Field Tests of Elevated Viaducts in Mexico City

The selected area of site PI was composed of two longitudinal frames connected by means of a TC girder. Fig. 2(b) shows the general configuration of the superstructure at site PI. All columns in the test site had the same $1.10\times 1.50\mathrm{m}$ oval cross section through their height, and were founded on 2.00-m-deep, $3.75\times 3.75\mathrm{m}$ square footings. Each footing was supported on four 12.50-m-long circular piles with a diameter of 0.60 m. The clear height of the columns was in the range of 10.12–11.20 m, and the main span of the deck was 35.00 m. The box girders were 2.00 m deep, 9.15 m wide, and had symmetric flanges. The roadway accommodated two traffic lanes.

The concrete compressive strength used for the design of the prestressed box girders was 59 MPa. The compressive strength of concrete for columns and footings was 44 MPa. The nominal values for the yield strength of prestressing steel and reinforcing steel were 1,862 and 412 MPa, respectively (Riobóo and Meli 2003).

Test site PI is located in the so-called firm zone of the seismic map for the metropolitan area of Mexico City. Structures in this zone are designed with a seismic coefficient of 0.16, which may be increased 50% to account for the importance of the structure. The dominant frequency of the soil at site PI, determined through ambient vibration tests, was in excess of 1.42 Hz.

Sites PV1 and PV2 had precast columns with a $1.80\times 2.40\mathrm{m}$ and $1.50\times 2.20\mathrm{m}$ oval cross section, respectively. Cross sections of columns in both sites were the same along their height. The lower 2.00-m-long portion of the columns was inserted in a $3.95\times 5.75\mathrm{m}$, chandelier-like, reinforced concrete footing with a depth of 2.65 m [Fig. 5(a)]. The gap left between the inserted columns and the footing was filled with a high-fluidity, high-strength mortar, and then, on the top surface of the footing, a posttensioned concrete collar was cast around the perimeter of the column in order to increase the overall stiffnesses of the assembly [Fig. 5(a)]. This type of foundation is different from the socket connection referred to by Haraldsson et al. (2013) and Osanai et al. (1996), which requires precise dimensioning and detailing of the column-footing joint. Such precision was not attainable at the fabrication sites, which led to the choosing of a posttensioned system despite being somewhat difficult to execute and thus requiring closer supervision.

Similarly to test site PI, each footing was supported by four 16.50-m-long circular piles with 0.80 m in diameter. The clear height of the columns in sites PV1 and PV2 was 14.20 and 13.60 m, respectively. The superstructure was composed of a TC girder, which rested as a simply supported member at the ends of two cantilevered TA girders. The main span of the deck at both sites was 43.00 m. In both cases, the box girders were 2.40 m deep and 12.65 m wide, accommodating three traffic lanes. The flanges at opposite sides of the girders were asymmetric at site PV1 and symmetric at site PV2 [Figs. 3(b and c)].

The concrete compressive strength used for the design of the prestressed box girders and the columns was 59 MPa. The compressive strength of concrete for the footings was 44 MPa. The mechanical properties of the prestressing steel and reinforcing steel in sites PV1 and PV2 were the same as those for test site PI. Sites PV1 and PV2 were located in the same seismic zone as site PI. The dominant frequency of the soil at both sites PV1 and PV2 was determined through ambient vibration tests and was found to be in excess of 1.4 Hz.

In site VB, the test region included four columns identified with the marks A, B, C, and D and whose clear heights were 11.00, 10.75, 9.75, and 9.25 m, respectively. The general configuration of the superstructure and foundation at site VB is shown in Figs. 2–5. In this case, the columns and their footings were prefabricated and cast integrally at the prestressing plant. The rectangular cross-section of the hollow columns changed over their height. Column dimensions were $1.83\times 2.50\mathrm{m}$ at their base, $1.40\times 2.50\mathrm{m}$ at their cross-section, with a $3.40\times 2.50\mathrm{m}$ rectangular capital at their top. The thickness of the walls on the hollow columns was approximately 0.40 m.

Each footing was $4.60\times 3.60\mathrm{m}$ in plan and 1.70 m deep. The longer side of the footing was perpendicular to the direction of traffic in the elevated viaduct. The footings rested on a 0.25-m-thick reinforced concrete slab and a 1.70-m-thick flowable fill. The same type of fill was provided around the footing to reach a depth of 2.20 m. The overall dimension of the footing and the surrounding flowable fill in plan view was around $7.60\times 6.60\mathrm{m}$. Four 0.90-m-diameter perforations were allocated in each footing to provide proper anchorage and development of the piles reinforcing steel and achieve a monolithic connection between the footing and the reinforced concrete piles previously cast in situ. The length of the piles ranged from 22.60 to 24.10 m, and their diameter was 0.80 m. The joints between the reinforced concrete piles of the foundation and the pier-footing assembly, and between said assembly and the box girders, were posttensioned in situ [Fig. 5(b)].

The superstructure of the elevated viaduct at test site VB was composed of a simply supported TC girder, which rested at the ends of two cantilevered TA girders. Each of the TA girders rested on a pair of columns forming monolithic frames in the longitudinal direction of the viaduct. The clear span was 34.00 m and the total length of the TA girder was 25.00 m. The box girders had a depth of 2.40 m and a width of 12.35 m, adequate for three traffic lanes.

Nominal compressive strength of concrete for all structural elements was 59 MPa. The nominal yield strength of prestressing steel was 1,862 MPa, whereas the nominal yield strength of reinforcing steel was 412 MPa.

