of the excavation along Chicago Avenue had the most impact on the school. The school transitioned from the sagging zone to the hogging zone near settlement point C1. This point is the northern end of the interior column lines.

Table 5-2 presents the deflection ratios computed from the data given in Figure 5-9b. The sag zone included settlement points C3, C5, C6, and W6. The hog zone included settlement points W13, C1, and C3. From the table and from Figure 5-9b it is seen that the interior hog along

Table 5-1. Maximum Deflection Ratios: East-West Direction

the north-south plane was negligible throughout the project. Also, the interior north-south sag was about half that of the interior east-west sag. Figure 5-9b shows that the overall tilt of the building progressively increased towards the north. Hogging was the primary deformational mode along the north side of the Warde School. Yet, the deflection ratio (hog) values along the north side were an order of magnitude less than the deflection ratio (sag) values along the west side. It can therefore be concluded that the sagging zone was the most critical deformational mode for the Warde School.

Table 5-2. Maximum Deflection Ratios: North-South Direction

5.2 DISTORTIONS

Distortion is defined herein as the differential deformation between two points, δ, divided by the distance item, . This definition of distortion is the measure of the shearing strain of a member. Angular distortion, β, can be obtained from the distortion by subtracting the rigid body tilt, , from the measured settlement. Thus, angular distortion is a measure of the rotation of a member at the support relative to the rigid body tilt. It is noted that the rigid body tilt of the Warde School was 1/15,000 when final grade was reached on Day 116. At the end of the project, the rigid body tilt was 1/3900. Given these small values, there is no significant difference between distortion and angular distortion for this building. This is to be expected for a building that is large enough such that only parts of it are affected by movements induced by excavation-related activities. Therefore, for practical purposes the distortions and angular distortions were the same for this project.

5.2.1 Computing Distortions from Settlement and Inclinometer Data

The distortion data presented herein was computed from settlement and lateral deformation data. Figure 5-10 presents the procedure used to compute distortions. The distortions based on settlements were computed between distances 4.5 m and 12 m from the center of the secant pile wall (marked by L₂ in the figure). Distortions based on inclinometer data were computed at the same relative location after the inclinometer data was rotated according to the procedure described in Section 4.3.4.3. Figure 4-24 in Chapter 4 showed that there was good agreement between the settlement and the inclinometer data, at least at the Inclinometer 1 location. This suggests that inclinometer data can be used to evaluate the distortions induced in adjacent structures when the excavation is made through saturated clays. The implicit assumption is that there is no volume change induced in the soil. This condition occurs in many excavations through soft clay. Agreement between distortions computed with inclinometers data and distortions computed with settlement data cannot be expected if volume changes occur in the soil beneath the structure. For example, if the Warde School was founded on footings a meter or two below ground surface, and hence on several meters of granular fill, the volume changes within the fill would alter the distribution of settlements from what would be indicated from the inclinometer data. Similar disparities would be observed if significant consolidation settlements occurred.

Hence, when excavating through soft clay, inclinometer data can be used to estimate distortions under an adjacent building, at least when the movements are small, as would be the case when a stiff system is used to support a well-constructed excavation. Large movements would result in localized strains within the soft clay and agreement between lateral movements measured at the wall and ground surface settlement points would be poor (Finno et al, 1989).

The agreement between the inclinometer and settlement data, when the movements are small, is particularly useful in assessing potential damage to structures that an abundance of settlement data are rarely available for projects because of the cost and, in many instances, the adversarial relation between the building owner and constructor. In many projects, inclinometer data are available and can be used to estimate distortions when no volume changes occur within the soil adjacent to the wall.

5.2.2 Development of Distortions During Construction

Distortion versus time was plotted along the west side and north side of the Warde School to illustrate the agreement between distortions computed with inclinometer data and settlement data and to evaluate the distortion response of the building at specific locations. Figure 5-11 plots distortion with respect to time along the west side of the school, in the plane perpendicular to the excavation face. Also shown is a summary of construction at that location. The settlement-derived distortions were computed from the differential settlement between two settlement points (W10 and C1, W9 and C3, and W8 and C5) divided by the distance between the two points. The distortions from Inclinometer 1 and Inclinometer 2 were computed as the difference in lateral deformation between depths of 9 m and 17 m, divided by a length of 8 m. Note that all distortions presented in this figure are located in the sagging zone (Figure 5-7).

The figure shows that the distortions computed from the Inclinometer 1 data matched those computed from settlement points W10 to C1 very well. However, the Inclinometer 2 distortions also matched the W10 to C1 distortions. It was expected that the Inclinometer 2 distortions would more closely agree with the distortions of the adjacent settlement points, W8 to C5. These distortions most likely did not agree because of the geometry of the excavation relative to the location of the building. The corner of the excavation has the effect of reducing the building settlement. This can be seen in the 3D contours of Figures 5-3, 5-4, and 5-5. In each of these figures, the settlement on the south end of the site is much less than the settlement on the north end. Consequently, settlement points W8 and C5 experienced less settlement than settlement points W10 and C1. This resulted in the W8 to C5 distortion being less than the W10 to C1 distortion. The data suggest that the distortions of the Warde School are a function of building size and orientation with respect to the excavation.

