Bridges and buildings are often supported on deep foundations. These foundations consist of groups of piles coupled together by concrete pile caps. These pile caps, which are often massive and deeply buried, would be expected to provide significant resistance to lateral loads. However, practical procedures for computing the resistance of pile caps to lateral loads have not been developed, and, for this reason, cap resistance is usually ignored. Neglecting cap resistance results in estimates of pile group deflections and bending moments under load that may exceed the actual deflections and bending moments by 100 % or more. Advances could be realized in the design of economical pile-supported foundations, and their behavior more accurately predicted, if the cap resistance can be accurately assessed. This research provides a means of assessing and quantifying many important aspects of pile group and pile cap behavior under lateral loads. The program of work performed in this study includes developing a full-scale field test facility, conducting approximately 30 lateral load tests on pile groups and pile caps, performing laboratory geotechnical tests on natural soils obtained from the site and on imported backfill materials, and performing analytical studies. A detailed literature review was also conducted to assess the current state of practice in the area of laterally loaded pile groups. A method called the "group-equivalent pile" approach (abbreviated GEP) was developed for creating analytical models of pile groups and pile caps that are compatible with established approaches for analyzing single laterally loaded piles. A method for calculating pile cap resistance-deflection curves (p-y curves) was developed during this study, and has been programmed in the spreadsheet called PYCAP. A practical, rational, and systematic procedure was developed for assessing and quantifying the lateral resistance that pile caps provide to pile groups. Comparisons between measured and calculated load-deflection responses indicate that the analytical approach developed in this study is conservative, reasonably accurate, and suitable for use in design. The results of this research are expected to improve the current state of knowledge and practice regarding pile group and pile cap behavior. / Ph. D.

Pile caps are used in foundation design to aid multiple single piles to act as a pile group to resist lateral forces that may cause overturning moments. The pile cap and pile group resist these forces by pile-soil-pile interaction, base and side friction along the pile cap-backfill interface, and passive earth resistance. Passive earth resistance has been neglected in design due to a limited amount of full-scale testing. This research presents the results of a combination of hydraulic actuator and eccentric-mass shaker full-scale testing of a pile cap with loose silty sand backfill to quantify the contribution of the passive earth resistance to the lateral force resistance. The test cap is 1.12 m tall and 5.18 x 3.05 m in plan view, connecting 12 steel pipe piles (324mm O.D) placed in a 4 x 3 pattern with center-to-center spacing of 4.4 and 3.3 pile-diameters in the long and short dimensions, respectively. The hydraulic actuator applied a static load to the system (backfill + pile group) while the eccentric-mass shaker introduced cyclic and dynamic loading to the system. The passive earth resistance accounted for approximately 22% of the total system resistance, with piles contributing approximately 78%. Furthermore, the results produce general correlations between cyclic and dynamic effects on degradation of the backfill provided by the testing and soil characteristics obtained, including target (static) displacement, dynamic displacement amplitude, stiffness, and damping. The dynamic displacement amplitudes during the eccentric mass shaker tests typically ranged between .4 and 2 mm for frequencies between 5 and 9.5 Hz representing behavior under reloading conditions rather than virgin loading conditions. Generally, the presence of the loose silty sand backfill nearly doubled the dynamic stiffness of the pile cap. The stiffness of the backfill and pile cap combined was typically between 100 and 200 kN/mm for frequencies between 4 and 8 Hz, while the stiffness for the backfill alone was typically a decreasing trend between 100 and 40 kN/mm for the same frequency range. The overall isolated loose silty sand damping ratio shows a general increasing trend with values from 32% to 55% for frequencies 3 and 8 Hz.