The soil at site VB was characterized by the existence of sandy layers up to a depth of 10 m, and the presence of sand layers within depths of 10 to 32 m. The shear wave velocity of these layers has been measured to range from 100 to $300\mathrm{m}/\mathrm{s}$. The firm deposits underneath the sand layers have shear wave velocities of around $400\mathrm{m}/\mathrm{s}$. The dominant frequency of the soil at site VB was determined through ambient vibration tests and was found to be around 1.08 Hz. The use of the approximate formula provided in the seismic design code of Mexico City for soft soils ($f=Vs/4H$, where $f$ is the dominant frequency, $Vs$ is the shear wave velocity of the medium, and $H$ is the thickness of the medium assumed as semi-infinite) results in a dominant frequency of 1.6 Hz. The use of this expression, however, was deemed inappropriate since site VB lies precisely on the limit between the transition and firm zones of the seismic zoning map of Mexico City. The geotechnical surveys conducted by Mooser et al. (1996) and Juárez et al. (2010) indicate that site VB is located in an alluvial fan, making it a geotechnical singularity in which the simplifications of the approximate formula cannot be assumed. Structures in this zone must be designed with a seismic coefficient of 0.32. A 50% increment of this value was enforced for the design of the viaduct as specified for important structures in the design code and standards for Mexico City.

The lateral load tests were carried out in sites PV1, PV2, and VB. The tests consisted of applying an increasing lateral load at the top of a single column by means of a 4,900-kN crane. The load was applied perpendicularly to the direction of traffic and as parallel to ground level as possible. A pair of ad hoc steel plates was designed and embedded in the concrete at the top of the columns to allow for the application of the load. A steel cable was used to pull the column by linking the embedded steel plates to the hook of the crane. The horizontality of the pulling cable was monitored by means of surveying equipment. The main purpose of the lateral load tests was to determine the lateral displacement of the column under cumulative loads, with a focus on the overall column-footing behavior. The magnitude of the lateral load was similar to the value corresponding to the calculated cracking moment, and the column’s behavior was kept in the cracked elastic range. In site PV1, the lateral load associated with the calculated cracking moment of the column was applied. For site PV2, the maximum applied lateral load was that corresponding to the cracking moment. In both sites, the cracking moment was computed on the basis of the calculated modulus of rupture ($0.7\surd f_c^{\prime }<f_t<\surd f_c^{\prime }$). Lateral displacements were measured by means of linear variable displacement transducers, potentiometers, and electronic surveying equipment at various heights of the columns under load (Fig. 6). Lateral displacements of neighboring columns in the sites were also measured. During the tests, the load was applied in incremental steps to allow for visual inspection of the column and for the surveying equipment to be utilized for the column and for the data collection of the surveying equipment.

A single lateral load test was carried out at site PV1, whereas two tests were conducted at site PV2 to assess the behavior of the column-footing assembly during construction. The first lateral load test at site PV2 was performed before the posttensioned collar slab was cast around the column, and the second test was carried out after said collar was cast and had reached its target strength. Due to space restraints, the pulling force at sites PV1 and PV2 was applied at an $18°\pm 1°$ angle with respect to ground level. Even though the application of a perfectly horizontal load was envisioned, the layout of the sites, the height of the columns, and the space and time restraints forced the use of a 4,900-kN lifting crane pulling the columns in an inclined manner. This loading scheme resulted in the columns being subjected to a combination of axial tension and lateral flexure, which is not uncommon under certain service load conditions. As with any lifting equipment, the pulling capacity of the crane is greatly diminished when the movement does not take place in a perfectly vertical manner. For an $18°\pm 1°$ angle, the maximum pulling force of the crane was 695 kN. The implications of applying the load in an inclined manner were (1) a reduction of 30% in the axial compression acting on the column, (2) the effective horizontal load being around 95% of the applied lateral load, and (3) a reduction of the applied moment as the eccentricity of the axial load changed.

Due to space restraints, the pulling force at sites PV1 and PV2 was applied at an $18°\pm 1°$ angle with respect to ground level. Two cycles were applied at site PV1 in which the target lateral loads were 235, 333, 431, 480, and 540 kN. At site PV2, two cycles were applied for the before-collar condition (target loads of 206, 382, 490, 549, 637, and 695 kN), and three cycles were applied for the after-collar condition (target loads of 186, 363, 549, and 628 kN).

The lateral load test in site VB consisted of applying a pulling force to the top of column B. Two target effective horizontal loads were set for the tests during construction (first stage): $\mathrm{Ti}1=230\mathrm{kN}$ and $\mathrm{Ti}2=555\mathrm{kN}$. These loads were under 25% of the calculated strength of the cantilevered columns and correspond to a total lateral drift of 0.05 and 0.12%, respectively. The pulling cable had a 28° and an 18° inclination with respect to ground level for the Ti1 and Ti2 target loads of the first stage tests, respectively. For the lateral load tests carried out after construction was completed (second stage), the following four target effective horizontal loads were set: $\mathrm{Tc}1=480\mathrm{kN}$, $\mathrm{Tc}2=526\mathrm{kN}$, $\mathrm{Tc}3=430\mathrm{kN}$, and $\mathrm{Tc}4=437\mathrm{kN}$. These loads were under 10% of the design values while the associated lateral drift was less than 0.02%. Due to space restraints, the pulling cable in site VB had an inclination of 24°.

