As we understand a concave surface is the one that curves inward, or is thinner in the middle than on the edges as depicted in the first figure.
On the other hand convex describes a surface which curves outward, or is thicker in the middle than on the edges as shown in the second figure.
Dams are built to block the flow of water. These create water en-catchment area behind the dam which can be used for storage of water, production of hydro-electricity, flood control, irrigation, city water supply, and other many human activities.
Let us have a look at two types of curved and one non-curved dams built as shown in the figures below.
Figure 1. Clywedog Reservoir, near Llanidloes, Wales, UK
Figure 2. Mount Bold Reservoir. South Australia
Figure 3. Hoover Dam, Nevada-Arizona border, USA
Figure 4. Bhakra Dam, Himachal Pradesh, India
We can see that both curved, concave and convex and straight dams have been built successfully. However, we understand that A concave surface downstream for a dam, as shown below, helps it to absorb the constant pressure of water that it must endure.