Open Access
Curved beam through matrices associated with support conditions
(2020) Gimena Ramos, Faustino; Gonzaga Vélez, Pedro; Valdenebro García, José Vicente; Goñi Garatea, Mikel; Reyes-Rubiano, Lorena Silvana; Ingeniería; Ingeniaritza
Open Access
Application of the elastic curve equation for the verification of structures assimilable to continuous beams
(World Scientific Publishing, 2024) Gimena Ramos, Faustino; Gonzaga Vélez, Pedro; Goñi Garatea, Mikel; Valdenebro García, José Vicente; Senosiain Carasusan, María Aranzazu; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Institute on Innovation and Sustainable Development in Food Chain - ISFOOD
This paper analyzes the beam under isolated and uniform loads, extending this calculation towards the structural type of the continuous beam, by means of a single expression of the elastic curve. A general expression of the bending is proposed, deduced by integrating the different differential equations of the elastica, associated to each section between discontinuities produced by the loads. In this paper, support reactions are incorporated into the load system. Therefore, the continuous beam is understood as a bar made up of sections aligned between discontinuities. With this, the isostatic beam, the hyperstatic beam and the continuous beam can be treated by means of the same integrated expression of the displacement, also called the Macaulay method. Equivalent notations are provided to the expression of bending for the cases of traction-compression and torsion, obtained through the same reasoning and sequence of operations. The formulation of elastic type and the associated operations shown allow us to cover the analysis of the generic structural form, which we can define as the beam of any number of spans, or continuous beam of >n spans. The load system is also generalized, being able to contemplate loads of a different nature and form of distribution, both static and mobile. The examples that have been developed always provide analytical results of solicitation and deformation. They intend to explain the systematic path followed from the approach of the structural problem to its mathematical modelling, and the resolution procedure developed to obtain useful values for the structural verification. In these examples, an increasing degree of complexity and generalization has been followed. The expressions obtained are validated by comparing them with those that are usual in the structural literature for the same or similar problems.
Open Access
Irrigation implementation promotes increases in salinity and nitrate concentration in the lower reaches of the Cidacos River (Navarre, Spain)
(Elsevier, 2020) Merchán Elena, Daniel; Sanz, L.; Alfaro, A.; Pérez, I.; Goñi Garatea, Mikel; Solsona, F.; Hernández García, Iker; Pérez, C.; Casalí Sarasíbar, Javier; Ingeniería; Ingeniaritza
The shift from rainfed to irrigated agriculture is associated with a change in the fertilization rates due to increases in expected production and the fact of growing more N demanding crops. In addition, the circulation of irrigation return flows (IRF) mobilizes soluble salts stored in soils or geological materials. As a consequence, it implies severe modifications in the dynamics and total amount of soluble salts and nitrogen exported, especially in semi-arid watersheds. In this study, long-term data collected by the regional authorities was used to assess the effects of irrigation implementation on salinity (using electrical conductivity, EC, as a proxy) and nitrate concentration (NO3 −) after the transformation of ca. 77 km2 from rainfed to irrigated agriculture in the Cidacos River (CR) watershed. The results indicate that water quality in the lower reaches of the CR was significantly modified after the diffuse incorporation of IRF. In contrast, neither EC nor NO3 − were different in those monitoring stations whose contributing watersheds did not include transformed area. In addition, the temporal dynamics in the analysed variables shifted from a rainfed land signal typical in the region to an irrigated land signal, and the hydrochemical type of the CR shifted from mixed-to-Na+-mixed-to-HCO3 – to mostly Na+-mixed type, typical of waters affected by IRF in the region. Groundwater EC and NO3 − also increased in those wells located within the irrigated area. Although there are great uncertainties in the actual amount of salt and N reaching the CR via IRF, the expected contribution of waste water spilled into the CR is minor in comparison to other sources, mostly agricultural sources in the case of N. The observed changes have promoted the designation of the lower reaches of the CR as 'affected' by NO3 − pollution, and the whole CR watershed as a Nitrate Vulnerable Zone, with the emergent question about whether irrigation implementation as carried out currently in Spain is against the environmental objectives of the Water Framework Directive.