The effect of the corner on the distortions of the school is further demonstrated in Figure 5-11 by comparing the distortions computed from the survey data. The magnitudes of the distortions are shown to be functions of the distance from the southeast corner of the excavation. The largest distortions were at the W10 to C1 location, which was about 23.8 m from the corner of the excavation. The distortions were smaller at the W9 to C3 location, which was approximately 15.2 m from the corner of the excavation and smaller still at the W8 to C5 location, which was approximately 7 m from the corner.

Figure 5-11 shows that the distortions were as much as approximately 0.001 (1/1000) in response to installing the secant pile wall. The distortion essentially remained constant until the excavation was advanced through the stiff clay crust to a depth of about 5.5 m. The first interior crack was observed on Day 73 when the distortion based on Inclinometer 1 data was 0.0011 (1/920). Thereafter, the distortion increased as the excavation was lowered until final excavated grade was reached between Day 108 and Day 116. The figure shows that installing the struts and tiebacks had little effect on the distortion rate. The first crack in the marble façade in the entranceway foyer was observed on Day 108. The distortion at the W9 to C3 location was 0.0018 (1/555) on Day 108. This is roughly the location of the marble entrance foyer. After completion of the excavation on Day 116, the distortion continued to increase, but at a slower rate than during excavation. These continuing distortions were caused by the reduction of the wall stiffness and by creep of the clay during the subway station renovation and backfill activities. By Day 177, the distortions became approximately constant. The maximum distortion value computed from the inclinometer data was approximately 0.0033 (1/300). The maximum value calculated from the settlement data (W10 to C1 location) was slightly less at 0.00317 (1/315).

Figure 5-12 presents the distortion versus time data for the north and south segments of the exterior west wall of the school. These distortions are in the north-south direction along the west elevation. Distortion was computed for the north segment using settlement points W12 and W11, and distortion in the south segment were computed using settlement points W7 and W8. These distortions represent the hogging zones on the west side of the school.

Distortions at the north and south segment locations were impacted greatly by the end effects of the excavation. The southern limit of the excavation was approximately at the settlement point W7 location, but the excavation extended north and east past the northwest corner point, W12 (see inset of Figure 5-12). As a result of the excavation end effects, the total excavation-induced settlements were greater at the north segment than at the south segment, but the differential settlements were greater at the south segment than at the north segment. This is also seen in the 2-D contours of Figures 5-3, 5-4, and 5-5. The excavation end effects ultimately resulted in the excavation-induced distortions between settlement points W7 and W8 being larger than those between settlement points W12 and W11.

The distortion for the north segment was approximately 0.00026 (1/3900) and approximately 0.00034 (1/2900) in the south segment in response to installing the east secant pile wall. It is observed that the north segment showed some variability in the initial data. This variability was due to utility relocation activities at the northwest corner of the school, which had only a temporary effect on the distortional response. The distortions for the north and south segments remained fairly constant and at similar levels until Day 70 because the excavation had not proceeded below the soft clay layer. During this period the excavation end effects had no impact on the distortions. However, as the excavation was advanced into the soft clay between Day 70 and Day 73, excavation end effects have a significant impart on the distortions. The distortions for the south segment increased to 0.00054 (1/1850) whereas the distortion for the north segment began to decrease. The first cracks in the south segment of the exterior west wall were observed on Day 127, at which time the distortion in the south segment reached 0.00108 (1/925). Cracks in the north segment were first observed on Day 129 and the distortion reached 0.00062 (1/1625). It is noticed that although the cracks occurred at about the same time in the north and south segments, cracking was observed in the north segment at a distortion almost half of that observed in the south segment. The north segment may have cracked at lower distortions than observed for the south segment because of the presence of direct tensile strains caused by the northward components of movements of the school in response to excavation activities along Chicago Avenue. These direct tensile strains are additive to the shear-induced strains created by the distortion of the foundation.

The distortions in the northwest corner of the Warde School are presented in the north-south direction in Figure 5-13 and in the east west-direction in Figure 5-14. Distortion in the north-south direction was computed from the north-south Inclinometer 5 data and from the differential settlement data between settlement points W13 and C1. The east-west distortions were computed from the east-west Inclinometer 5 data and the differential settlement data from settlement points W14 and W13, and W13 and W12. The Inclinometer 5 distortions were computed as the difference in lateral deformation between depths of 8 m and 16 m, divided by a length of 8 m.

