Dissertations / Theses on the topic 'P-multiplier'

In recent years, there has been an increase in demand for unified field multipliers for Elliptic Curve Cryptography in the electronics industry because they provide flexibility for customers to choose between Prime (GF(p)) and Binary (GF(2")) Galois Fields. Also, having the ability to carry out arithmetic over both GF(p) and GF(2") in the same hardware provides the possibility of performing any cryptographic operation that requires the use of both fields. The unified field multiplier is relatively future proof compared with multipliers that only perform arithmetic over a single chosen field. The security provided by the architecture is also very important. It is known that the longer the key length, the more susceptible the system is to differential power attacks due to the increased amount of data leakage. Therefore, it is beneficial to design hardware that is scalable, so that more data can be processed per cycle. Another advantage of designing a multiplier that is capable of dealing with long word length is improvement in performance in terms of delay, because less cycles are needed. This is very important because typical elliptic curve cryptography involves key size of 160 bits. A novel unified field radix-4 multiplier using Montgomery Multiplication for the use of G(p) and GF(2") has been proposed. This design makes use of the unexploited state in number representation for operation in GF(2") where all carries are suppressed. The addition is carried out using a modified (4:2) redundant adder to accommodate the extra 1 * state. The proposed adder and the partial product generator design are capable of radix-4 operation, which reduces the number of computation cycles required. Also, the proposed adder is more scalable than existing designs.

Installing load bearing piles within the reinforcement zone of mechanically stabilized earth (MSE) retaining walls is common practice in the construction industry. Bridge abutments are often constructed in this manner to adapt to increasing right-of-way constraints, and must be capable of supporting horizontal loads imposed by, traffic, earthquakes, and thermal expansion and contraction. Previous researchers have concluded that lateral pile resistance is reduced when pile are placed next to MSE walls but no design codes have been established to address this issue. Full –scale testing of statically applied lateral loads to four 24”x0.5” pipe piles, and cyclically applied lateral load to four 12.75”x0.375” pipe piles placed 1.5-5.3 pile diameters behind a 20-foot MSE wall was performed. The MSE wall was constructed using 5’x10’ concrete panels and was supported with ribbed strip and welded wire streel reinforcements. The computer software LPILE was used to back-calculate P-multipliers for the 24” piles. P-multipliers are used to indicate the amount of reduction in lateral resistance the piles experience due to their placement near the MSE wall. Previous researchers have proposed that any pile spaced 3.9 pile diameters (D) or more away from the MSE wall will have a P-multiplier of 1; meaning the pile experiences no reduction in lateral resistance due to its proximity to the wall. P-multipliers for piles spaced closer than 3.9D away from the wall decrease linearly as distance from the wall decreases. P-multipliers for the 24” piles spaced 5.1D, 4.1D, 3.0D, and 2.0D were 1, 0.84, 0.55, and 0.44 respectively. Lateral resistance of the 12.75” cyclically loaded piles decreased as the number of loading cycles increased. Lateral resistance of the piles when loads were applied in the direction of the wall was less than the lateral resistance of the piles when loads were applied away from the wall at larger pile head loads. The maximum tensile force experienced by the soil reinforcements generally occurred near the wall side of the pile face when the lateral loads were applied in the direction of the wall. Behind the pile, the tensile force decreased as the distance from the wall increased. Equation 5-4, modified from Rollins (2018) was found to be adequate for predicting the maximum tensile force experienced by the ribbed strip reinforcements during the static loading of the 24” pipe piles, particularly for lower loads. About 65% of the measured forces measured in this study fell within the one standard deviation boundary of the proposed equation.