Correct understanding of passive force behavior is particularly key to lateral evaluations of bridges because plastic deformation of soil backfill is vital to dissipation of earthquake energy and thermally-induced stresses in abutments. Only recently have studies investigated the effects of skew on passive force. Numerical modeling and a handful of skewed abutment tests performed in sand backfill have found reduced passive force with increasing skew, but previous to this study no skewed tests had been performed in gravel or Geosynthetic Reinforced Soil (GRS) backfills. The goal of this study was to better understand passive force behavior in non-skewed and skewed abutments with gravel and GRS backfills. Prior to this study, passive pressures in a GRS integrated approach had not been investigated. Gravel backfills also lack extensive passive force tests.Large-scale testing was performed with non-skewed and 30° skewed abutment configurations. Two tests were performed at each skew angle, one with unconfined gravel backfill and one with GRS backfill, for a total of four tests. The test abutment backwall was 11 ft (3.35 m) wide, non-skewed, and 5.5 ft (1.68 m) high and loaded laterally into the backfill. However, due to actuator loading constraints, all tests except the non-skewed unconfined gravel test were performed to a backfill height of 3.5 ft (1.07 m). The passive force results for the unconfined gravel test was scaled to a 3.5 ft (1.07 m) height for comparison.Test results in both sets of backfills confirmed previous findings that there is significant reduction in passive force with skewed abutment configurations. The reduction factor was 0.58 for the gravel backfill and 0.63 for the GRS backfill, compared to the predicted reduction factor of 0.53 for a 30° skew. These results are within the scatter of previous skewed testing, but could indicate that slightly higher reduction factors may be applicable for gravel backfills. Both backfills exhibited greater passive strength than sand backfills due to increased internal friction angle and unit weight. The GRS backfill had reduced initial stiffness and only reached 79% to 87% of the passive force developed by the unreinforced gravel backfill. This reduction was considered to be a result of reduced interface friction due to the geotextile. Additionally, the GRS behaved more linearly than unreinforced soil. This backfill elasticity is favorable in the GRS-Integrated Bridge System (GRS-IBS) abutment configuration because it allows thermal movement without developing excessive induced stresses in the bridge superstructure.

The effects of seismic forces and thermal expansion on bridge performance necessitate an accurate understanding of the relationship between passive force and backwall deflection. In past case studies, skewed bridges exhibited significantly more damage than non-skewed bridges. These findings prompted studies involving numerical modeling, lab-scale tests, and large-scale tests that each showed a dramatic reduction in passive force with increased skew. Using these results, a correlation was developed between peak passive force and backwall skew angle. The majority of these tests had length to height ratios of 2.0; however, for several abutments in the field, the length to height ratio might be considerably higher than 2.0. This change in geometry could potentially affect the validity of the previously found passive force reduction correlation. To explore this issue, laterally loaded, large-scale pile cap tests were performed with densely compacted sand at a length of 11 ft (3.35 m) and a height of 3 ft (0.91 m), resulting in a length to height ratio of 3.7. The backwall interface was adjusted to fit three various skew angles including: 0°, 15° and 30°. The behavior of both the pile cap and adjacent soil backfill were monitored under these conditions. The peak passive force for the 15° and 30° tests were found to be 71% and 45%, respectively, of the peak passive force for the 0° skew test. These findings are relatively consistent with previously performed tests. Passive forces peaked at deflections between 2% and 5% of the backwall height, decreasing with skew angle. All skews exhibited a log spiral failure plane that transitioned into a linear plane. These results also agreed with previously reported values for large-scale passive force-deflection tests. Rotation of the pile cap was detected in the direction opposite to the skew. Higher pressures were found to be on both corners of the pile cap than in the middle portion, as is suggested by the elastic theory.

Skewed bridges have exhibited poorer performance during lateral earthquake loading in comparison to non-skewed bridges (Apirakvorapinit et al. 2012; Elnashai et al. 2010). Results from numerical modeling by Shamsabadi et al. (2006), small-scale laboratory tests by Rollins and Jessee (2012), and several large-scale tests performed by Rollins et al. at Brigham Young University (Franke 2013; Marsh 2013; Palmer 2013; Smith 2014; Frederickson 2015) led to the proposal of a reduction curve used to determine a passive force skew reduction factor depending on abutment skew angle (Shamsabadi and Rollins 2014). In all previous tests, a uniform longitudinal load has been applied to the simulated bridge abutment. During seismic events, however, it is unlikely that bridge abutments would experience pure longitudinal loading. Rather, an inclined loading situation would be expected, causing rotation of the abutment backwall into the backfill. In this study, a large-scale test was performed where inclined loading was applied to a 30° skewed bridge abutment with sand backfill and compared to a baseline test with uniform loading and a non-skewed abutment. The impact of rotational force on the passive resistance of the backfill and the skew adjust factor was then evaluated. It was determined that inclined loading does not have a significant effect on the passive force skew reduction factor. However, the reduction factor was somewhat higher than predicted by the proposed reduction curve from Shamsabadi and Rollins 2014. This can be explained by a reduction in the effective skew angle caused by the friction between the side walls and the back wall. The inclined loading did not change the amount of movement required to mobilize passive resistance with ultimate passive force developing for displacements equal to 3 to 6% of the wall height. The rotation of the pile cap due to inclined loading produced higher earth pressure on the obtuse side of the skew wedge, as was expected.These findings largely resolve the concern that inclined loading situations during an earthquake may render the proposed passive force skew reduction curve invalid. We suggest that the proposed reduction curve remains accurate during inclined loading and should be implemented in current codes and practices to properly account for skew angle in bridge design.