Displacements and rotations at various locations of the columns in site VB were measured by means of potentiometers and biaxial inclinometers. Column B, subjected to the lateral pulling force, was measured with five horizontal potentiometers (H), six vertical potentiometers (P), and three inclinometers (I) [Fig. 6(b)]. Neighboring columns A and C were instrumented with five potentiometers and three inclinometers [Fig. 6(b)].

Displacement transducers were fixed to an independent steel structure erected in the vicinity of the columns, allowing for the measurement of their lateral displacement. In sites PV1 and PV2, located in areas of firm soils, the foundation of the steel frame was 1 m deep. An existing 3-m-high slope supported the frame laterally. In site VB, a rigid steel structure was used. The fundamental frequency of the steel frame was measured to be more than 6.5 times that of the soil at the site. The local rotation at the base of the steel frame was monitored during the tests and measured as $7\times {10}^{-6}\mathrm{rad}$ when the largest lateral loads were applied. Such a rotation at the base resulted in differences between measured and actual values for the lateral displacement that were under 4.5%. The steel structure served as an isolated frame of reference and was designed with enough rigidity so that any lateral deformation was negligible. Potentiometers and inclinometers were mounted directly on the surface of the columns by means of drilled anchors and aluminum plates. The use of surveying equipment made possible to corroborate the measured lateral displacements not only for the column subjected to lateral load but also in the two adjacent columns. The instrumentation schemes depicted in Fig. 6 and the surveying data acquired allowed for an accurate description of the deformed shape of the columns under various load conditions as well as for the computation of the rotation at their bases.

Static and dynamic vehicular load tests were carried out in sites PA, PV1, and VB. The vertical loads were imposed by means of T3-S3 and T3-S2 trucks. Four loaded trucks with an average weight of 573 kN and a single truck of 196 kN were used for the tests at sites PA and PV1. Five trucks with an average weight of 598 kN and a 160-kN truck were used at site VB. The purpose of these tests was to determine the lateral and vertical displacements of the superstructure under static, dynamic, and impact loads in order to compare them with the design values.

For the static vehicular tests, different arrays of parked trucks were envisioned. For the dynamic vehicular tests, the same trucks were driven at various speeds along the central lane of the elevated viaducts. In order to evaluate the influence of wearing-surface irregularities and to produce additional impact loads, some of the dynamic vehicular tests were run after setting a 50-mm-high, 500-mm-long, and 3-m-wide steel ramp, which served as a temporary speed bump on the asphalt wearing surface (Cantieni 1983; Bank and Pinjarkar 1989; Paultre et al. 1992). The run of the trucks over the speed bump without breaking replicated the occurrence of short-duration concentrated loads, commonly referred to as impact loads.

Accelerations and vertical displacements of the superstructure were recorded during the vehicular tests using servo-accelerometers and displacement transducers located at strategic points of the structure. Instrumentation at sites PI and PV1 included 9 accelerometers and 23 displacement transducers. The instrumentation deployment at site VB comprised 26 accelerometers and 33 displacement transducers. Accelerometers were mounted directly on the superstructure by means of aluminum plates. The displacement transducers ran from different points of the superstructure to the ground by means of steel pipes. This instrumentation scheme permitted the measurement of the vertical deflection of girders when subjected to various load conditions.

Ambient vibration tests were carried out at all four test sites. These tests were conducted before and after any other tests. The purpose of the ambient vibration tests was to determine the natural frequencies of the structure and the soil, and to assess if the lateral load tests or the vehicular load tests had any impact in the original dynamic properties of the structure. Various arrays of servo-accelerometers were deployed during the ambient vibration tests.

One column at each of test sites PV1 and PV2 was selected to evaluate the behavior of the cantilevered element under lateral loads and the effect of the posttensioned collar slab on the behavior of the column-footing ensemble. Due to the height of the columns and the space restraints around them, the lateral displacement was measured using displacement transducers (LVDTs) over the lowest 6.8 m of their height. The lateral displacements at higher column locations were determined with topographic equipment. When attempting to match the lateral displacements recorded by the LVDTs to the data obtained with the electronic surveying station, a large scatter was noticed in the survey data points. Thus, a methodology was proposed to determine the deformed shape of the column on the basis of all LVDT measurements in the lower portion of the column and a single topographic data point corresponding to the top of the column. Displacement data points were adjusted by subtracting the displacement measured at the footing, and their values compared with those of a simple model based on the deformed shape of a prismatic, perfectly elastic, homogeneous, and weightless cantilevered element subjected to a lateral load at its highest point. Even though the weight of the superstructure and the column may be quite large and generate permanent deformations, the procedure focuses on determining the deformation solely due to the application of the externally applied lateral load while ignoring any previous deformations due to permanent loads. If the column height is $H$ and the load applied is $P$, the lateral displacement of a cross-section located at a distance $y$ from the base of the column is given by Eq. (1)

However, the conditions in the field are somewhat different since there is self-weight, structural redundancy at the top of the column and the fixation at its base might not perfect as assumed for the development of Eq. (1). In order to account for these discrepancies, it is assumed that only a fraction ($K$) of the lateral load is required in the actual column to produce the same displacement as in the model

Defining $C$ as

Substituting Eq. (3) in Eq. (2), and solving for $C$ results in

By using Eq. (4), the values for $C$ and their statistical modes were calculated for each load step. In this process, it is assumed that the product $EI$ remained constant during the lateral load tests. The lateral displacement of the columns obtained after adjusting the surveyed data by using the described methodology were consistent with the displacements measured by the transducers. The values calculated for $C$ using Eq. (4) suggest that any relative movement between the column and its footing did not have a noticeable effect on the elastic response of the ensemble. It must be noted that the main purpose of this methodology is to relate measured lateral displacements with those provided by a simplified structural model.