Figure 5-13 shows that the initial Inclinometer 5 north-south distortions were almost exclusively in response to the installation of the secant pile wall along Chicago Avenue from Day 70 to Day 79. The distortions show a sharp increase during the installation of the wall and then began to flatten after the wall was completed. The Inclinometer 5 north-south distortions were approximately 0.0008 (1/1290) on Day 79. The distortions gradually increased, in response to the excavation along State Street, until the excavation along Chicago Avenue was advanced into the soft clay layer (Day 170). Afterwards, the distortions were primarily a result of the excavation activities along Chicago Avenue. The distortions computed from point W13 to C1 follow the same basic trend. The maximum distortion computed from the Inclinometer 5 north-south data was 0.0016 (1/625) and the maximum distortion attained at the W13 to C1 location was 0.00143 (1/700). These distortion levels were observed during the period corresponding to completion of the station renovations and beginning the backfill activities along the west side. No further north-south distortions were observed after backfill began along State Street (Day 225), which further demonstrated the influence of the excavation activities on these distortions.

Figure 5-14 shows that between Day 70 and Day 79 the east-west distortions of Inclinometer 5 developed in response to the installation of the secant pile wall along Chicago Avenue. Recall that Inclinometer 5 was located quite close to the secant pile wall and its movements were affected by this relative position. It is likely that the east-west movements at this time did not represent building movements. After Day 116, the inclinometer distortions began to increase primarily in response to the open excavation along State Street. The increase in the inclinometer distortion is attributed to the State Street excavation because between Day 116 and Day 170 the excavation along Chicago Avenue had not been advanced beneath the clay crust. Further evidence that these distortions were mainly caused by the State Street excavation activities is provided by the fact that increases in the inclinometer distortions stopped once backfilling began along State Street on Day 225.

Distortions computed from points W12, W13, and W14 follow similar trends, except that they were not influenced as much by installing the secant pile wall. Distortions at W14 to W13 did not increase until approximately Day 73 whereas W12 to W13 distortions did not increase until after Day 86. These rapid increases occurred after installation of the secant pile wall and more accurately reflect the response of the building to the construction activities than the east-west data from Inclinometer 5. From Figure 5-14, it is seen that the settlement-derived distortions increased from approximately 0.00021 (1/4700) to as much as 0.00085 (1/1175) as the State Street excavation was advanced from the from the top of the soft clay layer to the final grade. The W12 to W13 distortions essentially paralleled the inclinometer distortions after excavation was completed along State Street (Day 116), but were approximately 90 percent its magnitude. In any case, the data shown in Figures 5-11 through 5-14 show that inclinometer data can be used to reliably compute distortion in buildings, when excavation are made through saturated clay.

5.2.3 Comparison of Deflection Ratios and Distortions

Table 5-3 presents a comparison of deflection ratios and distortions computed in the east-west direction. The deflection ratios used for the table are those given in Table 5-1. Note that the first set of distortions given in the table is not the maximum distortions for the sagging and hogging zone reported in the previous section. The distortions in the sagging zone were computed from settlement points C1 and W11, and the distortions in the hogging zone were computed from settlement points C1 and W19.

Boscardin and Cording (1989) found that angular distortions were typically 2 to 3 times the deflection ratios. The data given for the sag zone indicates this ratio varies between 2 and 4, while the data in the hog zone shows that the angular distortions were approximately 3 to 7 times the deflection ratios.

Tablalong the west side. No further north-south distortions were observed after backfill began along State Street (Day 225), which further demonstrated the influence of the excavation activities on these distortions. Figure 5-14 shows that between Day 70 and Day 79 the east-west distortions of Inclinometer 5 developed in response to the installation of the secant pile wall along Chicago Avenue. Recall that Inclinometer 5 was located quite close to the secant pile wall and its movements were affected by this relative position. It is likely that the east-west movements at this time did not represent building movements. After Day 116, the inclinometer distortions began to increase primarily in response to the open excavation along State Street. The increase in the inclinometer distortion is attributed to the State Street excavation because between Day 116 and Day 170 the excavation along Chicago Avenue had not been advanced beneath the clay crust. Further evidence that these distortions were mainly caused by the State Street excavation activities is provided by the fact that increases in the inclinometer distortions stopped once backfilling began along State Street on Day 225. Distortions computed from points W12, W13, and W14 follow similar trends, except that they were not influenced as much by installing the secant pile wall. Distortions at W14 to W13 did not increase until approximately Day 73 whereas W12 to W13 distortions did not increase until after Day 86. These rapid increases occurred after installation of the secant pile wall and more accurately reflect the response of the building to the construction activities than the east-west data from Inclinometer 5. From Figure 5-14, it is seen that the settlement-derived distortions increased from approximately 0.00021 (1/4700) to as much as 0.00085 (1/1175) as the State Street excavation was advanced from the from the top of the soft clay layer to the final grade. The W12 to W13 distortions essentially paralleled the inclinometer distortions after excavation was completed along State Street (Day 116), but were approximately 90 percent its magnitude. In any case, the data shown in Figures 5-11 through 5-14 show that inclinometer data can be used to reliably compute distortion in buildings, when excavation are made through saturated clay. 5.2.3 Comparison of Deflection Ratios and Distortions Table 5-3 presents a comparison of deflection ratios and distortions computed in the east-west direction. The deflection ratios used for the table are those given in Table 5-1. Note that the first set of distortions given in the table is not the maximum distortions for the sagging and hogging zone reported in the previous section. The distortions in the sagging zone were computed from settlement points C1 and W11, and the distortions in the hogging zone were computed from settlement points C1 and W19. Boscardin and Cording (1989) found that angular distortions were typically 2 to 3 times the deflection ratios. The data given for the sag zone indicates this ratio varies between 2 and 4, while the data in the hog zone shows that the angular distortions were approximately 3 to 7 times the deflection ratios.