Skewed bridges have exhibited poorer performance during lateral earthquake loading in comparison to non-skewed bridges (Apirakvorapinit et al. 2012; Elnashai et al. 2010). Results from numerical modeling by Shamsabadi et al. (2006), small-scale laboratory tests by Rollins and Jessee (2012), and several large-scale tests performed by Rollins et al. at Brigham Young University (Franke 2013; Marsh 2013; Palmer 2013; Smith 2014; Frederickson 2015) led to the proposal of a reduction curve used to determine a passive force skew reduction factor depending on abutment skew angle (Shamsabadi and Rollins 2014). In all previous tests, a uniform longitudinal load has been applied to the simulated bridge abutment. During seismic events, however, it is unlikely that bridge abutments would experience pure longitudinal loading. Rather, an inclined loading situation would be expected, causing rotation of the abutment backwall into the backfill. In this study, a large-scale test was performed where inclined loading was applied to a 30 skewed bridge abutment with sand backfill and compared to a baseline test with uniform loading and a non-skewed abutment. The impact of rotational force on the passive resistance of the backfill and the skew adjust factor was then evaluated. It was determined that inclined loading does not have a significant effect on the passive force skew reduction factor. However, the reduction factor was somewhat higher than predicted by the proposed reduction curve from Shamsabadi and Rollins 2014. This can be explained by a reduction in the effective skew angle caused by the friction between the side walls and the back wall. The inclined loading did not change the amount of movement required to mobilize passive resistance with ultimate passive force developing for displacements equal to 3 to 6% of the wall height. The rotation of the pile cap due to inclined loading produced higher earth pressure on the obtuse side of the skew wedge, as was expected.These findings largely resolve the concern that inclined loading situations during an earthquake may render the proposed passive force skew reduction curve invalid. We suggest that the proposed reduction curve remains accurate during inclined loading and should be implemented in current codes and practices to properly account for skew angle in bridge design.

