Natural Radiation on Mars is much higher compared with Earth. The thin atmosphere provides only a small shielding effect against cosmic radiation. It provides moderate protection against solar radiation. Mars also lacks the magnetosphere that protects Earth.
1 millisievert [mSv] = 0.1 rad [rd]
Types of Radiation
Radiation comes in a variety of forms:
|X-Rays and Gamma Rays||1||Radiation belts, solar radiation, and bremsstrahlung electrons|
|Cosmic radiation, inner-radiation belts, and solar radiation|
0.05 ev (thermal)
|Nuclear interactions in the sun; on Mars, produced when cosmic radiation interacts with regolith|
|Cosmic radiation, Cosmic rays|
|Heavy Ions||Varies widely||Cosmic radiation|
|Table 1: Types of radiation|
(RBE is a measure of the damage done to living tissue, relative to gamma rays)
Cosmic radiation comprises 85% protons, 14% alpha particles, and 1% heavy ions. Solar radiation includes the same radiation types, but it a higher proportion of protons and its heavy primaries have lower energy levels. The high-energy heavy primaries in cosmic radiation can penetrate materials that effectively block lower-energy radiation.
Limits for humans
Exposure to dangerous levels of radiation causes radiation sickness and cancer. The average exposure to radiation on Earth due to natural sources is 6.2 mSv per year. The highest natural exposure is recorded in Ramsar, Iran, where people are exposed up to 260 mSv/y for many generations, with no reported harmful effects. This is 13 times the maximum exposure allowed radiation workers each year. Importantly, this level of radiation is what Mars settlers (living inside shelters of reasonable cost) would expect. So the 'high' levels of the back ground radiation at Ramsar is good news for Mars settlement. A recent study showed that the people living in this city showed increased immunity to gamma ray exposure, tho if this is from evolutionary adaption over many generations, or from the immune system being 'exercised' regularly is not known. 
It should be emphasized, that low level radiation doses spread over a long period of time (long enough that the bodies natural functions have time to repair the damage), are far less dangerous than large doses received in a short amount of time. (In fact numerous studies show health benefits from extremely low levels of radiation.)  See also: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6149023/. https://www.sciencedaily.com/releases/2017/09/170913104428.htm. https://www.ajronline.org/doi/full/10.2214/ajr.179.5.1791137. https://en.wikipedia.org/wiki/Radiation_hormesis
Some people believe that ANY exposure to radiation, no matter how slight, poses some risk. Small dose - small risk of cancer. High dose - high risk of cancer. This is the No Minimum Threshold theory of radiation dosage. This works quite well with fast radiation doses high enough to cause cancers later in life, but the evidence is much weaker for low level does over a long period of time. No Minimum Threshold is used by regulatory agencies when they wish to be extremely conservative about radiation risks.  
Nevertheless, there are defined legal limits for exposure during work for several professional activities, such as for X-ray assistants, airplane personnel, etc. The International Commission on Radiation Protection recommends that occupational (work-related) radiation exposure be limited to 50 millisieverts (mSv) per year, and limited to 100 mSv over any 5-year period. NASA's radiation dose limits for astronauts are established in NASA-STD-3001.
There is scientific uncertainty surrounding the health hazard from cosmic and solar radiation, because most past research on the health effects of radiation studied only x-rays and gamma rays.
Limits for plants
"In general, plants are relatively radiation resistant when growing and extremely resistant as dormant seeds." Radiation should not interfere with raising plants as food sources, at least not on the time scales of exploration missions.
Table 2 shows the limits for plants(source of table required, in space or on mars?). It shows that in practically all cases plants can survive radiations events that are likely for Mars without any kind of protection.
However, a 2021 study in the Netherlands, conducted on two types of plants, has shown that radiation at the Mars surface may reduce yields substantially. Germination of plants in a protected environment before setting them out in greenhouses might be a potential mitigation measure but further research is needed.
Effects of the Martian atmosphere
Most SPE particles will be stopped by the atmosphere before they reach the surface. However, interactions with atmospheric particles can produce neutrons; those neutrons can reach the surface, so the health hazard is not eliminated.
Cosmic radiation protons are likely to penetrate the atmosphere. Cosmic ray heavy ions may fragment in the atmosphere, producing lower-mass ions that can still harm astronauts on the surface.
Mars' thin atmosphere allows more ultraviolet light to reach the surface, compared to Earth. However, habitat structural materials and standard space suits should be sufficient to protect humans from UV radiation.
Mars atmosphere effect depends on the considered inclination, as the incoming radiations will cross more matter if it's coming from the horizon rather than from the zenith. For inclination angles greater than ~45°, the atmospheric thickness is in the range from 20-30 g/cm2, and for lower inclination angles, the atmospherie thickness can exceed 100 g/cm2.