Table 5-3. Comparison of Deflection Ratio and Distortions

5.2.4 Distribution of Distortions

Figure 5-15 presents distortion contour maps developed from all the building foundation settlement data. The contours are given for Day 73 (the onset of damage), Day 116 (end of excavation along State Street), and Day 365 (the post-construction damage survey). These contour data will not necessarily be the same as the contour data given in Section 5.1.1 because these data include interpolations of settlement data in areas were no settlement was measured. The actual measured settlement and the interpolated settlement are used to produce discrete points of distortions. The distortions between these discrete points are also interpolated to produce the contour lines. In the previous sections, the distortion data were produced from the two nearest settlement points in the area of question.

It is apparent from the figure that the highest levels of distortion corresponded to the region of the school that experienced a sagging mode of deformation. The boundary between the hogging and sagging regions has been superimposed onto the distortion maps. The area of higher distortion is parallel to the north-south hallway and is located between the west wall of the hallway and the west wall of the school. In general, the distortions at the onset of damage (5-15a) were higher on the south side of the school than were on the north side because the excavated depth was greater at the south end of the excavation at this time. The general pattern of distortions at the end of excavation along State Street (5-15b) was similar to that observed for Day 73. However, the maximum distortions moved further north, between survey points W10 and W9 (see inset of Figure 5-12) and the distortions on the north side of the school were larger than those on the south side. The redistribution in the distortions reflected the progress of the excavation, and the area of peak distortion corresponded to the area of maximum settlement. The peak distortion at this time was about 0.0019. The distortion contours on Day 365 had a similar pattern as the contours for Days 73 and 116. Similar to the Day 116 contours, the peak distortion moved further north. The peak distortion was located adjacent to survey point W10 and was approximately 0.0031. Distortions along the north wall of the school partially reflect the excavation along Chicago Avenue.

5.3 TILT OF FOUNDATION WALLS

Tiltmeters were installed along the perimeter basement walls of the Warde School to measure inclination of the foundation wall directly. The responses of the tiltmeters to the excavation and construction activities are given in Figure 5-16. The tiltmeters were mounted on base plates that were attached to the wall, and measured tilt in the directions noted in the building inset of Figure 5-16. The devices were typically placed about 1.5 m above the basement floor.

Along the west wall of the school, T7 and T8 indicated that the central portion of the wall tilted to the east in response to the settlement pattern shown by points W11 and W10 in Figure 5-8b. This pattern is consistent with the sagging deformation mode in the central portion of the school. The tilt at the south end of the west wall indicated by T9 was negligible, because the excavation along State Street did not extend that far south.

Along the north wall, T3 indicated that the wall rotated to the north in response to the settlement pattern shown by W13 and C1 in Figure 5-9b. This pattern is consistent with the hogging deformation mode in the north portion of the school. Tilt at the east end of the north wall indicated by T1 was negligible, because it was far from the excavation along Chicago Avenue. The small tilts recorded between Days 60 and 90 at this location were related to utility relocation. The simultaneous excavations along State Street and Chicago Avenue affected the patterns of wall rotations in the northwest corner of the school. The north-south components of tilt recorded in T3 and T6 clearly show that tensile strains were induced in the structure at the northwest corner. These direct tensile strains contributed to the cracking on the north segment of the west wall, as suggested in Section 5.2.2. Tiltmeter T3 shows the north wall of the school rotating towards the north, but Tiltmeter T6 shows the north segment of the west wall rotating towards the south. The east-west tilt recorded by T4 and T5 reflect the hogging deformations illustrated in Figure 5-8a near points W12 and W13. In general, the tiltmeter data agreed with the trends in the settlement data.

5.4 EXCAVATION-RELATED DAMAGE

Excavation-related damage within the Warde School was primarily in the form of cracking of interior infill walls and exterior masonry walls. A summary of the significant construction activity along State Street and building damage is presented in Table 5-4. The construction activity in the table is given for the area adjacent to the Inclinometer 1 location. As indicated in the table, no damage was observed in the Warde School during the secant pile wall installation activities. Damage was first observed on Day 73 when the cross-lot struts were in place and the excavation had extended into the soft clay layer at 5.5 m below ground surface. Cracking was first observed in rooms along the west side of the school on all three floors. The initial damage mostly consisted of diagonal hairline cracks about 300 to 500 mm long in non-loading bearing walls. It was observed that the occurrences of cracking were greater on the second and third levels than on the first level.