Full scale lateral load testing was performed on four 12.75x0.375 pipe piles spaced at 3.9, 2.9, 2.8, and 1.7 pile diameters behind an MSE wall which was constructed for this research to determine appropriate reduction factors for lateral pile resistance based on pile spacing behind the back face of the wall. The load induced on eight soil reinforcements located at various transverse distances from the pile and at different depths was monitored to determine the relationship between lateral load on the pile and load induced in the reinforcement. Each pile was loaded towards the wall in 0.25 in. increments to a total deflection of 3.0 in. Additionally, wall panel displacement was also monitored to determine if it remained in acceptable bounds. The results of the research indicate that pile resistance tends to decrease as spacing decreases. P-multipliers for the 3.9, 2.9, 2.8, 1.7D tests were found to be 1.0, 1.0, 1.0, and 0.5, respectively using back-analysis with the computer model LPILE. However, these multipliers are higher than expected based on previous testing and research. Piles spaced further than 3.8D can be assumed to have no interaction with the wall. The resistance of piles spaced closer to the wall than 3.8D can be modeled in LPILE using a p-multiplier less than 1.0. The reinforced backfill can be modeled in LPILE using the API Sand (1982) method with a friction angle of 31º and a modulus of approximately 60 pci when a surcharge of 600 psf is applied. If no surcharge is applied, a friction angle of 39º and modulus of 260 pci is more appropriate. Maximum wall panel displacement was highest for the 2.8D test and was 0.35 in. at 3.0 in. of pile head displacement. For all the other tests, the maximum wall displacement at 3.0 in. of pile head displacement was similar and was approximately 0.15 inches. Induced load in the soil reinforcement increases with depth to the 2nd or 3rd layer of reinforcement after which it decreases. Induced load in the reinforcement increases as pile spacing decreases. Induced load in the reinforcement decreases rapidly with increased transverse distance from the pile. Induced load in the reinforcement can be estimated using a regression equation which considers the influence of pile load, pile spacing behind the wall, reinforcement depth or vertical stress, and transverse spacing of the reinforcement.

A team from Brigham Young University and I performed full-scale lateral load tests on individual and grouped 12.75x0.375 inch pipe piles spaced at varying distances behind an MSE wall. The individually loaded pile which acted as a control was spaced at 4.0 pile diameters from the wall face, and the three grouped piles which were loaded in unison were spaced at 3.0, 2.8, and 1.8 pile diameters from the wall face and transversely spaced at 4.7 pile diameters center-to-center. The purpose of these tests was to determine the extent of group effects on lateral pile resistance, induced loads in soil reinforcements, and MSE wall panel deflections compared to those previously observed in individually laterally loaded piles behind MSE walls. The computer model LPILE was used in my analysis of the measured test data. The p-multipliers back-calculated with LPILE for the grouped piles were 0.25, 0.60, and 0.25 for the grouped piles spaced at 3.0, 2.8, and 1.8 pile diameters from the wall, respectively. These values are lower than that predicted for piles at the same pile-to-wall spacings using the most recent equation for computing p-multipliers. I propose the use of an additional p-multiplier for grouped piles near an MSE wall, a group-effect p-multiplier, to account for discrepancies between individual and grouped pile behaviors. The group effect p-multipliers were 0.35, 0.91, and 0.74 for the grouped piles spaced at 3.0, 2.8, and 1.8 pile diameters from the wall, respectively. The average group-effect p-multiplier was 0.66. Additionally, I used LPILE to analyze test data from Pierson et al. (2009), who had previously performed full-scale lateral load tests of individual and grouped shafts. In said analysis, the group of three 3-foot diameter concrete shafts spaced at 2.0 shaft diameters from the wall face and transversely spaced at 5.0 shaft diameters center-to-center had an average group effect p-multiplier of 0.78. As in previous studies, the induced forces in soil reinforcements in this study were greatest either near the locations of the test piles or at the MSE wall face. The most recent equation for calculating the maximum induced force in a soil reinforcement strip was reasonably effective in predicting the measured maximum loads when superimposed between the test piles, with 65% and 85% of the data points falling within the one and two standard deviation boundaries, respectively, of the original data used to develop the equation. Deflection of the MSE wall panels was greater during the grouped pile test than was previously observed for individually loaded piles under similar pile head deflections--with a maximum wall deflection of 0.31 inch compared to the previous average of 0.10 inch for pile head deflections of about 1.25 inches.