The lateral displacements of adjacent columns were measured at sites PV1 and PV2. Throughout the tests, the displacements observed in neighboring columns remained under 50% of those measured for the column under direct lateral loading. The former is indicative that a portion of the lateral load was transferred to adjacent members through the participation of the box girders in the load-resisting mechanism.

During the before-collar tests, the first flexural crack in column B was observed when the lateral load was increased from 382 to 490 kN. Considering the variation of the maximum tensile stress for the transition between uncracked and cracked sections for Class T prestressed members (Table R18.3.3 of ACI 318-11; ACI 2011), the lateral load associated with the cracking moment was calculated to be between 500 and 675 kN. The first flexural crack was measured to be 0.07 mm wide and 200 mm long when the lateral load had been increased to 549 kN. This crack was not visible after the removal of the lateral load. During the second lateral load cycle, the flexural crack was visible again when the lateral load reached 382 kN. Additional flexural cracks located in the lowest 1.5-m-long region of the column appeared as the lateral load reached 637 and 695 kN. After the lateral load was removed, some flexural cracks remained visible. The maximum width of flexural cracks present after the load tests was 0.10 mm. The width of the cracks that remained visible was under the limit set in the code for the service load condition. Even though the presence of these cracks was undesirable, they are unlikely to affect the structural response of the members under service and ultimate loads. It must be noted that the assumption of the $EI$ product to be constant for the derivation of Eq. (4) would not be true after flexural cracking has developed. However, for the target loads of the tests, the errors induced by this discrepancy were under 4%.

After the before-collar tests were concluded, an additional displacement transducer was placed in the region where flexural cracking had concentrated (1.24 m from the base of the column) in order to estimate average deformations in that region. The relationship between the average strains at the base of the column measured during the application of the three cycles of lateral load, the lateral load, and the equivalent moment are shown in Fig. 7. The deformations are compared with strains computed on the basis of the classic Euler–Bernoulli beam theory. The measured strains agreed well with those calculated. Fig. 7 shows similar trends for all load cycles, including hysteretic behavior associated with reduction in the axial compressive stresses for lateral loads larger than 180 kN. The axial decompression was due to the presence of tensile stresses induced by the flexural moment at the base of the column.

During the after-collar tests, the width and length of the flexural cracks that had appeared during the before-collar tests increased. Nevertheless, the width of flexural cracks was less than 0.10 mm for lateral loads up to 695 kN. For all before-collar and after-collar tests, no cracks were visible in any of the adjacent columns. Despite the appearance of cracks during the load tests, no repair or rehabilitation was deemed necessary.

When comparing the lateral displacement of the columns for the before-collar and after-collar condition at site PV2, it was observed that they were practically identical for lateral forces under 206 kN. For larger lateral forces, however, the lateral displacements of the column in the after-collar condition were consistently smaller that those corresponding to the before-collar condition (Fig. 8). It was evident that the cast of the posttensioned collar slab resulted in an increase of the lateral stiffness of the structure, thus reducing its lateral displacement.

For both the before-collar and after-collar tests, the lateral displacements measured at the base of column B were consistently larger than those measured at the footing. This behavior could be associated with the presence of the grout-filled joint between the column and the footing, which induced a strain concentration. However, after the posttensioned collar was in place, the displacements measured at the grout-filled joint were reduced 38% with respect to those measured during the before-collar tests. Moreover, the measured angular rotations at the bend of column B were compared with the calculated rotations assuming a cantilevered column. The results consistently showed that the translational and rotational restraints imposed by the superstructure should not be ignored.

In site VB, the column marked with letter B in Figs. 1(a) and 3(b) was subjected to monotonically increasing lateral loads. The tests were conducted at two stages of construction. Two target loads (Ti) were set for the tests during the first stage of construction (cantilevered column) and four target loads (Tc) were established for the tests of the second stage (construction completed). The lateral displacement at various points along the height of column B was measured by potentiometers. Fig. 9 shows the data points obtained for the effective horizontal load tests carried out for both stages of construction. Fig. 9(a) shows the approximate lateral deflection shape of column B for target loads of 230 and 431 kN.

It is evident that all lateral displacements reduced from the first to the second stage tests. Indeed, the presence of the superstructure resulted in a reduction of all lateral displacements of column B by a factor of around 4. Fig. 9(b) presents the results of Fig. 9(a) after a normalization of the lateral displacements was done. The coincidence of all data points indicates that the deformed shape of column B did not change from the first to the second stage tests. The presence of the superstructure did not modify the distribution of lateral displacements over the height of the columns even if is significantly reduced their magnitude. However, the local deformation at the base of column B, inferred by both lateral displacements and rotations in that zone, did change from the tests of the first stage to those of the second stage.

The instrumentation scheme deployed at site VB allowed for the estimation of the static translational and rocking stiffnesses associated with soil-structure interaction (SSI) in the transverse direction of the viaduct. The first-stage test data, corresponding to the cantilevered column, was used for the estimation. Fig. 10 presents the lateral load versus base displacement and the moment versus base rotation plots recorded for the two target effective horizontal loads applied during the first stage tests ($\mathrm{Ti}1=230\mathrm{kN}$ and $\mathrm{Ti}2=555\mathrm{kN}$). The translational stiffnesses were obtained as the slope of linear fits to the data points in Fig. 10(a). A single line was enough to describe the quasi-linear behavior of the test points corresponding to the first target lateral load (Ti1). For the second target lateral load (Ti2), a trilinear fit described the test points best. The cutoff points for the trilinear fit were identified at 147 and 343 kN.

