The mechanical strength of the soil is the maximum resistance of soil to mechanical stresses, without deformation and fracture37. The Q of soil can be measured by Automatic Micro Penetrometer, which uses a proprietary software called KMP2 to allow the user to obtain accurate data on the Q of the soil sample by adjusting the depth and velocity of the cone penetrating into the soil. The selectable diameter of the cone is 1–5 mm. Six velocities varying from 2 to 30 mm min−1 were created for the penetration of the cone Penetrometer into the soil sample. The display of Q values measured when the cone is inserted into the soil allows the user to capture the data from the logger without storing them on the computer. An automatic recording of Q values in text format or ASCI allows the user to read and use the input and output data (results) stored in the Excel software. In the results section, every 0.5 mm penetration in the soil, one piece of data is recorded and reported by the KMP2 software. This section also reports the total average Q, the highest and the lowest measured values, and the measurement time.

To measure the soil Q characteristic curve (SPRC), five undisturbed soil samples from the 10–15 cm depth layer and five undisturbed soil samples from the 30–35 cm depth received different water levels. To homogenize the water distribution, the 10 soil samples were placed in plastic bags for four weeks. After water equilibrium was obtained, the Q values were measured using an in vitro Automatic Micro Penetrometer with a penetration rate of 5 mm min−1 in 3 replications with the vertices arranged in a triangle on 10 samples38. The water content of soil samples was measured and converted to volumetric moisture content using BD values21. The SPRC model was fitted to the measured soil Q data using the Solver program. In order to measure SPRC, van Genuchten's35 adjusted model was applied in Eq. (8):

In this equation, Q is the soil penetration resistance (MPa), θ the soil volumetric moisture (cm3 cm−3), Ql the lowest soil predicted resistance (MPa), Qh the highest soil predicted resistance (MPa), α (cm3 cm−3), and n(–) the fitting parameters of the model related to the turning point and gradient of the function of mechanical resistance to the SW content.