Figure 1

Figure 2
![Stiffness parameters of standard drained triaxial test results: (1) for the MC model, (2) for the HS model, (3) for the HSS model [66]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKM6MJKKME%2F20251219%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251219T215457Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEOn%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJIMEYCIQCNskA8fnssX9y9OP3dh2I1YpNjWx86RdmhBcFTuMv2vwIhAOYCN%2B5xvh%2F4kDvajK7%2BkUUo0x1cAFSdtFmdT5POMDydKsQFCLL%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEQAhoMOTYzMTM0Mjg5OTQwIgxjdUDx%2B7euKKG39wsqmAWQDqMfokeyM%2BAxqKTAu2dEMPCX%2BzuPWVApmpDH02EH9azEHMdCLfVW7lYiTps4nx7iL40eEqqVy19%2BMmptiMytdaTGMq71IWISM%2BQDI5nQ1d4tj2BrikIMVkjW5Z%2BuKVwIbY1%2F2N9%2BnxhVJb%2B3BQ9998Uov4rEAFQtQffxrBgZXiD2NTwPRRgwF1d2U8dSh3R2AJAPa2m8PuGh%2BbFMAirZsi2BHsT953LHwt4wv3Q0TF9H84kPSmDBSR7i83UFbesE5i2j1wxHGJv5lDjZqEGXxKV9vReNpueGZokVUC%2F3jnsqYIHYIrmOUmwkHD6pJGvcjjbHn33kEiKj5Vf%2FXn6qKCVUM1LVd5A%2FbH3gP94oKuUK%2BTvxy0YMIpBMSU4KRe%2BSOvJKCOlnvEc3vFKrKBUMsJnCoThKAA0cwxny0A6qOUWxrSEi0mrvw822h2Si9PhmEI5iwByrFOgkETzv%2FdXZ2jjqugNVmQr6d%2FZzi2m9U4TAPCvfmgrtNm6l%2FzLBiBvnBOVLbuxYBQ%2FqN5lkQdMiaBIeHTFGQpeTnsGLCCCtT%2BkU48sjhfShlzRuuiuKJ490zO3w4TpcbYWOoFHigvyEHMVY7hx9Aj9BEQM4rSsjZ1ceZGqG624Jnr3geMKmbjpw4swZz8goIy%2BHtbbIK7KRBzRGgqfEApy7fJRdx0CCVUKXC7F8o5EGf0BApxdRMJryFC3Vk5Y082j9X2AEqFVYtLENyaCxT2nQJVMXjSqnTDJ2mQ5jNIuROTT1cRIYrg%2BJ%2FuXn5SwHPmC20nfVcaeewNrTOAsfL%2Bf6dYhvuD%2FSHRPgpyyf19Y1CLP6kREUj3h4zD%2FJ2hvU1ygP1%2F%2FDrD%2B%2BCSddcAN8m9t1ndO8OX1gGXCMwc6cCfNPMIH9lcoGOrABlScjrIgAT02q7PpFYaDxtZCE8YbnLqUCGu98ZtV710NFIwO40WPqrMxucSrnIS0E0K587UL30tAuPeQC6UmjEOuaEVlYHxSCP29M%2Fo8y9jmPTQftmZTveMrAz3Up4zhJpNFEO0wyqG0uYuKJIuBkSQKLukM4FTRdwQrlgDsRi0qugyTO0z84h%2BaMROEyyZSgGKWQaD%2FjcK14duJVZD9ex9KzloDj4s1iPRXTMPWae7Y%3D&X-Amz-Signature=f81e231c3c0df54369ead306529ed0e76bd030568e6c459ffaa0d45875881a5a&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 3