Table 5-4. Summary of Construction Activity and Building Damage

The maximum lateral deformation on Day 73 was 12 mm. As the excavation was lowered to a depth of 12 m on Day 108 and the maximum lateral movement increased to 22 mm, cracks developed in the marble façade in the entranceway foyer on State Street. Also, hairline cracks were observed cracks in the basement, along the west end of the north foundation wall. The general excavation along the west side of the school was completed on Day 116. At this time, previously observed cracks widen and extended on all levels. During station renovation and backfill, only a few instances of new damage were observed; existing cracks generally became larger during this time. Step cracks were observed in the mortar of the south and north segments of the exterior west wall on Days 127 and 129, respectively.

5.4.1 Damage on the First Floor Level

Figure 5-17 presents a plan view of the first level and identifies the areas where damage was observed. The figure shows the locations of cracks at Day 73 and Day 365. These days reflect the onset of cracking and the post-construction damage survey dates, respectively. The damage location plan in the figure shows that the majority of the damage on the first floor developed in east-west trending walls. The first observation of cracking damage on the first level developed in the south wall of the assistant principal’s secretary’s office (5-17a). The largest crack in this wall was a diagonal crack radiating upwards and towards the west at a 45-degree angle. Also, a horizontal crack was located near the bottom of the wall. On Day 73, the diagonal crack was approximately 610 mm long and had a maximum width of about 2 mm to 3 mm. The horizontal crack was about 405 mm long and had a maximum width of 1 mm to 2 mm. By Day 365, the widths of these diagonal and horizontal cracks had increased to about 6 mm and 4 mm, respectively. A vertical crack developed in Room 103 (5-17b) during the excavation activities. The vertical crack was approximately 610 mm long and emanated from the top corner of the connection between the beam and the column.

Figure 5-18 presents additional first floor damage that occurred to the marble façade on both the north and south walls of the entranceway foyer. The cracks in the north wall (5-18a) were typically diagonal cracks at the corners of the marble panels and at the corners of fixtures inset into the wall. Most of these cracks were inclined at about 45 degrees and radiated upwards towards the west. This pattern of cracking indicates that the north wall cracks were caused by shear distortions. The damage along the south wall (5-18b) consisted of long horizontal cracks that tended to follow the preferential pathways created by grain variations in the marble panels. The horizontal cracks all emanated from the ends of the panels and radiated inwards. The south wall cracks were most likely the result of out-of-plane bending, or possibly out-of-plane shear, because the upper ends of the cracked panels were not flush with lower ends. The initial cracks in the foyer were detected in the north and south walls on Days 108 and 109, respectively. Cracks in the north wall tended to develop in the upper half of the wall, while cracks in the south wall tended to develop in the lower half of the wall. The marble panels for both walls became misaligned in response to the excavation-related movements. A crack, 3 mm wide and 102 mm long, developed on Day 207 in the marble base near the floor along the south end of the foyer, well after the excavation along State Street had been completed (Day 116) and the Escalator #4 pit slab had been poured (Day 177).

Figure 5-19 presents an overlay of the distortion contours, the hogging and sagging regions, and the crack locations for the first level. The evaluations are given for Day 73 (5-19a) and Day 365 (5-19b). It is apparent from the figure that cracking occurred in areas of highest distortion, with most of the cracking occurring in the sagging zone. The distortion for the south wall of the secretary’s office on Day 73 was 0.00090 (1/1100). No damage was observed in the north partition and infill walls of the Assistant Principals office. Figure 5-19b shows that the distortions were slightly less at the south foyer wall than they were at the north wall, and would help explain why cracks were observed in the north wall of the entranceway foyer before the south wall.

5.4.2 Damage on the Second Floor Level

The damage location plan and characteristic cracks for the second floor level are presented in Figure 5-20. The figure shows that more damage was noted on the second level than on the first level. Furthermore, the damage first observed on Day 73 occurred almost exclusively between the west wall of the school and the west wall of the north-south hallway.

The initial damage on the second level typically consisted of horizontal cracks emanating from doorways within the upper portions of the walls. The damage that developed on the second level later in the project were vertical and diagonal cracks. In the three northern classrooms on the second floor (Room 210, Room 208, and Room 207), the damage consisted of horizontal cracks in the south walls near the doors (see Figure 5-20a), vertical cracks in the north walls, and diagonal cracks in the east walls. In the rooms on either side of the library (Room 206 and Room 202), the cracks consisted of vertical cracks in the corners of the east walls, horizontal cracks at the beam-wall interface along the tops of the north walls and vertical cracks also along the tops of the north walls. Some vertical cracks were observed emanating from the corners of doors on the second level. These cracks were at locations where doorframes had racked. In some instances, the racking of the doorframes was bad enough to require replaning of the doors. The partition wall in the library apparently shifted to the east, which caused the floor tiles near the door to bubble up. These tiles had to be removed and resized. Also, several horizontal cracks were observed in the north walls of the east-west hallway.