For estimating the rocking stiffnesses of the SSI system at site VB, the plots in Fig. 10(b) were used. For the lateral load test to the first target load (Ti1), a single line was sufficient to represent the quasi-linear distribution of the moment versus base rotation data points. For the test to the second target load (Ti2), a singularity was observed for a moment of around $\mathrm{3,430}\mathrm{kN}·\mathrm{m}$, corresponding to an effective horizontal load of around 343 kN. Note that the same line fits the data points for both target load tests up to a moment of $\mathrm{3,000}\mathrm{kN}·\mathrm{m}$, associated with a lateral load of 300 kN. Also note that the onset of the second line fit for the moment versus base rotation data points ($\mathrm{3,430}\mathrm{kN}·\mathrm{m}$) coincides with the onset of the third segment of the line fit for the effective horizontal load versus lateral deflection data points (343 kN). The values for the static translational and rocking stiffnesses obtained from the linear fit of the test data of column B in test site VB are summarized in Table 2.

The static vehicular load tests consisted of parking a number of loaded and unloaded trucks on the superstructure. Four arrays for the location of trucks were used in sites PI and PV1 [Fig. 11(a)]. Five arrays were used in site VB [Fig. 11(b)]. The arrays at each site were designed on the basis of producing both the maximum vertical displacements at the midspan cross-section of the box girders (TC), and the largest lateral displacements of the instrumented columns (B).

The experimental data corresponding to the vertical displacements at various points of the superstructure were used to plot its approximate deformed shape at selected cross-sections of the test sites under various load conditions. Fig. 8 shows the variation of the vertical displacements measured at sites PV1 and VB in three cross-sections of the superstructure. The three lines shown for each plot in Fig. 12 correspond to the approximate deformed shape at the cross-sections identified as A, B, and Midspan in Fig. 11. Note that the vertical displacements for Arrays IV and V in site VB are presented in the same plot.

For the lateral load test to the first target load (Ti1), a single line was sufficient to represent the quasi-linear distribution of the moment versus base rotation data points. For the test to the second target load (Ti2), a singularity was observed for a moment of around $\mathrm{3,430}\mathrm{kN}·\mathrm{m}$, corresponding to a lateral load of around 343 kN. Note that the same line fits the data points for both target load tests up to a moment of $\mathrm{3,000}\mathrm{kN}·\mathrm{m}$, associated with a lateral load of 300 kN. Also note that the onset of the second line fit for the moment versus base rotation data points ($\mathrm{3,430}\mathrm{kN}·\mathrm{m}$) coincides with the onset of the third segment of the line fit for the lateral load versus lateral deflection data points (343 kN).

The maximum midspan deflections for the box girders in all sites were observed under the Array II configuration, which consisted of all trucks present in the exterior lane of the viaduct (Fig. 11). The magnitude for these deflections at sites PI, PV1, and VB were 37.0, 11.7, and 12.0 mm, respectively. These deflections were obtained after taking into account the displacements observed at the supports as well as the local deflections at the flanges of the box girders. In all cases, the measured deflections were less than those allowed by the AASHTO specifications.

Prior to the static vehicular tests, preexisting cracks were marked and identified for their monitoring during the tests. The maximum width measured for preexisting flexural cracks at site PI was 0.15 mm. The maximum crack widths measured before the tests at sites PV1 and VB were less than 0.03 mm. During the static vehicular load tests, the maximum flexural crack widths measured in site PI were 0.35 mm. The maximum crack widths at sites PV1 and VB were 0.05 mm. All flexural cracks returned to their original state once the tests were concluded. The measurement of crack widths was done using an Elcometer 143 crack width meter (Elcometer, Rochester Hills, MI). Inspection of the underside of the superstructure for cracks was possible with the use of Genie articulated and telescopic booms (Terex, Redmond, Washington).

The results of Array I and Array II of the static vehicular load tests at sites PV1 and VB showed that the distribution of vertical displacements in the cross-sections under study followed a linear trend (Fig. 12). This observation points to the conclusion that the cross-section displaced and rotated as a rigid body with respect to its support point at the column bend. It might be also concluded that the main source of the vertical displacements of the cross section was the local deformation of the column. The fact that the whole cross-section of the superstructure is able to rotate and displace as a rigid body supports the idea that the connection between the column and the box girder had an adequate stiffness. From the designer’s point of view, this would be the desired behavior for a posttensioned connection.

In sites PV1 and PV2, an approximate method to calculate the lateral displacement of the column under static vehicular load was envisioned assuming the column was a prismatic element with an infinite axial stiffness and an equivalent fixed base estimated by adjusting the lateral displacements of a cantilevered column to those measured during the tests. In the method, the demand associated with each of the arrays was represented by a concentrated load and moment applied at the top of the column. The load corresponded to the weight of the trucks and the moment was that associated with the eccentricity of the loads. The displacements calculated with the approximate method showed good agreement with those measured during the tests.

The dynamic vehicular tests conducted at sites PI, PV1, and VB consisted of the recording of acceleration and displacement data while trucks drove across the test site at different speeds. For the study of impact loading, a temporary speed bump was installed. The speed of the trucks varied from 10 to $73\mathrm{km}/\mathrm{h}$.