The main topic of this thesis concerns the behavior of concrete pile cap supported by four piles with two varying positions of longitudinal reinforcements. The positions include top of piles and bottom of the pile cap. For this purpose, non-linear finite element models of a pile cap are created using software ATENA 3D. The goal was to observe which position of reinforcement yields the higher bearing capacity and to observe the failure modes in the models. To achieve the above goals, a short review of theoretical background concerning shear phenomena is performed. This, in order to enhance the knowledge regarding shear stresses, shear transfer mechanism, factors affecting shear capacity, modes of shear failure and relate them to the behavior of pile cap. Furthermore, the calculation of shear resistance capacity based on Eurocode 2 using strut and tie method and sectional approach is presented. The numerical analysis started by creating four pile cap models in ATENA 3D. The difference between the models being the position and ratio of longitudinal reinforcement. The purpose behind two reinforcement ratios were to observe the behavior of pile cap model in two cases: a) when failure occurs prior to yielding of reinforcement; b) when failure occurs while reinforcement is yielding. The models are then analyzed using software ATENA Studio. The results revealed that placing the reinforcement on top of piles in case (a) increased the capacity of the model by 23.5 % and in case (b) increased the capacity by 18.5 %. This because the tensile stresses were found to be concentrated on top of piles rather than the bottom of the pile cap. The final failure mode in the model with top reinforcement position was crushing of the inclined compressive strut at the node beneath the column and in the model with bottom reinforcement position, the splitting of the compressive strut due to tensile stresses developed perpendicular to the inclined strut. The potential advantage of placing the reinforcement at the bottom were a better crack control in serviceability limit state and a slightly less fragile failure mode compared to the top position of reinforcement. A parametric study was performed in the model as well to observe the effects of various parameters on the results obtained. It was found that fracture energy had the most significant effect on the results obtained. Finally, a comparison between the results of numerical analysis and analytical design approaches based on strut and tie method and sectional approach was performed. The comparison reveals that the design values obtained based on strut and tie method for the model were very conservative. In particular, the equation for the strength of inclined compressive strut based on Eurocode 2 was very general. / Det huvudsakliga ämnet för den här avhandlingen handlar om beteendet hos pålfundament som stöds av fyra pålar med två olika positioner av längsgående armering. Positionerna inkluderar toppen av pålarna och botten av slagdynan. För detta ändamål skapas icke-linjära finita elementmodeller av en slagdyna med mjukvaran ATENA 3D. Målet var att observera vilket armeringsläge som ger den högre bärkapaciteten och att identifiera brottmekanismen i modellerna. För att uppnå ovanstående mål utförs en kort genomgång av teoretisk bakgrund rörande skjuvningsfenomen. Detta för att förbättra kunskapen om skjuvspänningar, skjuvöverföringsmekanism, faktorer som påverkar skjuvkapacitet, skjuvbrott och relaterar dem till beteendet hos slagdynan. Beräkningen av skjuvmotståndet baserad på Eurocode2 med hjälp av Srut and tie-metod och sektionsmetod. Den numeriska analysen började med att skapa fyra pålfundament i ATENA 3D. Skillnaden mellan modellerna är positionen och förhållandet mellan längsgående armering. Syftet bakom två armeringsförhållanden var att observera beteendet hos slagdynan i två fall: a) när brott inträffar innan armering plasticeras; b) när brott inträffar medan armeringen plasticeras. Modellerna analyseras sedan med hjälp av programvaran ATENA Studio. Resultaten visade att placering av armeringen ovanpå pålarna i fall a) ökade modellens kapacitet med 23,5% och i fall (b) ökade kapaciteten med 18,5%. Detta på grund av att dragspänningarna visade sig vara koncentrerade på toppen av pålarna snarare än på botten av slagdynan. Det slutliga brottet i modellen med topparmeringsposition var krossning av det lutande tryckstaget vid noden under pelaren. I modellen med bottenarmeringsposition delades kompressionsstaget på grund av dragspänningar vinkelrätt mot det lutande staget. The potential advantage of placing the reinforcement at the bottom were a better crack control and slightly less fragile failure mode compared to the top position of reinforcement. En parametrisk studie genomfördes också i modellen för att observera effekterna av olika parametrar på de erhållna resultaten. Det visade sig att brottenergi hade den mest signifikanta effekten på de erhållna resultaten. Slutligen genomfördes en jämförelse mellan resultaten från numerisk analys och analytiska designmetoder baserade på strut and tie-metoden och sektionsmetoden. Jämförelsen avslöjar att de designvärden som erhölls baserat på strut and tie-metoden för modellen var mycket konservativa. I synnerhet var ekvationen för kapaciteten hos det lutande tryckstag baserad på Eurocode 2 mycket generell.

Skewed bridges have exhibited poorer performance during lateral earthquake loading when compared to non-skewed bridges (Apirakvorapinit et al. 2012; Elnashai et al. 2010). Results from small-scale laboratory tests by Rollins and Jessee (2012) and numerical modeling by Shamsabadi et al. (2006) suggest that skewed bridge abutments may provide only 35% of the non-skewed peak passive resistance when a bridge is skewed 45°. This reduction in peak passive force is of particular importance as 40% of the 600,000 bridges in the United States are skewed (Nichols 2012). Passive force-deflection results based on large-scale testing for this study largely confirm the significant reduction in peak passive resistance for abutments with longitudinal reinforced concrete wingwalls. Large-scale lateral load tests were performed on a non-skewed and 45° skewed abutment with densely compacted sand backfill. The 45° skewed abutment experienced a 54% reduction in peak passive resistance compared to the non-skewed abutment. The peak passive force for the 45° skewed abutment was estimated to occur at 5.0% of the backwall height compared to 2.2% of the backwall height for the non-skewed abutment. The 45° skewed abutment displayed evidence of rotation, primarily pushing the obtuse side of the abutment into the backfill, significantly more than the non-skewed abutment as it was loaded into the backfill. The structural and geotechnical response of the wingwalls was also monitored during large-scale testing. The wingwall on the obtuse side of the 45° skewed abutment experienced nearly 6 times the amount of horizontal soil pressure and 7 times the amount of bending moment compared to the non-skewed abutment. Pressure and bending moment distributions are provided along the height of the wingwall and indicate that the maximum moment occurs approximately 20 in (50.8 cm) below the top of the wingwall. A comparison of passive force per unit width suggests that MSE wall abutments provide 60% more passive resistance per unit width compared to reinforced concrete wingwall and unconfined abutment geometries at zero skew. These findings suggest that changes should be made to current codes and practices to properly account for skew angle in bridge design.