Figure 5-21 presents an overall evaluation of the damage on the second floor level of the school. Figure 5-21a shows that the damage first observed on Day 73 occurred primarily within the central interior of the school where sagging had developed in response to the excavation along State Street. Initial damage observed in the hogging zones occurred at lower distortion levels than were observed in the sagging zones. Two of the incidents of cracking outside the sagging zone occurred near the boundary of the sag and hog region. The damage in the northeast corner of Room 208 (see Figure 5-20 damage plan) was a vertical hairline crack in the plaster coating of the column. The first observed damage in the east-west trending walls in the library developed in a partition wall, which spanned an area of high distortion. From the contour on Day 73, the distortion at the foundation level below the partition wall was about 0.0009 (1/1100). Cracking developed in the far north infill wall of the library within a few days after Day 73. The distortion contours in Figure 5-21b show the region of highest distortions remained located between the west wall of the north-south hallway and the west wall of the school. Consequently, most of the damage observed in the central portion of the school developed within this area. Less damage developed east of the north-south hallway in the central portion of the school. Figure 5-21b shows that damage developed in the south wall of Room 208 and along the north wall of the east-west hallway in the corresponding location in the form of horizontal cracks in the upper portions of the walls.

5.4.3 Damage on the Third Floor Level

The damage location plan and characteristic cracks for the third floor level are presented in Figure 5-22. The figure shows that the damage was as extensive on the third level as that observed on the second level. Also, similar to the second floor level, the damage first observed on Day 73 occurred primarily within the central interior of the school. Comparing Figures 5-20 and 5-22 it is seen that the distribution of damage on the second and third levels were similar. However, the incidents of first observed damage On Day 73 were less on the third level than on the second level.

The damage observed on the third level were primarily diagonal cracks (Figure 5-22). The third level cracks also tended to be wider and longer than the cracks observed on the first and second levels. On Day 78, five days after the first interior cracks were observed, typical crack widths on the third level were approximately 0.75 mm. The crack shown in Figure 5-22 was 2-mm wide on Day 78. These widths are compared to a typical width of 0.2 mm on the first and second levels during this same time. Throughout subsequent construction, most cracks on the third level lengthened, but widened only slightly. Cracking damage in the east-west trending walls were characterized by large diagonal cracks that often occurred in the middle of the walls and radiated upwards at 45 degrees towards the west. Diagonal cracks that were smaller in width were also observed emanating from the corners of electrical outlets and in-wall cabinets in the east-west trending walls. Corner diagonal cracks were observed in the south walls of rooms north of the north-south hallway and in the north walls of the rooms south of the north-south hallway. Vertical corners cracks also developed at the interface between the south load bearing wall and the infill wall. Vertical cracks on the third level were typically located in the north-south trending walls on the eastern end of the school (the portion from the north-south hallway to the eastern face). In particular, vertical cracks developed at the top of the westwall in Room 301 and at the top of the east wall of the north-south hallway, between the Boardroom and Room 301.

Figure 5-23 summarizes the damage to the third level of the school. All damage first observed on Day 73 on the third level occurred within sagging zone. More damage occurred at the southeast end of the school at the third level than was observed on the first and second levels. This is especially the case along the east wall of the north-south hallway. Because this area was in the hogging zone, bending stresses induced in the structure from the hogging mode were higher in the upper levels.

5.4.4 Damage to Exterior Walls

The damage location plan and the typical cracks observed along the exterior of the Warde School are given in Figure 5-24. The hogging deformation mode predominated the north and south segments of the exterior west wall and the north exterior wall. The crack along the north wall of the school (5-24a) was vertical crack located approximately 2.7 m above ground and approximately 600 mm from the west end of the wall. The crack went through both mortar and stone. The cracks on the north (5-24b) and south segments of the west wall were diagonal shear step cracks through the mortar. The step cracks were inclined at about 45 degrees and radiated towards the center of the building.

5.4.5 Damage Summary

The damage observed in the Warde School can be characterized as "negligible" to "slight" according to the damage severity classification presented by Burland et al. (1977). Their classifications are as follows:

• "Negligible" damage as hairline cracks with widths less than 0.1 mm,
  
  
• "Very slight" damage as fine cracks easily treated during normal redecoration and cracks in exterior brickwork visible on close inspection with widths less than 1 mm, and
  
  
• "Slight" damage as cracks that can easily be filled with redecoration probably required, exterior cracks visible with some repointing possibly required for water tightness and a maximum crack with less than 5 mm. Also, doors and windows may stick.

The severity of damage was within estimates made during design of the excavation support system.

Most of the damage occurred along the west side of the school in the area where distortions were largest, and when the maximum distortions increased from 1/1000 at the end of wall installation to 1/400 at the end of excavation. Further increases in distortion to 1/315 during station renovation and backfill caused little new damage. No damage to structural elements of the school was observed throughout the project.