The maximum accelerations recorded for the dynamic vehicular load tests were 40 and $668\mathrm{m}/{\mathrm{s}}^2$ for the free and speed bump conditions, respectively. In order to estimate the dynamic amplification factors (DAF) with respect to the displacements for static vehicular load tests, the displacement records for the dynamic vehicular tests were first filtered using a low-pass filter to eliminate vibration components (Billing 1984), and then the equivalent static trace was obtained. Afterwards, the quotients of maximum amplitudes were obtained for the filtered and unfiltered records.

For the free drive tests of 490-kN and 686-kN loaded trucks, the highest DAFs at midspan were 1.60, 1.68, and 1.14 for sites PI, PV1, and VB, respectively. The vertical deflections at midspan estimated with the former DAF were 7.8, 2.5, and 2.6 mm, respectively. For the speed bump condition in sites PI, PV1, and VB, the highest DAFs at midspan were 1.70, 1.80, and 2.13, respectively. In this case, the vertical deflections associated were 26.9, 4.2, and 2.8 mm, respectively. All deflections calculated using the obtained DAF were less than the deflections measured during the static vehicular load tests.

The largest values for the DAF were obtained for the speed bump condition and the run of the 160-kN and 196-kN unloaded trucks. The values obtained for sites PI, PV1, and VB were 4.20, 2.87, and 3.68, respectively. The corresponding deflections at midspan were 6.7, 0.4, and 1.1 mm. The range of DAF obtained throughout the dynamic vehicular load tests agrees well with values reported for bridges with similar characteristics (Paultre et al. 1992).

Ambient vibration tests were conducted before and after any other tests in order to monitor any change in the original properties of the structure in all four sites. The ambient vibration tests focused on determining the fundamental frequencies of the structure in the direction perpendicular to traffic and the most relevant frequencies of the girders.

The fundamental lateral frequency of the structure at site PV1 was determined to be 1.12 Hz, which remained identical after the lateral load tests were concluded. In contrast, the first and second natural frequencies of the cantilevered column at site PV2 showed a slight reduction of around 3% from the before-collar to the after-collar tests. Indeed, as shown by the reduction in the lateral displacement of the column-footing assembly after the posttensioned collar was cast, the presence of the collar increased the stiffnesses of the structural system. Furthermore, the development of flexural cracks during the before-collar tests contributed to the change in the natural frequencies of the assembly. The first two translational frequencies for the column in the before-collar condition in site PV2 were 1.12 and 1.51 Hz. For the after-collar condition, these frequencies changed to 1.10 and 1.47 Hz. In the case of site VB, the fundamental frequencies in the transverse direction of the viaduct were determined to be 5.9 and 1.4 Hz for the first stage (cantilevered column) and second stage (construction completed), respectively.

The natural frequencies determined by the ambient vibration tests match very well those determined through the dynamic vehicular load tests at all test sites. Furthermore, the design firm provided the authors with its calculations of the fundamental lateral frequencies of the viaducts on the basis of their structural modeling. Table 3 summarizes the natural frequencies determined during these tests. Also, Table 3 shows the natural frequencies of the soil-structure ensemble determined on the basis of the structural model developed by the design firm for sites PV1 and VB. Data for other sites were not available. The largest differences between the measured and calculated natural frequencies ranged from 7 to 24%. The differences for the ratio of lateral/vertical frequencies ranged from 3 to 11%. The natural frequencies calculated in the transverse direction for sites PI, PV1, and PV2 were less than the corresponding dominant frequency of the soil (larger than 1.42 Hz). In contrast, the natural frequency estimated for the transverse direction for site VB was larger than that for the soil at the site (around 1.08 Hz).

The fundamental frequency determined for the vertical component of the main span girder was only available for sites PV1 and VB (Table 3). The difference between calculated and observed values at these sites was 12 and 15%, respectively. The fundamental modal shapes in the lateral and vertical direction for all test sites are shown in Fig. 13. A good agreement between the values calculated by the design firm and those obtained during the tests for sites PV1 and VB may be observed in Fig. 13. The latter is also confirmed by values for the modal assurance criterion (MAC) (Allemang 2003). The value of the MAC calculated between analytical and experimental modal shapes at the central span for sites PV1 and VB was larger than 0.95 for the first translational and vertical modes, and larger than 0.84 for the second vertical mode (asymmetric). The range of vertical frequencies identified are similar to those reported for comparable structures (Paultre et al. 1992).

The equivalent viscous damping was determined through ambient vibration tests at sites PV1 and VB. The value associated with the fundamental frequency of the main girder in the vertical direction ranged from 2 to 6% of the critical damping for both sites. The equivalent viscous damping associated with the lateral fundamental frequency ranged from 0.5 to 1.5%, and from 1 to 2% of the critical damping for sites PV1 and VB, respectively.

The effect of foundation stiffness on the structural analysis of the viaducts was evaluated by comparing the measured natural frequencies of the structure with those obtained by means of specialized software and by means of the procedure indicated in the local design code (NTCDF 2004). The translational and rocking stiffnesses of the cantilevered column and its foundation at site VB, including SSI effects, were calculated using DYNA5 (Novak et al. 1995) and NTCDF (2004). In the DYNA5 model, the soil profile was defined and the group effect of the piles was taken in to account. In contrast, the NTCDF code does not consider the group effect of piles. The stiffness of the footing-pile assembly was obtained as the sum of the stiffnesses of the footing and the pile group, which were calculated separately. Furthermore, the following two construction conditions were considered: (1) before the ring of flowable fill was present, and (2) after the ring was cast. The stiffnesses were obtained for two frequency-dependent scenarios corresponding to the natural frequencies determined through the ambient vibration tests for the first (cantilevered column) and second stages (construction completed). A frequency-independent (static) scenario was also evaluated. The results of these analyses are shown in Table 4.

