I started out thinking this was more or less what Lisa suggests; I was going to suggest "footing(s)". But I now think I was barking up the wrong tree.

The thing is there are lots of references to the "arranque del muro sobre la cimentación", which obviously refers to the bottom of the wall resting on the foundations, so it seemed natural to assume that it could mean the bottom of the foundations themselves. But I started coming across a different use of "arranque" in relation to foundations, and I think this is the relevant one here.

It refers, essentially, to the resistance of the piles to traction, their tensile strength. "Arranque" is related to "arrancar": being torn up, uprooted, as it were. Here's a document (just an example; one of many) that talks about it. It's about road foundations, but the principles are the same.

It defines three kinds of forces that have to be resisted:
"• Hundimiento.
• Arranque.
• Rotura del terreno por empujes horizontales."

They're defined as follows:

"• Hundimiento: Se produce cuando las cargas verticales agotan la resistencia del terreno a compresión.
• Arranque: Se produce cuando existen pilotes traccionados y se alcanza el agotamiento por esfuerzo rasante [shearing force] en el fuste [shaft] del pilote.
• Rotura horizontal del terreno: Se produce cuando las presiones horizontales (o en general transversales al eje del pilote) agotan la capacidad del terreno, según un plano horizontal"
(transversal a dicho eje)."
http://www.fomento.es/NR/rdonlyres/63A5CC1B-E7B9-4638-AE45-8...

Well, I think these are the three things referred to in your text. The "resistencia del terreno en la vertical" refers to compressive, downward forces. The "resistencia horizontal" is obviously about lateral forces, and the "arranque" is about uplift, subjecting the piles to tensile forces which, beyond a certain point, can cause them to shear. This is "arranque". There's a reference later to "Resistencia de rotura o arranque (por fuste) en condiciones de tiro (a tracción)".

The word EN documents on the subject tend to use is uplift or uplift forces:

"LATERAL AND UPLIFT FORCES ON DEEP FOUNDATIONS"
[...]
"Uplift resistance of piles"
Design for Earthquakes
https://books.google.es/books?id=v5L4ih-Du3MC&pg=PA183&lpg=P...

"Foundation selection considerations to be evaluated include:
• the ability of the foundation type to meet performance requirements (e.g., deformation, bearing resistance, uplift resistance, lateral resistance/ deformation) for all limit states, given the soil or rock conditions encountered"
https://www.dot.ny.gov/divisions/engineering/technical-servi...

So I think "arranque" is short for "resistencia al arranque".

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Note added at 2 hrs (2015-09-24 19:06:18 GMT)
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Here's a similar use of "arranque" clearly meaning "resistencia al arranque":

"El hundimiento, arranque, tope estructural y resistencia horizontal de los pilotes fue verificado"
http://www.portsdebalears.com/imagenes/Lcd_1242045843.O.1298...