It must be realized that self-weight deformations induce strains in a structure. The additional distortions caused by the excavation-induced movements results in additional strains that, if imposed on an undeformed structure, may not cause damage. But when these strains are imposed on a structure that has already deformed in response to the applied building loads, these excavation-induced strains may result in damage at apparent distortion levels smaller than applicable to self-weight loading. The damage reported herein was caused by a combination of the two sources of movements, but, as in the case of all reported damage to buildings adjacent to an excavation, the measured performance of the building only reflected the effects of the excavation-induced movements. Hence the impact of the self-weight induced strains on the onset of cracking remains uncertain.

It is noted that the response of larger multi-story buildings to hogging and sagging deformations is more complicated than may be allowed by simple beam theory. This is because these structures respond to deformations as a function of the type of connections between the floor and the columns, the rigidity of the floor slab, and the location and rigidity of the interior shear walls. A finite element model is required to account for the many different variables that make up a building system.

5.5 CRACK GAUGE DATA

The diagonal wall crack located on the south wall of the third floor faculty room was instrumented with a crack gauge (Figure 5-22). This wall crack was first observed on Day 73. The crack gauge was applied to the crack on Day 124 and measured change in horizontal and vertical width. The data from the crack gauge is presented in Figure 5-25. The figure compares the crack response to relevant excavation activity and distortions computed from data from Inclinometer 2, settlement points W9 and C5, and Tiltmeter T7. It is noted that the crack opening data presented in the figure is the resultant of the cumulative change in the horizontal and vertical widths of the crack, after the gauge was applied. The final crack width given in the figure was not necessarily the total crack width. The width of the crack varied between 0.5 mm and 1 mm when the gauge was first set across the crack.

Figure 5-25 shows that the crack opening increased from 0.1 mm to 1.0 mm between Day 130 and Day 144. However, the increase in distortion during this period was only from 0.00235 (1/425) to 0.0025 (1/400) and the depth of excavation adjacent to the crack location remained constant at a depth of 12.2 m. The east secant pile wall was chipped to the flange between Days 137 and 140. The chipping activity resulted in a reduction in the bending stiffness of the wall, which led to increased movements. The crack opening increased to approximately 1.3 mm from Day 144 to Day 161. This increase was a result of advancing the excavation for the escalator pit to the final depth of 13.2 m. Between Day 161 and Day 190, the cracking opening increased to a width of approximately 3.9 mm. Afterwards, the amount of increase in the crack opening became substantially less. Subway station renovations along State Street were completed between Day 190 and Day 224. The crack opening remained constant after the backfill activities began on Day 225. The total cumulative change in the width of the opening was 4.3 mm. The total final width of the crack opening was estimated to be approximately 4.8 mm to 5.3 mm.

5.6 ANALYSIS OF DAMAGE

5.6.1 Crack Types Observed

Cracking damage to the perimeter concrete and masonry bearing walls and the interior infill walls in the Warde School occurred as a result of tensile strains exceeding the tensile capacity of the material. Shear and bending deformations resulted from differential vertical displacement of building and combined to exceed the structure’s capacity to deform without cracking.

Based on inclinometer results shown in Figures 4-14 and 4-16, horizontal strains developed in the ground in response to the excavation. However, the magnitude of these horizontal ground strains that get transferred to the building as horizontal building strains depends on the type of structure affected by the movements. The Warde School rests on a load-bearing wall supported by a continuous reinforced strip footing around the building perimeter. In addition, there is sufficient tensile reinforcement at the connections between the floors and columns such that the lateral ground strains would not be transferred to the superstructure. Thus, no direct horizontal ground strains were included in the analysis of the building response. This position is supported by optical survey data that showed the horizontal deformations of the settlement points on the walls and columns of the school were negligible.

Figure 5-26 summarizes the typical crack types and orientations encountered in the Warde School. Although there were some variations observed, the crack types and orientations presented in the figure represent the majority of cracking damage encountered in the school. The figure shows that vertical tension cracks were encountered in most infill walls. Vertical tension cracks are caused by the horizontal tension that develops in a wall in response to bending. In the hogging deformation mode, tensile strain develops in the upper fiber. Thus, vertical cracks are located near the top of a hogging wall (5-26a). Conversely, tensile strain develops along the bottom fiber in the sagging deformation mode, which is why vertical cracks are located at the bottom of a sagging wall (5-26b). In both sagging and hogging modes of deformation, vertical cracks extend from the tension fiber toward the neutral axis. The length of the vertical cracks is a function of the radius of curvature of the deformation and the flexural rigidity of the wall (MacGregor, 1997). Horizontal cracks in infill walls presumably occurred in response to out-of-plane bending. The width and length of these cracks are governed by the out-of-plane flexural strength of the infill wall. Vertical and horizontal stress concentration cracks were observed emanating from the corners of several doors and windows in wall undergoing sagging. These were tension cracks caused by bending deformations.