Open Access
Geomorphological instantaneous unit hydrograph model with distributed rainfall
(Elsevier, 2019) Goñi Garatea, Mikel; López Rodríguez, José Javier; Gimena Ramos, Faustino; Ingeniería; Ingeniaritza
Two variants of the Instantaneous Unit Hydrograph model based on a Geomorphological association of linear Reservoirs (IUHGR), incorporating the Spatial Variability of Rainfall (SVR), have been developed. The proposed models are based on the Geomorphological Reservoirs (GR) scheme consisting of a cascade of linear reservoirs aggregating sub-watersheds. The model, in its first version, was formulated so that it incorporated a spatial variability pattern of rainfall associated with a certain frequency and oriented towards its application in the field of hydrological design. This model was considered to be stationary in the time (GRSVR(s)) for being linked to some design conditions. The second version of the model is applicable to the simulation of real events, where there is a dynamic (GRSVR(m)) spatial distribution of rainfall that varies in time, as in the case of the movement of rainstorms. Both models permit the input of relevant information on the spatial variability of the rainfall, taken from different rain gauge records, without losing the simplicity of the GR model with a single parameter, which represents the hydrological time response of the watershed. The models have been calibrated and validated with the data from one gauged watershed in northern Spain. The analysis conducted in both cases showed that the models which contemplated the spatial variability of the rainfall, GRSVR(s) and GRSVR(m), were capable of simulating rainfall variability effects in the surface runoff hydrograph better than the GR model, which averages the precipitation values recorded in the different rain gauges.
Embargo
Soil-tunnel interaction under the effect associated with the longitudinal direction
(Elsevier, 2024-07-23) Gimena Ramos, Faustino; Goñi Garatea, Mikel; Gonzaga Vélez, Pedro; Valdenebro García, José Vicente; Ingeniería; Ingeniaritza; Institute of Smart Cities - ISC; Institute on Innovation and Sustainable Development in Food Chain - ISFOOD
Longitudinal structural analysis of shield tunnels is studied by considering the tunnel as a Timoshenko beam based on elastic foundations under Vlasov's theory. This article presents the structural behavior of a Timoshenko-Vlasov beam jointly, using a single differential system that brings together all the equilibrium and deformation equations. Solving the presented formulation, shield tunnels can be covered under any type of action, ground pressure and support or boundary conditions. This new compacted notation facilitates the possibility of expressing the interaction between soil and structure by introducing the variability of longitudinal support conditions on the elastic springs. This differential system is resolved with the numeric procedure named Finite Transfer Method. To verify the effectiveness of the procedure followed, the structure of the subway tunnel in Shanghai has been modeled and the results obtained have been compared with those offered in the literature. The proposed model has been exemplified by introducing the variability of longitudinal elastic spring conditions representing actual soil behavior.
Open Access
Alternative approach to the buckling phenomenon by means of a second order incremental analysis
(Springer Nature, 2023) Gimena Ramos, Faustino; Goñi Garatea, Mikel; Gonzaga Vélez, Pedro; Valdenebro García, José Vicente; Ingeniería; Ingeniaritza
This article addresses the problem of determining the solicitation and deformation of beams with geometric imperfection, also called real beams under a compression action. This calculation is performed by applying the Finite Transfer Method numerical procedure under first-order effects with the entire compression action applied instantaneously and applying the action gradually under second-order effects. The results obtained by this procedure for real sinusoidal or parabolic beams are presented and compared. To verify the potential of the numerical procedure, the first and second-order effects of a beam with variable section are presented. New analytical formulations of the bending moment and the transverse deformation in the beam with sinusoidal imperfection subjected to compression are also obtained, under first and second-order analysis. The maximum failure load of the beams is determined based on their initial deformation. The results of solicitation and deformation of the real beam under compression are compared, applying the analytical expressions obtained and the numerical procedure cited. The beams under study are profiles with different geometric characteristics, which shows that it is possible to obtain maximum failure load results by varying the relationships between lengths, areas and slenderness. The increase in second-order bending moments causes the failure that originates in the beam, making it clear that this approach reproduces the buckling phenomenon. The article demonstrates that through the Finite Transfer Method the calculation of first and second-order effects can be addressed in beams of any type of directrix and of constant or variable section.