Low gravity effects on atmospheric thickness
Note that the radiation protection given by the Martian atmosphere is higher than would be expected considering the air pressure. Pressure can be thought of the weight of the air above you in the atmosphere. Mars' gravity is 38% of Earths. So the weight of that air is less than it would be on Earth. On other words, more air must be above you on Mars to give the same pressure, compared to Earth. For example, you might think that since Mars' air pressure is 0.6% of Earth's, the radiation protection would also be 0.6%. However, the mass of air above you on Mars is 1/38% or 2.6 times thicker than that pressure on Earth. If we were to terraform Mars to have 10% Earth's pressure, the radiation protection by that atmosphere would be 26%. If we were to give Mars an atmosphere of 50% Earth's air pressure, then the Martian atmosphere's radiation protection would be 132% that of Earth.
Effects of cosmic rays striking the regolith
When cosmic rays strikes regolith, it can cause the impacted atoms to emit their own radiation. Surrounding regolith particles absorb much of this radiation, with the exception of neutrons. Neutrons generated in this way are called albedo neutrons. These neutrons have the potential to add substantially to the radiation dose for astronauts on the surface.
Neutrons are well absorbed by water, so blocks of ice or water around habitats would be useful radiation protection. Lithium hydride is thought to be the most effective neutron absorber ever discovered, and it might be built into the floor of long term habitats.  (Lithium hydroxide reacts with water, so it must be kept away from the humid interior of the settlement.) Alternatively, the regolith or water thickness may be extended to also protect against secondary neutrons.
Dose received by an unprotected human on Mars
The equivalent dose rate from cosmic radiation on Earth's surface at sea level is .26 mSv per year  (this makes up ~10% of the annual natural radiation dose, and it increase with altitude). Based on measurements made by the Curiosity rover, the corresponding figure for the surface of Mars is approximately 230 mSv/year. More generally, one model estimated that the dose equivalent rate on the surface of Mars ranges from 156.4 mSv/year (at solar maximum) to 273.8 mSv/year (at solar minimum). A 2005 report by the Mars Human Precursor Science Steering Group estimated that (at solar minimum) the dose from cosmic radiation would be 1.2 +/- 0.5 mSv/day; this includes 0.4 +/- 0.4 mSv/day from albedo neutrons.
Solar Proton Events
Curiosity also measured the temporary increase in radiation during a single SPE. The results indicate an increase in equivalent dose rate of approximately 25% over a 1-day interval. This figure will vary depending on the intensity of a particular SPE.
Effect on material
Radiation can change the properties of plastics and metals, making them brittle after a period of time.
Long term habitats should be equipped with a radiation shielding, thick enough to reduce the radiation to a level equal to Earth, that is, almost zero. Best protection may be achieved with houses built in natural caves or set into cliffs or hillsides. (If, however, it is decided that radiation levels equal to the city of Ramsar, Iran, are safe enough, then the thickness of the radiation shielding suggested below can be reduced up to 13 fold.)
Early exploration habitats could have water tanks, or sand bags above where people live. When radiation goes thru water, every 18 cm reduces the radiation by half. So a water tank 108 cm thick (6 halvings) will reduce the radiation level by 64 times. (As a bonus, water is a good neutron absorber.) Packed soil has a halving-distance of 9.1 cm, so 55 cm of hard soil would provide a similar level of protection. In general, it is far better to use local materials for radiation protection, rather than hauling them from Earth. See: https://www.imagesco.com/geiger/lead-shielding-guide.html.
Space suits must be designed with radiation in mind. The suit should provide adequate shielding for the occupant. It may be necessary to design suits with several grades of protection. Suits designed for short-term use can carry lighter shielding which would reduce weight and improve maneuverability. That said, radiation protection from suits will be much less than inside habitats, so minimizing time on the surface will be the largest protection. Going outside during solar storms would likely be banned.
"In this work, it is shown that on the Martian surface, almost any amount of aluminum shielding increases exposure levels for humans. The increased exposure levels are attributed to neutron production in the shield and Martian regolith as well as the electromagnetic cascade induced in the Martian atmosphere. This result is significant for optimization of vehicle and shield designs intended for the surface of Mars." 
"An in-situ shielding strategy will also be of little help unless several hundred g/cm2 of regolith is utilized. Such a strategy would probably require large scale excavation making it an unlikely candidate. Instead, the shielding strategy would rely primarily on material optimization. Options, such as replacing aluminum structures with high hydrogen content carbon composites, could be pursued."  This opinion is open to argument as in-situ resources utilization for any type of settlement should make large amounts of regolith available for construction. It mainly is true for the very first level of habitats.
The use of g/cm2 can be translated into an equivalent thickness that depends on the material density. For martian regolith at 2000 kg/m3, a thickness of 1m of regolith is 200 g/cm2. Water (or ice) is 100 g/cm2. So the minimum covering for a long term settlement would be 5m or more. For water, although the radiation absorption is better the density is lower, so about the same thickness would be required for protection. (to be discussed)
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