![Characteristic stiffness-strain behavior in logarithmic scale (after Atkinson and Sallfors [36] and Mair[76]) (Atkinson, 2000)[77].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKM6MJKKME%2F20251219%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251219T215457Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEOn%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJIMEYCIQCNskA8fnssX9y9OP3dh2I1YpNjWx86RdmhBcFTuMv2vwIhAOYCN%2B5xvh%2F4kDvajK7%2BkUUo0x1cAFSdtFmdT5POMDydKsQFCLL%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEQAhoMOTYzMTM0Mjg5OTQwIgxjdUDx%2B7euKKG39wsqmAWQDqMfokeyM%2BAxqKTAu2dEMPCX%2BzuPWVApmpDH02EH9azEHMdCLfVW7lYiTps4nx7iL40eEqqVy19%2BMmptiMytdaTGMq71IWISM%2BQDI5nQ1d4tj2BrikIMVkjW5Z%2BuKVwIbY1%2F2N9%2BnxhVJb%2B3BQ9998Uov4rEAFQtQffxrBgZXiD2NTwPRRgwF1d2U8dSh3R2AJAPa2m8PuGh%2BbFMAirZsi2BHsT953LHwt4wv3Q0TF9H84kPSmDBSR7i83UFbesE5i2j1wxHGJv5lDjZqEGXxKV9vReNpueGZokVUC%2F3jnsqYIHYIrmOUmwkHD6pJGvcjjbHn33kEiKj5Vf%2FXn6qKCVUM1LVd5A%2FbH3gP94oKuUK%2BTvxy0YMIpBMSU4KRe%2BSOvJKCOlnvEc3vFKrKBUMsJnCoThKAA0cwxny0A6qOUWxrSEi0mrvw822h2Si9PhmEI5iwByrFOgkETzv%2FdXZ2jjqugNVmQr6d%2FZzi2m9U4TAPCvfmgrtNm6l%2FzLBiBvnBOVLbuxYBQ%2FqN5lkQdMiaBIeHTFGQpeTnsGLCCCtT%2BkU48sjhfShlzRuuiuKJ490zO3w4TpcbYWOoFHigvyEHMVY7hx9Aj9BEQM4rSsjZ1ceZGqG624Jnr3geMKmbjpw4swZz8goIy%2BHtbbIK7KRBzRGgqfEApy7fJRdx0CCVUKXC7F8o5EGf0BApxdRMJryFC3Vk5Y082j9X2AEqFVYtLENyaCxT2nQJVMXjSqnTDJ2mQ5jNIuROTT1cRIYrg%2BJ%2FuXn5SwHPmC20nfVcaeewNrTOAsfL%2Bf6dYhvuD%2FSHRPgpyyf19Y1CLP6kREUj3h4zD%2FJ2hvU1ygP1%2F%2FDrD%2B%2BCSddcAN8m9t1ndO8OX1gGXCMwc6cCfNPMIH9lcoGOrABlScjrIgAT02q7PpFYaDxtZCE8YbnLqUCGu98ZtV710NFIwO40WPqrMxucSrnIS0E0K587UL30tAuPeQC6UmjEOuaEVlYHxSCP29M%2Fo8y9jmPTQftmZTveMrAz3Up4zhJpNFEO0wyqG0uYuKJIuBkSQKLukM4FTRdwQrlgDsRi0qugyTO0z84h%2BaMROEyyZSgGKWQaD%2FjcK14duJVZD9ex9KzloDj4s1iPRXTMPWae7Y%3D&X-Amz-Signature=86d2b26c2ef77d752ba37ffeb2f6cf93ffb6966711255e7a255c7121a85f783a&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9
![Nodal displacement vectors for the wharf supported piles (m)[28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_009.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKM6MJKKME%2F20251219%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251219T215457Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEOn%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJIMEYCIQCNskA8fnssX9y9OP3dh2I1YpNjWx86RdmhBcFTuMv2vwIhAOYCN%2B5xvh%2F4kDvajK7%2BkUUo0x1cAFSdtFmdT5POMDydKsQFCLL%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEQAhoMOTYzMTM0Mjg5OTQwIgxjdUDx%2B7euKKG39wsqmAWQDqMfokeyM%2BAxqKTAu2dEMPCX%2BzuPWVApmpDH02EH9azEHMdCLfVW7lYiTps4nx7iL40eEqqVy19%2BMmptiMytdaTGMq71IWISM%2BQDI5nQ1d4tj2BrikIMVkjW5Z%2BuKVwIbY1%2F2N9%2BnxhVJb%2B3BQ9998Uov4rEAFQtQffxrBgZXiD2NTwPRRgwF1d2U8dSh3R2AJAPa2m8PuGh%2BbFMAirZsi2BHsT953LHwt4wv3Q0TF9H84kPSmDBSR7i83UFbesE5i2j1wxHGJv5lDjZqEGXxKV9vReNpueGZokVUC%2F3jnsqYIHYIrmOUmwkHD6pJGvcjjbHn33kEiKj5Vf%2FXn6qKCVUM1LVd5A%2FbH3gP94oKuUK%2BTvxy0YMIpBMSU4KRe%2BSOvJKCOlnvEc3vFKrKBUMsJnCoThKAA0cwxny0A6qOUWxrSEi0mrvw822h2Si9PhmEI5iwByrFOgkETzv%2FdXZ2jjqugNVmQr6d%2FZzi2m9U4TAPCvfmgrtNm6l%2FzLBiBvnBOVLbuxYBQ%2FqN5lkQdMiaBIeHTFGQpeTnsGLCCCtT%2BkU48sjhfShlzRuuiuKJ490zO3w4TpcbYWOoFHigvyEHMVY7hx9Aj9BEQM4rSsjZ1ceZGqG624Jnr3geMKmbjpw4swZz8goIy%2BHtbbIK7KRBzRGgqfEApy7fJRdx0CCVUKXC7F8o5EGf0BApxdRMJryFC3Vk5Y082j9X2AEqFVYtLENyaCxT2nQJVMXjSqnTDJ2mQ5jNIuROTT1cRIYrg%2BJ%2FuXn5SwHPmC20nfVcaeewNrTOAsfL%2Bf6dYhvuD%2FSHRPgpyyf19Y1CLP6kREUj3h4zD%2FJ2hvU1ygP1%2F%2FDrD%2B%2BCSddcAN8m9t1ndO8OX1gGXCMwc6cCfNPMIH9lcoGOrABlScjrIgAT02q7PpFYaDxtZCE8YbnLqUCGu98ZtV710NFIwO40WPqrMxucSrnIS0E0K587UL30tAuPeQC6UmjEOuaEVlYHxSCP29M%2Fo8y9jmPTQftmZTveMrAz3Up4zhJpNFEO0wyqG0uYuKJIuBkSQKLukM4FTRdwQrlgDsRi0qugyTO0z84h%2BaMROEyyZSgGKWQaD%2FjcK14duJVZD9ex9KzloDj4s1iPRXTMPWae7Y%3D&X-Amz-Signature=b0806387f3d68d76fb46e58e204ee219c678b2e0cab83097267bc9a8709c9f44&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 10

Figure 11
![Total pore pressure contours (Pa)[28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647378c74e662f30ba53f7fe/j_sgem-2019-0050_fig_011.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKM6MJKKME%2F20251219%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251219T215457Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEOn%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJIMEYCIQCNskA8fnssX9y9OP3dh2I1YpNjWx86RdmhBcFTuMv2vwIhAOYCN%2B5xvh%2F4kDvajK7%2BkUUo0x1cAFSdtFmdT5POMDydKsQFCLL%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEQAhoMOTYzMTM0Mjg5OTQwIgxjdUDx%2B7euKKG39wsqmAWQDqMfokeyM%2BAxqKTAu2dEMPCX%2BzuPWVApmpDH02EH9azEHMdCLfVW7lYiTps4nx7iL40eEqqVy19%2BMmptiMytdaTGMq71IWISM%2BQDI5nQ1d4tj2BrikIMVkjW5Z%2BuKVwIbY1%2F2N9%2BnxhVJb%2B3BQ9998Uov4rEAFQtQffxrBgZXiD2NTwPRRgwF1d2U8dSh3R2AJAPa2m8PuGh%2BbFMAirZsi2BHsT953LHwt4wv3Q0TF9H84kPSmDBSR7i83UFbesE5i2j1wxHGJv5lDjZqEGXxKV9vReNpueGZokVUC%2F3jnsqYIHYIrmOUmwkHD6pJGvcjjbHn33kEiKj5Vf%2FXn6qKCVUM1LVd5A%2FbH3gP94oKuUK%2BTvxy