Wroth studied civil engineering at the University of Cambridge ( Emmanuel College). After his military service in the artillery and a time as a school teacher, he continued his studies as a research student at Kenneth Harry Roscoe, where he received his doctorate in 1958 (The behavior of soils and other granular media When Subjected to shear ). With Roscoe and Andrew Noel Schofield he put in an essay in 1958 the foundations of Critical State Soil Mechanics. After that, he was a civil engineer with Mansell and Partners (where he oversaw include the construction of prestressed high street Hammersmith Flyover in west London ). From 1961 he was back in Cambridge as a lecturer and Fellow of Churchill College. After the death of Roscoe, he headed the soil mechanics research group in Cambridge from 1970 until the appointment of Schofield in 1974 to the professorship. In 1975 he was Reader in Soil Mechanics. In 1978 he became a professor at the University of Oxford and a Fellow of Brasenose College. He was most recently Executive Board of the Faculty of Engineering. In 1990 he returned to Cambridge as Master of his old college, but died shortly afterwards.
With Schofield he wrote the monograph published in 1968 Critical State Soil Mechanics ( McGraw Hill ). He also developed field instrumentation for in situ tests (such as the self- boring pressure meter ) as part of its efforts to ensure always so realistic experimental conditions and methods of measurement as possible. He expressed this in 1984 in his Rankine Lectureund 1985 he wrote with Guy T. Houlsby a review article in which they were skeptical about the fact that the usual measurement methods of soil mechanics could provide the information necessary for complex modeling of the soil parameters.
He was married twice, from his first marriage (since 1954) he had four children. During his studies ( he graduated with honors ), he distinguished himself also athletic and also played international hockey for Wales.