## 10 Discussion
### Comparison of the Proposed Coefficients with Existing Solutions and Experimental Results
Figure 9: \(K_{pe}\) vs. \(\varphi^{\prime}\) curves for the active state obtained by the proposed solution for various \(k_{h}\) values and \(k_{v}=k_{h}/2\) (curves referring to cohesionless soils). From Figures 7-10 it is also inferred that the proposed solution is less conservative for the active case and more conservative for the passive case. However, the question is not to find a solution that is more conservative, but a solution that effectively reflects reality; and this because the cost of an overconservative design can be just as much of a problem as the cost of a future failure [40]. Over the last decades, a great number of experimental, numerical, and analytical studies led to a consensus that the M-O method yields conservative earth pressure values and excessively conservative values for  
Figure 11: The angle of the resultant body force in the soil from vertical. Figure 12: Example curves showing the continuity of the proposed curves against the noncontinuity between the M-O and M-O-K methods. Eurocode 8-5 ensures the continuity between the active and the passive state with an arbitrary modification of the M-O and M-O-K methods (dashed curves). Figure 10: \(K_{pe}\) vs. \(\varphi^{\prime}\) curves for the active state obtained by Mononobe–Okabe–Kapila (M-O-K) method for various \(k_{h}\) values and \(k_{v}=k_{h}/2\). The dashed lines were drawn based on modification of the M-O-K method identical to the one given in Eurocode 8-5 for the M-O method. Peak Ground Accelerations (_PGA_) in excess of 0.4 g (e.g., [40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53]). Generally, these studies refer to the active state, although some of them refer to the M-O-K solution for the passive state [47; 54]. Some authorities have already recognized the conservatism of the M-O solution adopting as standard design practice the use of a reduction coefficient for the expected peak ground acceleration [37; 39; 55; 56]. For example, AASHTO [37] suggests \(k_{h}=(1/2)PGA\), whilst the Building Seismic Safety Council [56] suggests \(k_{h}=(2/3)PGA\); the latter has been based on the centrifuge model tests of [PERSON] and [PERSON] [46]. Centrifuge tests have the advantage of avoiding the limitations of the 1-g shaking table, whilst scaling laws can be accurately followed. However, they also present challenges particularly when it comes to the ability of conventional instrumentation to adequately respond at frequencies dictated by the scaled model response characteristics [40]; this is further discussed in Section 10.3. The \(K_{\text{ae}}\)-\(\varphi^{\prime}\) relation for \(k_{h}\) values corresponding to seismic coefficients equal to the 2/3 and 1/2 of PGA is also shown in Figure 8 (first and second values in brackets, respectively). In this respect, it is amazing how this correction brings the M-O coefficient values so close to the coefficient values derived by the proposed solution (please compare Figure 7 with Figure 8, but using the \(k_{h}\) values given in brackets in Figure 8). The proposed solution compares also excellently to the \"loma prieta sc\" and \"kobe tak090\" centrifuge tests performed on cantilever walls by [PERSON] and [PERSON] (see \"Figure 4.26\" in [44]). The specific tests were chosen due to their excellent calibration as confirmed by the static earth pressure distributions (\"\[K_{pe,M-O-K}=\frac{\cos^{2}(\varphi^{\prime}-\psi+\beta)}{\cos\psi\cos^{2} \beta\cos(\delta-\beta+\psi)\bigg{(}1-\sqrt{\frac{\sin(\varphi^{\prime}+ \delta)\sin(\varphi^{\prime}-\psi+\alpha_{s})}{\cos(\delta-\beta+\psi)\cos( \alpha_{s}-\beta)}}\bigg{)}^{2}}, \tag{57}\]022\" in [44]). Actually, the problem with both M-O and M-O-K solutions is found in the procedure followed for the derivation of the well-known coefficients of Equations (56) and (57). It is reminded that both M-O and M-O-K solutions are extensions of the well-known [PERSON]'s solution for earth pressures.