It was observed that many infill walls initially experienced diagonal cracking. This behavior agreed with the conclusions of Burland and Wroth (1974) who found that for walls with relatively low stiffness in shear or a significant degree of tensile restraint, such as may be observed in infill walls of a frame structure, diagonal tensile strain will be the limiting factor. Diagonal shear cracks are caused by diagonal tensile strain and they appear as inclined cracks. In walls with high puncture ratios (area of openings/area of full wall), these cracks emanate mostly from the corners of the openings (5-26b) (Dulacska, 1992). In walls with low puncture ratios, inclined shear crack typically occur in the middle of the wall (5-26a). Inclined shear cracks in a sagging zone radiate outwards and upwards from the region of maximum curvature of the foundation. Vertical shear cracks occur in corners, near the interface between the wall and column. These cracks are caused by high vertical shear stresses transmitted along the wall-column interface as the column moves relative to the wall (5-26a).

The reinforced exterior load bearing walls were relatively stiff in direct tension and their length to width ratio was less than 1. As was discussed in Section 2.3, Boscardin and Cording (1989) and Burland and Wroth (1974) have shown that diagonal strain is most critical for a short beam that is more flexible in shear than in direct tension. This explains the appearance of the step mortar cracks in the north and south segments of the west exterior walls (5-26d).

5.6.2 Initiation of Selected Cracks

Crack damage was compared to tiltmeter- and settlement-derived distortions at selected locations where there was sufficient enough data such that the progression of distortions could be related to the initiation of cracking. Distortions computed from tiltmeter data were developed by taking the tangent of the tilt angle. For interior cracking, only settlement-derived distortions because there were no tilmeters located on any interior columns. For exterior cracking, the tiltmeter distortions were then compared to settlement-derived distortions at locations corresponding to tiltmeter locations.

5.6.2.1 Onset of Interior Cracking

Figure 5-27 shows the settlement-derived distortions computed in the east-west direction between settlement points W10 and C1, W9 and C3, and W8 and C5. These distortions show the distortional response in the sagging zone along the west side of the school and also show the onset of interior cracking. The first interior cracks were observed primarily in the sagging zone, on all three levels, on Day 73. At this time, the W10 to C1 distortion was 0.00109 (1/920), the W9 to C3 distortion was 0.00085 (1/1180), and the W8 to C5 distortion was 0.00077 (1/1300). From this point, the distortion increased at a rate proportional to the rate of excavation until the east secant pile wall was chipped between Day 110 and Day 140. The first crack in the marble façade of the entranceway foyer was observed on Day 108. The entranceway foyer is situated approximately at the W9 to C3 location. The distortion at this location on Day 108 was roughly 0.002 (1/500). After this date, new hairline cracks were observed throughout the building and previously noted cracks widened and lengthened. A new crack was observed at the base of the south wall in the entranceway foyer on Day 207. The W9 to C3 distortion at this time was 0.0029 (1/350).

5.6.2.2 Onset of Exterior Cracking

Figure 5-28 presents the distortion data along the north segment of the west wall of the school. The tiltmeter-derived distortion data at this location are obtained from Tiltmeter T6, which measured the tilt of the foundation wall in the north-south direction. These distortion data are compared to distortions obtained from settlement points W12 to W11. It is apparent from the figure that there was good agreement between the tiltmeter distortions and the settlement-derived distortions.

The T6 distortion was approximately 0.0002 (1/5000) on Day 73, and increased to 0.00067 (1/1500) on Day 108. Shortly thereafter, the southward tilt and consequently, the distortions gradually deceased as the north end of the wall settled in response to the excavation along Chicago Avenue. The T6 distortion was approximately 0.00059 (1/1690) on Day 129. This was the day damage first appeared in the north segment of the west wall. Less distortion developed in this wall because point W12 incrementally settled more than point W11 (Figure 5-9) as a result of it being closer to the Chicago Avenue excavation than point W11. Note that this wall was not damaged when subjected to the larger distortions of 0.00067 (1/1500) on Day 108. After Day 108, the wall at this location was subjected to tensile strains, as indicated by the direction of tilt in T3 and T6 (Figure 5-16). Increased tilt of the north wall of the school towards the north and the increased tilt of the north segment of the west wall towards the south resulted in horizontal tensile strains being induced this wall segment. The combination of the induced horizontal tensile strains and the bending tensile strains caused the north segment of the west wall to crack at smaller distortions to which the wall had been subjected previously

The distortion along the north side of the Warde School is presented in Figure 5-29. Tiltmeter T4 was used to represent the east-west tilt of the north wall and was compared to distortion derived from settlement points W12 to W13. From the figure, it is seen that the trends of the two data are similar, but the tiltmeter-derived distortion is less than the settlement-revived distortion. The top of the north basement wall tilted towards the west in response to the excavation along State Street and, the north wall experienced hogging deformations. The first crack in the west corner of the north basement foundation wall was observed on Day 108 as the T4 distortion increased to approximately 0.00031 (1/3250). The settlement-derived distortion at this time was 0.00056 (1/1800). The distortions continued to increase to values as high as 0.00116 (1/