A series of lateral load tests were performed on a full-scale pile cap with three different backfill conditions, namely: with no backfill present, with densely compacted clean sand in place, and with loosely compacted clean sand in place. In addition to being displaced under a static loading, the pile cap was subjected to low frequency, small displacement loading cycles from load actuators and higher frequency, small displacement, dynamic loading cycles from an eccentric mass shaker. The passive earth pressure from the backfill was found to significantly increase the load capacity of the pile cap. At a displacement of about 46 mm, the loosely and densely compacted backfills increased the total resistance of the pile cap otherwise without backfill by 50% and 245%, respectively. The maximum passive earth pressure for the densely compacted backfill occurred at a displacement of approximately 50 mm, which corresponds to a displacement to pile cap height ratio of 0.03. Contrastingly passive earth pressure for the loosely compacted backfill occurred at a displacement of approximately 40 mm. Under low and high frequency cyclic loadings, the stiffness of the pile cap system increased with the presence of the backfill material. The loosely compacted backfill generally provided double the stiffness of the no backfill case. The densely compacted backfill generally provided double the stiffness of the loosely compacted sand, thus quadrupling the stiffness of the pile cap relative to the case with no backfill present. Under low frequency cyclic loadings, the damping ratio of the pile cap system decreased with cap displacement and with increasing stiffness of backfill material. After about 20 mm of pile cap displacement, the average damping ratio was about 18% with the looser backfill and about 24% for the denser backfill. Under higher frequency cyclic loadings, the damping ratio of the pile cap system was quite variable and appeared to vary with frequency. Damping ratios appear to peak in the vicinity of the natural frequency of the pile cap system for each backfill condition. On the whole, damping ratios tend to range between 10 and 30%, with an average of about 20% for the range of frequencies and displacement amplitudes occurring during the tests. The similar amount of damping for different ranges of frequency suggests that dynamic loadings do not appreciably increase the apparent resistance of the pile cap relative to slowly applied cyclic loadings.

Passive force-deflection behavior for densely compacted backfills must be considered in bridge design to ensure adequate resistance to both seismic and thermally induced forces. Current codes and practices do not distinguish between skewed and non-skewed bridge abutment geometries; however, in recent years, numerical models and small-scale, plane-strain laboratory tests have suggested a significant reduction in passive force for skewed bridge abutments. Also, various case studies have suggested higher soil stresses might be experienced on the acute side of the skew angle. For these reasons, three large-scale tests were performed with abutment skew angles of 0, 15 and 30 degrees using an existing pile cap [11-ft (3.35-m) wide by 15-ft (4.57-m) long by 5.5-ft (1.68-m) high] and densely compacted sand backfill confined by MSE wingwalls. These tests showed a significant reduction in passive force (approximately 38% as a result of the 15 degree skew angle and 51% as a result of the 30° skew angle. The maximum passive force was achieved at a deflection of approximately 5% of the backwall height; however, a substantial loss in the rate of strength gain was observed at a deflection of approximately 3% of the backwall height for the 15° and 30° skew tests. Additionally, the soil stiffness appears to be largely unaffected by skew angle for small displacements. These results correlate very well with data available from numerical modeling and small-scale lab tests. Maximum vertical backfill displacement and maximum soil pressure measured normal to the skewed backwall face were located on the acute side of the skew for the 15° and 30° skew test. This observation appears to be consistent with observations made in various case studies for skewed bridge abutments. Also, the maximum outward displacement of the MSE wingwalls was located on the obtuse side of the skew. These findings suggest that changes should be made to current codes and practices to properly account for skew angle in bridge design.