From Table 4, it is discernable that the differences between the calculated stiffnesses for the static and dynamic cases are practically negligible. Similar results for the translation and rocking stiffnesses of a group of $2\times 2\mathrm{piles}$ derived by Kaynia and Kausel (1982) using a rigorous theoretical model confirmed that there is little difference between the static and the dynamic values computed. As for the effect of considering the presence of the ring of flowable fill, it increased the translational and rocking stiffness an average of around 23 and 180%, respectively. The comparison of the results in Table 4 with the estimated stiffnesses presented in Table 2 indicates that the ring of flowable fill should always be included in the analytical model.

Fig. 14 presents the results given in Table 4 in a plot, which also shows the variation of the translational (Kt) and rocking (Kr) stiffnesses calculated with DYNA5 and the NTCDF (2004) code as a function of the frequency of the footing-pile ensemble for both the before-ring and after-ring of flowable fill conditions. Fig. 14 includes data points corresponding to the estimated translational and rocking stiffness presented in Table 2. An ample range of frequencies (0–25 Hz) was considered in the analyses to better cover the whole dynamic response of the structure. The design firm addressed the soil-structure interaction using the procedure established by Zeevaert (1983). The equivalent translational and rocking stiffnesses obtained were $268\mathrm{MN}/\mathrm{m}$ and $\mathrm{11,788}\mathrm{MN}·\mathrm{m}/\mathrm{rad}$, respectively. Both values are significantly lower than those obtained during the tests and than those calculated using either DYNA5 or the NTCDF code with the flowable fill ring present.

In order to evaluate the general hypotheses assumed in the structural analysis of the design firm, the model was used to evaluate the response of the cantilevered column at site VB. The model considered the presence of a point load of 230 kN at the top of the cantilevered column-footing ensemble. A second set of analyses was run for an effective horizontal load of 555 kN. In order to further understand the effect of the foundation stiffness on the response of the system, four values were considered: (1) design firm–calculated values (${\mathrm{A}}_{\text{Designer}}$); (2) DYNA5-calculated values for the before-ring of flowable fill condition (${\mathrm{A}}_{\mathrm{DYNA}5}$); (3) DYNA5-calculated values for the after-ring of flowable fill condition (${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$); and (4) estimated values derived from the ambient vibration tests (${\mathrm{A}}_{\text{Exp}}$). The values obtained using the simplified equations of the NTCDF (2004) code were very similar to those obtained for the ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$ model; thus, they are not presented in this paper.

Fig. 15 shows the lateral displacement and rotation profiles calculated with the four values of foundation stiffness selected, as well as the displacements and rotations measured during the first stage of the lateral load tests conducted at site VB. The model that best matched the measured displacements and rotations was ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$. The largest difference between the results of the ${\mathrm{A}}_{\text{Exp}}$ and ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$ models was observed at the top of the column, and was less than 12%.

The differences between the ${\mathrm{A}}_{\text{Designer}}$ model and the models based on DYNA5 values (${\mathrm{A}}_{\mathrm{DYNA}5}$ and ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$) reflect the fact that the design firm used smaller SSI stiffnesses than those inferred from the lateral load tests. Furthermore, the four values for the foundation stiffness were used in the full model developed by the design firm for the structural analysis. In this case, however, an effective horizontal load of 431 kN was applied at the top of the column. The results of the analysis using the values for the ${\mathrm{A}}_{\text{Exp}}$ case indicated that 95% of the lateral load was resisted by just three columns as follows: 32% by column A, 43% by column B, and 20% by column C.

Fig. 16 shows the lateral displacements of columns A, B, and C, which were calculated with the full structural model and the four foundation stiffnesses. Additionally, Fig. 16 shows the displacements measured during the second stage of the lateral load tests at site VB. Similarly to the cantilevered column model, the best match for the measured displacements was the model with ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$ values. The differences between the results of the ${\mathrm{A}}_{\text{Exp}}$ and ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$ models were less than 10%. Once again, the fact that the plots corresponding to the ${\mathrm{A}}_{\text{Designer}}$ model lay further to the right of other models in the plots of Fig. 16 indicate that the hypotheses used by the design firm resulted in conservative estimations. Due to the fact that the spectral accelerations remain constant throughout a wide range of structural periods for the soft soil and the transition zones in Mexico City, the design forces will remain constant, thus making the design more conservative when stiffnesses are underestimated (NTCDF 2004).

Finally, the fundamental frequencies for the cantilevered column and the full structural model were calculated. Table 5 summarizes the results of the analysis. The average differences between the frequencies calculated with the ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$ and ${\mathrm{A}}_{\text{Exp}}$ models and those determined with the ambient vibration tests was 4 and 9% for the cantilevered column and full structural model, respectively. The average differences for the ${\mathrm{A}}_{\text{Designer}}$ and ${\mathrm{A}}_{\mathrm{DYNA}5}$ models were 19 and 24%, respectively.