Il lavoro tratta gli effetti delle interazioni sociali tra compagni di scuola o di classe (c.d. peer effects) sugli apprendimenti degli studenti delle scuole medie. Il periodo di frequenza della scuola media rappresenta un momento critico nello sviluppo dell’adolescente che passa molto tempo con i compagni (a scuola e fuori da scuola) determinando forti legami di amicizia che ne influenzano lo sviluppo. Nel primo e nel secondo capitolo si tratta dell’effetto delle interazioni sociali tra studenti nativi e non nativi sull’apprendimento. Il terzo capitolo analizza il comportamento di cheating durante gli esami ufficiali come una forma di collaborazione che scaturisce da interazioni sociali. Il lavoro contribuisce alla letteratura esistente identificando gli effetti delle interazioni sociali con metodi innovativi e fornendo un’interpretazione stilizzata dei risultati mediante semplici modelli teorici. La tesi utilizza una banca dati innovativa che unisce i risultati dei test Invalsi in matematica e italiano (Esame Finale del I Ciclo, e Programma di Valutazione Nazionale, a.s. 2007-08, 2008-09, 2010-11), a dati amministrativi sulle scuole e dati censuari sulla popolazione (Censimento 2001). I risultati mostrano che le interazioni sociali influenzano in maniera significativa i risultati scolastici degli studenti.
I focus on social interactions among junior high school students attending the same class or the same school. Junior high school is generally considered by educational psychologists as the period in which friendships ties are usually formed and interactions with school mates take a relevant part of students’ time at school and outside school. In first and in the second chapter I focus on the effect on attainment of social interactions between native and non-native students. The third chapter deals with students’ cheating as a form of social interaction among classmates taking an official exam. The thesis contributes to the existing literature in proposing different empirical strategy to identify social interactions parameters and linking the results to stylized theoretical frameworks to shed light on the possible social mechanisms driving the estimated effects. The three chapters exploit rich and newly available datasets combining test score results in Math and Language from INVALSI (First Cycle Final Exam and National Evaluation Program, s.y. 2007-08, 2008-09, 2010-11), school administrative records, and the Italian Population Census Survey 2001. The results of the research demonstrate a strong role played by social interactions among school mates in affecting students’ attainment.

Pile foundations for bridges must often resist lateral loads produced by earthquakes and thermal expansion and contraction of the superstructure. Right-of-way constraints near bridge abutments are leading to an increased use of mechanically stabilized earth (MSE) walls below the abutment. Previous research has shown that lateral pile resistance can be greatly reduced when piles are placed close to MSE walls but design codes do not address this issue. A full-scale MSE wall was constructed and 24 lateral load tests were conducted on pipe, square and H piles spaced at distances of about 2 to 5 pile diameters from the back face of the wall. The MSE wall was constructed using welded-wire grid and ribbed strip inextensible reinforcements. This paper focuses on four lateral load tests conducted on steel pipe piles located behind a 20-ft section of MSE wall reinforced with welded-wire grids. Results showed that measured lateral resistance decreases significantly when pipe piles are located closer than about 4 pile diameters from the wall. LPILE software was used to back-calculate P-multipliers that account for the reduced lateral resistance of the pile as a function of normalized spacing from the wall. P-multipliers for this study were 0.95, 0.68, and 0.3 for piles spaced 4.3, 3.4 and 1.8 pile diameters from the wall, respectively. Based on results from this study and previous data, lateral pile resistance is relatively unaffected (p-multiplier = 1.0) for piles spaced more than approximately 3.9 pile diameters (3.9D) from the MSE wall. For piles spaced closer than 3.9D, the p-multiplier decreased linearly as distance to the wall decreased. P-multipliers were not affected by differences in reinforcement length to height (L/H) ratio or reinforcing type. Lateral pile loads induce tensile forces in the soil reinforcement such that, as pile load increases the maximum induced tensile force increases. Results also indicate that maximum tensile forces typically occurred in the soil reinforcement near the pile location. Past research results were combined with data from this study and a statistical regression analysis was performed using all data associated with welded-wire grid reinforcements. A regression equations was developed to predict the peak induced tensile force in welded-wire grids based on independent variables including lateral pile load, normalized pile distance (S/D), transverse distance (T/D), L/H ratio, and vertical stress. The equation has an R2 value of 0.79, meaning it accounts for approximately 79% of variation for all welded-wire grid reinforcements tested to date.

Three progressively larger statnamic lateral load tests were performed on a 2.59 m diameter drilled shaft foundation after the surrounding soil was liquefied using down-hole explosive charges. An attempt to develop p-y curves from strain data along the pile was made. Due to low quality and lack of strain data, p-y curves along the test shaft could not be reliably determined. Therefore, the statnamic load tests were analyzed using a ten degree-of-freedom model of the pile-soil system to determine the equivalent static load-deflection curve for each test. The equivalent static load-deflection curves had shapes very similar to that obtained from static load tests performed previously at the site. The computed damping ratio was 30%, which is within the range of values derived from the log decrement method. The computer program LPILE was then used to compute the load-deflection curves in comparison with the response from the field load tests. Analyses were performed using a variety of p-y curve shapes proposed for liquefied sand. The best agreement was obtained using the concave upward curve shapes proposed by Rollins et al. (2005) with a p-multiplier of approximately 8 to account for the increased pile diameter. P-y curves based on the undrained strength approach and the p-multiplier approach with values of 0.1 to 0.3 did not match the measured load-deflection curve over the full range of deflections. These approaches typically overestimated resistance at small deflections and underestimated the resistance at large deflections indicating that the p-y curve shapes were inappropriate. When the liquefied sand was assumed to have no resistance, the computed deflection significantly overestimated the deflections from the field tests.

