Studying the process of divertor detachment and the associated complex interplay of plasma dynamics and atomic physics processes is of utmost importance for future fusion reactors. While simplified analytical models exist to interpret the general features of detachment, they are limited in their predictive power, and complex two-dimensional (2D) or even three-dimensional (3D) codes are generally required to provide a self-consistent picture of the divertor. As an intermediate step, one-dimensional (1D) models of the scrape-off layer (SOL) can be particularly insightful as the dynamics are greatly simplified, while still self-consistently including various source and sink terms at play, as well as additional important effects such as flows. These codes can be used to shed light on the physics at play, to perform fast parameter scans, or to interpret experiments. In this paper, we introduce the SPLEND1D (Simulator of PLasma ENabling Detachment in 1D) code: a fast and versatile 1D SOL model. We present in detail the model that is implemented in SPLEND1D. We then employ the code to explore various elements of detachment physics for parameters typical of the Tokamak à Configuration Variable, including the atomic physics and other processes behind power and momentum losses, and explore the various hypotheses and free parameters of the model.