Optimization of Structural Design in Steel Buildings Based on the Site-Specific Design Spectra of the Mexico Seismic Regulations

This scenario is the most suitable for today’s structural engineers. It involves enhancing geotechnical studies with geophysical tests, specifically through the “Down-Hole (DH)” test, “Cross-Hole (CH)” test, and environmental vibration records. The DH test is conducted in a borehole, typically the same one used for the SPT geotechnical exploration survey. Essentially, it entails measuring the arrival time of S and/or P waves using triaxial geophones placed at various depths in the test well (usually at one-meter intervals). An impulse is generated at a surface near the test hole. This test facilitates the creation of a velocity profile for the soil, known as a “Domocrona”. Therefore, the characterization of the soil is based on velocity magnitudes [16]. Subsequently, this information allows for the derivation of other soil properties, such as the dynamic elastic modulus (E), Poisson’s ratio (μ), and the shear rigidity modulus (G). The CH test additionally allows us to obtain the damping coefficient of the soil (ξ_s) of each subsoil layer. On the flip side, the soil’s vibration period, Ts, is a crucial property that must be studied, as it delineates the dynamic behavior of the soil. This parameter can be determined in two ways: (i) via records from accelerographic stations and (ii) through measuring environmental vibration records. Subsequently, spectral ratio techniques, such as H/V or the Nakamura [17,18] technique, are applied to ascertain the dominant frequencies (f_s) or their inverse of the period (T_s). The H/V spectral ratio has found extensive use in various seismic microzonings due to its cost effectiveness in acquisition and analysis in countries such as the United States, Japan, Italy, and Spain [19,20,21]. In Table 2, the data of the stratigraphic profile: thickness (h_i), volumetric weight (γ_si), and shear-wave propagation velocities (V_si), are presented for the seismic zone B site of Figure 1, located in Tabasco state. This information is extracted from geotechnical (SPT test) and geophysical (Down-Hole test) studies conducted up to a depth of 45 m for this site. Figure 4 showcases the H/V spectral ratio for this site. The H/V spectral ratio is obtained from an environmental vibration record and using the Geopsy program [22].

Figure 4 shows that the dominant frequency for the study site is 1.09 H_z, corresponding to a period of T_s = 0.91 s. Conversely, utilizing the data of Table 2; the thickness (h_i), soil unit weight (γ_si), and the shear-wave propagation velocity (V_si) of each layer subsoil in Equation (1) yields a period of T_s = 0.67 s (1.49 H_z). This period differs from the direct measurement obtained through the Nakamura technique (Ts = 0.91 s). This discrepancy indicates that the geotechnical and geophysical study, conducted up to 45 m depth, was insufficient to fully characterize the soil deposit, as a rocky soil stratum had not been encountered at that depth. Consequently, it is better to use, for this case, environmental vibration records to adequately characterize the fundamental period of the site. The variation in the measurement of the soil stratigraphy parameters should be duly acknowledged. Hence, it is advisable to characterize the anticipated uncertainty associated with these parameters and employ a probabilistic approach to integrate it into the estimation of the site’s frequency or fundamental period in Equation (1). The probabilistic approach can also be applied when determining the transfer function (FT) that simulates the propagation of seismic waves from the rock stratum to the surface soil.