Using the full structural model of site VB, the lateral displacements of the column were calculated for the vehicular load tests. Similarly to the analysis for the effect of the foundation stiffness, four values (${\mathrm{A}}_{\text{Designer}}$, ${\mathrm{A}}_{\mathrm{DYNA}5}$, ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$, and ${\mathrm{A}}_{\text{Exp}}$) for the SSI stiffness were used and all five arrays for the load distribution were considered. Only the results of Array II, which showed the largest lateral displacements, are presented in the section.

The best prediction for the calculated lateral displacements of columns A, B, and C when subjected to the Array II condition were obtained when the values of ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$ and ${\mathrm{A}}_{\text{Exp}}$ were used in the full structural model. The average difference between the calculated and measured displacements at the top of column B was under 9% for both ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$ and ${\mathrm{A}}_{\text{Exp}}$. In contrast, the difference between the calculated and measured displacements for the models using the values of ${\mathrm{A}}_{\text{Designer}}$ and ${\mathrm{A}}_{\mathrm{DYNA}5}$ were 36 and 21%, respectively. These differences are attributed to the fact that the SSI stiffnesses used by the design firm were conservatively smaller than those determined through the tests.

The vertical displacements of the box girder calculated with the full structural model resulted in similar values, regardless of the SSI stiffness used. The variation among the vertical displacements calculated with the four stiffness values was less than 2%. The largest differences between the calculated and measured vertical displacements were under 20%, which were observed for the load conditions of Array IV and V.

Lastly, the fundamental frequencies of vibration in the transverse and vertical directions of the viaduct were calculated using the full structural model and the four SSI stiffnesses. Table 6 summarizes the transverse fundamental frequencies calculated for an unloaded condition and for Array III, which imposed a total load of 1,249 kN and represents 64% of the service load used for the design of the superstructure.

The natural frequencies determined for the unloaded model using the values for ${\mathrm{A}}_{\mathrm{DYNA}5\text{-}\mathrm{R}}$ and ${\mathrm{A}}_{\text{Exp}}$ differ from those estimated with the dynamic vehicular load tests in less than 9%. In contrast, the frequencies calculated with the values for ${\mathrm{A}}_{\text{Designer}}$ and ${\mathrm{A}}_{\mathrm{DYNA}5}$ differ 24 and 16%, respectively, from the estimation based on the dynamic vehicular load tests (Table 3). The lateral to vertical ratio of frequencies for the ${\mathrm{A}}_{\text{Designer}}$ and the ${\mathrm{A}}_{\text{Exp}}$ models is 3.7 and 3.2, respectively. The last value is close to the test-observed ratio of 3.3. The fundamental vibration frequencies in the vertical direction were 3.95 and 4.14 Hz for the models with the values for ${\mathrm{A}}_{\text{Designer}}$ and ${\mathrm{A}}_{\text{Exp}}$, respectively. These values have a difference of around 15% with respect to those determined with the dynamic vehicular load tests (Table 3).

The lateral displacements for the lateral load tests and the static vehicle load tests were compared for all sites. Fig. 13 shows the plots for the lateral load tests in sites PV1, PV2, and VB. Fig. 13 shows the plots for Arrays I and II of the static vehicle load tests at sites PI, PV1, and VB.

The lateral displacement at the top of column B for site PV2 was 1.8 times that corresponding to site PV1, which is comparable in terms of lateral load applied, height, and superstructure width (three traffic lanes). This might be attributed to the flexural cracking in the column, the cracking of the grout joint, the possibility of some voids in joint, the effect of the superstructure on the behavior of the column, or a combination of all four.

The deflected shape of column B in site VB showed a top displacement that was 61 and 79% of the corresponding displacement in sites PV1 and PV2. The difference was due to a shorter column, thus, a smaller overturning moment ($\mathrm{5,205}\mathrm{kN}·\mathrm{m}$). The lateral displacements measured at the top of column B for Array I of the static vehicle tests in site VB were 35% larger than those measured at the same height and under the same load condition for site PV1. A similar comparison for Array II of the static vehicle tests showed that the displacements in sites PI and VB were 400 and 212% larger, respectively, than those at site PV1.

Furthermore, the asymmetric load distribution of Arrays I and II (Fig. 17) resulted in lateral displacements of the columns that were much larger than those measured during the lateral load tests. Static vehicle load tests with Arrays I and II indicate that the box girder with the smallest displacements is the one in site PV1, which had asymmetric flanges and three traffic lanes. In contrast, the superstructure with symmetric flanges and two traffic lanes at site PI was the most deformable.

The effect of increasing the number of trucks may be seen by comparing the plots for Arrays I and II measured at sites PV1 and VB. The lateral displacement measured at the top of column B for the Array II load configuration in sites PV1 and VB was 1.1 and 2.4 times, respectively, than that measured for Array I. Note that Array II included four trucks in site PV1 and six trucks in site VB. Array I involved two trucks at both test sites. The increment in lateral displacement suggests that at least four trucks should be considered if the structural design is dominated by the live load condition.

The initial flexural stiffness of column B was similar in sites PV1, PV2, and VB. In contrast, the stiffness of column B in site PI was around 6 times smaller. Indeed, the larger flexibility of column B in site PI resulted in much larger lateral displacements than those at other test sites. Furthermore, the circulation of loaded trucks along the two-lane section in site PI induced larger vibrations than those observed in the three-lane testing sites. The vibrations in site PI resulted in the oscillation of light posts to the point of generating discomfort and even a sense of insecurity in at least one of the truck drivers. It is suggested that the stiffness of columns supporting elevated viaducts be checked to avoid uncomfortable vibrations.