Bridges often use pile foundations behind MSE walls to help resist lateral loading from seismic and thermal expansion and contraction loads. Overdesign of pile spacing and sizes occur owing to a lack of design code guidance for piles behind an MSE wall. However, space constraints necessitate the installation of piles near the wall. Full scale lateral load tests were conducted on piles behind an MSE wall. This study involves the testing of four HP12X74 H-piles and four HSS12X12X5/16 square piles. The H-piles were tested with ribbed strip soil reinforcement at a wall height of 15 feet, and the square piles were tested with welded wire reinforcement at a wall height of 20 feet. The H-piles were spaced from the back face of the MSE wall at pile diameters 4.5, 3.2, 2.5, and 2.2. The square piles were spaced at pile diameters 5.7, 4.2, 3.1, and 2.1. Testing was based on a displacement control method where load increments were applied every 0.25 inches up to three inches of pile deflection. It was concluded that piles placed closer than 3.9 pile diameters have a reduction in their lateral resistance. P-multipliers were back-calculated in LPILE from the load-deflection curves obtained from the tests. The p-multipliers were found to be 1.0, 0.85, 0.60, and 0.73 for the H-piles spaced at 4.5, 3.2, 2.5, and 2.2 pile diameters, respectively. The p-multipliers for the square piles were found to be 1.0, 0.77, 0.63, and 0.57 for piles spaced at 5.7, 4.2, 3.1, and 2.1 pile diameters, respectively. An equation was developed to estimate p-multipliers versus pile distance behind the wall. These p-multipliers account for reduced soil resistance, and decrease linearly with distance for piles placed closer than 3.9 pile diameters. Measurements were also taken of the force induced in the soil reinforcement. A statistical analysis was performed to develop an equation that could predict the maximum induced reinforcement load. The main parameters that went into this equation were the lateral pile load, transverse distance from the reinforcement to the pile center normalized by the pile diameter, spacing from the pile center to the wall normalized by the pile diameter, vertical stress, and reinforcement length to height ratio where the height included the equivalent height of the surcharge. The multiple regression equations account for 76% of the variation in observed tensile force for the ribbed strip reinforcement, and 77% of the variation for the welded wire reinforcement. The tensile force was found to increase in the reinforcement as the pile spacing decreased, transverse spacing from the pile decreased, and as the lateral load increased.

Although it is well established that spacing of piles within a pile group influences the lateral load resistance of that group, additional research is needed to better understand trends for large pile groups (greater than three rows) and for groups in sand. A 15-pile group in a 3x5 configuration situated in sand was laterally loaded and data were collected to derive p-multipliers. A single pile separate from the 15-pile group was loaded for comparison. Results were compared to those of a similar test in clays. The load resisted by the single pile was greater than the average load resisted by each pile in the pile group. While the loads resisted by the first row of piles (i.e. the only row deflected away from all other rows of piles) were approximately equal to that resisted by the single pile, following rows resisted increasingly less load up through the fourth row. The fifth row consistently resisted more than the fourth row. The pile group in sand resisted much higher loads than did the pile group in clay. Maximum bending moments appeared largest in first row piles. For all deflection levels, first row moments seemed slightly smaller than those measured in the single pile. Maximum bending moments for the second through fifth rows appeared consistently lower than those of the first row at the same deflection. First row moments achieved in the group in sand appeared larger than those achieved in the group in clay at the same deflections, while bending moments normalized by associated loads appeared nearly equal regardless of soil type. Group effects became more influential at higher deflections, manifest by lower stiffness per pile. The single pile test was modeled using LPILE Plus, version 4.0. Soil parameters in LPILE were adjusted until a good match between measured and computed responses was obtained. This refined soil profile was then used to model the 15-pile group in GROUP, version 4.0. User-defined p-multipliers were selected to match GROUP calculated results with actual measured results. For the first loading cycle, p-multipliers were found to be 1.0, 0.5, 0.35, 0.3, and 0.4 for the first through fifth rows, respectively. For the tenth loading, p-multipliers were found to be 1.0, 0.6, 0.4, 0.37, and 0.4 for the first through fifth rows, respectively. Design curves suggested by Rollins et al. (2005) appear appropriate for Rows 1 and 2 while curves specified by AASHTO (2000) appear appropriate for subsequent rows.

