We present the results from the optical component of a survey for damped Lyman-alpha systems (DLAs) towards radio-loud quasars. Our quasar sample is drawn from the Texas radio survey with the following primary selection criteria: z_em > 2.4, optical magnitudes B < 22 and 365 MHz flux density S_365 > 400 mJy. We obtained spectra for a sample of 45 QSOs with the William Herschel Telescope, Very Large Telescope and Gemini-North, resulting in a survey redshift path Delta z = 38.79. We detect nine DLAs and one sub-DLA with a mean absorption redshift <z> = 2.44. The DLA number density is n(z) = 0.23^{+0.11}_{-0.07}, in good agreement with the value derived for DLAs detected in the Sloan Digital Sky Survey at this redshift. The DLA number density of our sample is also in good agreement with optically-complete radio-selected samples, supporting previous claims that n(z) is not significantly affected by dust obscuration bias. We present N(HI) column density determinations and metal line equivalent width measurements for all our DLAs. The low frequency flux density selection criterion used for the quasar sample implies that all absorbers will be suitable for follow-up absorption spectroscopy in the redshifted HI 21 cm line. A following paper (Kanekar et al.) will present HI 21 cm absorption studies of, and spin temperature determinations for, our DLA sample.
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