Open Access
Factors controlling sediment export in a small agricultural watershed in Navarre (Spain)
(Elsevier, 2012) Giménez Díaz, Rafael; Casalí Sarasíbar, Javier; Grande Esteban, Ildefonso; Díez Beregaña, Javier; Campo-Bescós, Miguel; Álvarez-Mozos, Jesús; Goñi Garatea, Mikel; Proyectos e Ingeniería Rural; Landa Ingeniaritza eta Proiektuak; Gestión de Empresas; Enpresen Kudeaketa; Gobierno de Navarra / Nafarroako Gobernua
It is recognised that the hydrological and erosion processes in watersheds are very much conditioned by the (inter)action of a number of variables. This paper covers a 15-year period of studying those factors that have a major influence on the sediment yield and transport during individual hydrological events in a small Mediterranean agricultural watershed. Multivariate statistical techniques such as cluster analysis and principal component analysis were applied for the interpretation of datasets. In addition, the relationships between suspended sediment concentration and discharge (hysteretic loops) were also analysed. The hydrological response of the studied watershed is mainly controlled by the antecedent condition of the flow. Most of the runoff and sediment are generated during the wet season when vegetation cover is scant and saturation overland flow occurs promptly as a response to almost any rainfall events. In contrast, during the dry seasons even if high-intensity rainfalls normally occur, very scant runoffs are, however recorded, at the exit of the watershed. Most of the eroded sediment seems to come from riparian areas. The discharge registered at the watershed outlet up to 1 h prior to the flood is a very good surrogate for antecedent soil moisture.
Open Access
Pohlke theorem: demonstration and graphical solution
(Springer, 2017) Gimena Ramos, Faustino; Gimena Ramos, Lázaro; Goñi Garatea, Mikel; Gonzaga Vélez, Pedro; Proyectos e Ingeniería Rural; Landa Ingeniaritza eta Proiektuak
It is known that the axonometric defined by Pohlke, is geometrically known as a means of representing the figures of space using a cylindrical projec-tion and proportions. His theorem says that the three unit vectors orthogonal axes of the basis in the space can be transformed into three arbitrary vectors with com-mon origin located in the frame plane. Another way of expressing this theorem is given in three segments mismatched and incidents at one point in a plane, there is a trirectangular unitary thriedra in the space that can be transformed in these three segments. This paper presents a graphical procedure to demonstrate a solution of Pohlke¿s theorem. To do this, we start from previous work by the authors on the axonometric perspective. Graphic constructions that allow a single joint invariant description of relationships between an orthogonal axonometric oblique axono-metric system and systems associated thereby. At a same time of the geometric lo-cus generated by the diagonal magnitude positioned at any direction in the plane of the picture. This magnitude is the square root of the sum of the squares of the projection of the three segments representing axonometric on arbitrary magnitude.
Open Access
Geometric locus associated with thriedra axonometric projections. Intrinsic curve associated with the ellipse generated
(Springer, 2017) Gonzaga Vélez, Pedro; Gimena Ramos, Faustino; Gimena Ramos, Lázaro; Goñi Garatea, Mikel; Proyectos e Ingeniería Rural; Landa Ingeniaritza eta Proiektuak
In previous work on the axonometric perspective, the authors presented some graphic constructions that allowed a single and joint invariant description of the relations between an orthogonal axonometric system, its related orthogonal views, and oblique axonometric systems associated with it. Continuing this work and using only the items drawn on the frame plane, in this communication we start from the three segments, representing trirectangular unitary thriedra, joined in the origin and defining an axonometric perspective. Each is projected onto any direc-tion and the square root of the summa of the squares of these projections is deter-mined. We call this magnitude, orthoedro diagonal whose sides would be formed by the three projections axonometric unit segments. If the diagonal size is built from the origin of coordinates and onto the direction used, this describes a locus here called intrinsic curve associated with the ellipse. When the starting three segments represent an orthogonal axonometric perspective, the intrinsic curve as-sociated with the ellipse is a circle.
Open Access
Análisis regional de frecuencias de las precipitaciones diarias extremas en Navarra. Elaboración de los mapas de cuantiles
(IWA Publishing, Editorial UPV, FFIA, 2019) López Rodríguez, José Javier; Goñi Garatea, Mikel; San Martín González, Iban; Erro Eslava, Juan; Ingeniería; Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
La determinación de la ley de frecuencias de precipitaciones resulta imprescindible para el diseño de diferentes infraestructuras hidráulicas así como para el análisis y determinación de zonas inundables. El objetivo de este artículo es presentar los cuantiles de las precipitaciones diarias extremas en el territorio de la Comunidad Foral de Navarra, obtenidos mediante un análisis regional de frecuencia (ARF), y su representación espacial. Se ha partido de las 142 estaciones pluviométricas manuales, localizadas en la Comunidad Foral de Navarra y en el entorno de la misma, con duración de registro superior a 20 años. El Análisis Regional de Frecuencias (ARF) se ha realizado según la metodología de Hosking y Wallis, obteniendo seis regiones homogéneas y sus funciones de distribución más adecuadas. Para la elaboración de los mapas se han aplicado dos métodos de interpolación: el de la distancia inversa ponderada; y el geoestadístico Kriging ordinario. Después del análisis comparativo se ha elegido el Kriging.