Obiettivo di questo lavoro è studiare i fattori socio-economici responsabili del cambiamento nella distribuzione del reddito dovuto a un cambiamento nel contesto politico di riferimento, in Vietnam durante il periodo delle riforme. La metodologia adottata analizza i cambiamenti nella distribuzione del reddito sia a livello micro che a livello macro. A livello micro, l'analisi indaga sulle caratteristiche individuali e familiari da cui dipende il livello e la distribuzione della spesa. E' possibile inoltre valutare gli effetti diretti di cambiamenti nel quadro politico di riferimento. Il livello macro di analisi consente di individuare le caratteristiche strutturali della disuguaglianza nella distribuzione del reddito personale e di isolare anche gli effetti indiretti delle politiche. Gli strumenti analitici selezionati in questo studio sono un modello supply-driven, rappresentato da un modello di microsimulazione e un modello demand-driven, costituito dalla Matrice di Contabilità Sociale. In particolare, il modello di microsimulazione ha consentito la derivazione di una distribuzione controfattuale e la disaggregazione della variazione della disuguaglianza in Vietnam in: effetto di prezzo, effetto di una variazione della componente non osservata dei salari, effetto dovuto a cambiamenti nelle scelte occupazioni e effetti dovuti a cambiamenti nella popolazione. Utilizzando una nuova metodologia di scomposizione ad un livello microscopico dei moltiplicatori derivati dalla SAM, è stato possibile derivare e isolare tutti gli effetti diretti e indiretti di uno shock esogeno sulla distribuzione personale del reddito.
The aim of this work is to investigate the socio-economic factors that affect in income distribution changes caused by changes in the policy framework in Vietnam during the period of reforms. The adopted methodology analyzes policy induced changes in income distribution both at the micro and the macro level. At the micro level, the analysis of inequality can help identifying the socio-economic factors affecting the level of household expenditure and its distribution and evaluating direct effects of policies. The macro level identifies the structural characteristics of inequality and evaluates also the indirect effects of policies on the personal income distribution. The two analytical tools have been selected have been a supply driven model represented by the microsimulation model and a demand driven model, constituted by the Social Accounting Matrix. The microsimulation model allowed deriving a counterfactual distribution of income and disaggregating change in the Vietnamese income inequality into four effects: price effect, effect of a change in the unobservable component of wages, occupational choice effect and population effect. Using a new technique of decomposition of SAM-based multipliers in 'microscopic' detail, the macro model allowed deriving all the direct and indirect effects of an exogenous shock to personal income distribution.

A full scale MSE wall was constructed and piles were driven at various distances behind the wall. Lateral load testing was conducted and the performance of the pile, wall, and reinforcement were measured. The piles were 12.75 inch pipe piles, and the wall was reinforced with welded wire grid reinforcement. The objective of the testing was to characterize the relationship between the lateral pile resistance and the distance of the pile behind the back face of the MSE wall. Load-displacement curves are presented for the piles located behind the wall at 66 inches (5.3 diameters), 55 inches (4.3 diameters), 41 inches (3.2 diameters), and 24 inches (1.9 diameters). The lateral resistance of the piles decreases as the spacing behind the wall decreases. The results of the testing have been matched in LPILE using p-multipliers to reduce the lateral resistance. A curve has been developed showing the variation of p-multiplier with normalized pile spacing behind the wall, including data from previous studies. The curve suggests that a p-multiplier of 1 (no reduction in lateral resistance) can be used when the normalized distance from the back face of the wall to the center of the pile is at least 4 pile diameters. The p-multiplier decreases relatively linearly for smaller spacings.

Cette thèse étudie quelques problèmes d’analyse harmonique sur les groupes quantiques compacts. Elle consiste en trois parties. La première partie présente la théorie Lp élémentaire des transformées de Fourier, les convolutions et les multiplicateurs sur les groupes quantiques compacts, y compris la théorie de Hausdorff-Young et les inégalités de Young.Dans la seconde partie, nous caractérisons les opérateurs de convolution positifs sur un groupe quantique fini qui envoient Lp dans L2, et donnons aussi quelques constructions sur les groupes quantiques compacts infinis. La méthode pour étudier les états non-dégénérés fournit une formule générale pour calculer les états idempotents associés aux images deHopf, qui généralise un travail de Banica, Franz et Skalski. La troisième partie est consacrée à l’étude des ensembles de Sidon, des ensembles _(p) et des notions associées pour les groupes quantiques compacts. Nous établissons différentes caractérisations des ensembles de Sidon, et en particulier nous démontrons que tout ensemble de Sidon est un ensemble de Sidon fort au sens de Picardello. Nous donnons quelques liens entre les ensembles de Sidon, les ensembles _(p) et les lacunarités pour les multiplicateurs de Fourier sur Lp, généralisant un travail de Blendek et Michali˘cek. Nous démontrons aussi l’existence des ensembles de type _(p) pour les systèmes orthogonaux dans les espaces Lp non commutatifs, et déduisons les propriétés correspondantes pour les groupes quantiques compacts. Nous considérons aussi les ensembles de Sidon centraux, et nous prouvons que les groupes quantiques compacts ayant les mêmes règles de fusion et les mêmes fonctions de dimension ont des ensemble de Sidon centraux identiques. Quelques exemples sont aussi étudiés dans cette thèse. Les travaux présentés dans cette thèse se basent sur deux articles de l’auteur. Le premier s’intitule “Lp-improving convolution operators on finite quantum groups” et a été accepté pour publication dans Indiana University Mathematics Journal, et le deuxième est un travail intitulé “Lacunary Fourier series for compact quantum groups” et a été publié en ligne dans Communications in Mathematical Physics
This thesis studies some problems in the theory of harmonic analysis on compact quantum groups. It consists of three parts. The first part presents some elementary Lp theory of Fourier transforms, convolutions and multipliers on compact quantum groups, including the Hausdorff-Young theory and Young’s inequalities. In the second part, we characterize positive convolution operators on a finite quantum group G which are Lp-improving, and also give some constructions on infinite compact quantum groups. The methods for ondegeneratestates yield a general formula for computing idempotent states associated to Hopf images, which generalizes earlier work of Banica, Franz and Skalski. The third part is devoted to the study of Sidon sets, _(p)-sets and some related notions for compact quantum groups. We establish several different characterizations of Sidon sets, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets, _(p)-sets and lacunarities for Lp-Fourier multipliers, generalizing a previous work by Blendek and Michali˘cek. We also prove the existence of _(p)-sets for orthogonal systems in noncommutative Lp-spaces, and deduce the corresponding properties for compact quantum groups. Central Sidon sets are also discussed, and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central Sidon sets. Several examples are also included. The thesis is principally based on two works by the author, entitled “Lp-improvingconvolution operators on finite quantum groups” and “Lacunary Fourier series for compact quantum groups”, which have been accepted for publication in Indiana University Mathematics Journal and Communications in Mathematical Physics respectively

Liquefied natural gas (LNG) storage tanks are often supported by very large pile groups (≥ 100 piles). As these superstructures tend to be located along coastal areas, there is often a high risk of extreme lateral loading caused by either seismic, flooding or hurricane activity. In many cases, the foundation design can be governed by the required lateral resistance. At present, the responses of large pile groups subjected to lateral loading are not well understood. Published guidance for design is premised upon experimental testing of smaller pile groups (< 25 piles), and no additional commentary is provided to advise the design for groups of a larger scale. A typical approach for design of laterally loaded pile groups uses the beam on Winkler foundations method, where nonlinear p-y curves are reduced by a p-multiplier to account for the group effects. Alternatively, an average p-multiplier known as a group reduction factor (GRF) can be used. Chapter 1 details the study of using 3D continuum finite element (FE) models to measure the group effects in large pile groups using p-multipliers and GRF. Soil conditions, pile spacing, pile number, and pile head condition were varied to observe their effects. The study also looked at the effect of the circular configuration of pile groups used in LNG tank foundations. The design standards and prevailing methods were shown to overestimate trailing row p-multipliers for large pile groups, particularly with larger pile spacing. Based on the study data and published data, a predictive equation was proposed for estimating GRF of a laterally loaded large pile group. In addition, geotechnical engineers tend to evaluate the lateral responses of pile groups regardless of the presence of superstructures. It is not known whether this approach is suited for large infrastructure such as LNG storage tanks and their respective foundations. Chapter 2 captures the results from 3D finite element (FE) models used to observe the integrated tank and piled foundation behaviour and evaluate whether the current design approach used in practice is suitable. In addition, changes to soil-foundation stiffness, including varying soil conditions and pile spacing, were made to observe their effects. The results found that the foundation responses in the integrated model varied significantly from models which only considered the foundation. It was also found that the amount of LNG in the tank, soil conditions, and pile spacing also affected the lateral pile responses, particularly the leading and trailing piles.
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