0YMIpBMSU4KRe%2BSOvJKCOlnvEc3vFKrKBUMsJnCoThKAA0cwxny0A6qOUWxrSEi0mrvw822h2Si9PhmEI5iwByrFOgkETzv%2FdXZ2jjqugNVmQr6d%2FZzi2m9U4TAPCvfmgrtNm6l%2FzLBiBvnBOVLbuxYBQ%2FqN5lkQdMiaBIeHTFGQpeTnsGLCCCtT%2BkU48sjhfShlzRuuiuKJ490zO3w4TpcbYWOoFHigvyEHMVY7hx9Aj9BEQM4rSsjZ1ceZGqG624Jnr3geMKmbjpw4swZz8goIy%2BHtbbIK7KRBzRGgqfEApy7fJRdx0CCVUKXC7F8o5EGf0BApxdRMJryFC3Vk5Y082j9X2AEqFVYtLENyaCxT2nQJVMXjSqnTDJ2mQ5jNIuROTT1cRIYrg%2BJ%2FuXn5SwHPmC20nfVcaeewNrTOAsfL%2Bf6dYhvuD%2FSHRPgpyyf19Y1CLP6kREUj3h4zD%2FJ2hvU1ygP1%2F%2FDrD%2B%2BCSddcAN8m9t1ndO8OX1gGXCMwc6cCfNPMIH9lcoGOrABlScjrIgAT02q7PpFYaDxtZCE8YbnLqUCGu98ZtV710NFIwO40WPqrMxucSrnIS0E0K587UL30tAuPeQC6UmjEOuaEVlYHxSCP29M%2Fo8y9jmPTQftmZTveMrAz3Up4zhJpNFEO0wyqG0uYuKJIuBkSQKLukM4FTRdwQrlgDsRi0qugyTO0z84h%2BaMROEyyZSgGKWQaD%2FjcK14duJVZD9ex9KzloDj4s1iPRXTMPWae7Y%3D&X-Amz-Signature=729da7527e9b1068b021adcd6027d6ec55f71033865a96a4bc709c1c11ea57bd&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 12

Soil parameters used for HS model
| Parameters | Unit | Dense sand | Loose sand | Rockfill |
|---|---|---|---|---|
| kN/m2 | 6.032 × 104 | 1.638 × 104 | 2.232 × 104 | |
| kN/m2 | 4.826 × 104 | 1.310 × 104 | 1.786 × 104 | |
| kN/m2 | 1.810 × 104 | 4.914 × 104 | 6.696 × 104 | |
| Pref | kN/m2 | 100 | 100 | 100 |
| M | - | 0.5 | 0.5 | 0.5 |
| - | 0.3982 | 0.4524 | 0.2929 | |
| Rf | - | 0.9 | 0.9 | 0.9 |
Additional input parameters of HSS model_
| Parameters | Unit | Dense sand | Loose sand | Rockӿll |
|---|---|---|---|---|
| γ0.7 | - | 4.918 × 10–4 | 3.629 × 10–4 | 4.246 × 10–4 |
| kN/m2 | 1.051 × 105 | 9.108 × 104 | 1.038 × 105 |
Lateral and vertical displacement time histories at the top and at the toe of the rock dike_
| Model | Lateral and vertical displacements at the rock dike top | Lateral and vertical displacements at the rock dike toe |
|---|---|---|
| MC | ||
| HS | ||
| HSS |
Soil parameters used for the MC model_
| Parameters | Unit | Dense sand | Loose sand | Rockfill |
|---|---|---|---|---|
| φ | ° | 37 | 33.2 | 45 |
| ψ | ° | 21 | 7 | 0 |
| C | kN/m2 | 0.5 | 0.5 | 15 |
| ν | - | 0.3 | 0.3 | 0.2 |
| E | kN/m2 | 6.032 × 104 | 1.638 × 104 | 2.232 × 104 |
Pile and deck properties_
| Parameters | Unit | Pile | Deck |
|---|---|---|---|
| EA | kN/m | 162.75 × 104 | 17.85 × 106 |
| EI | kN.m2/m | 70.49 × 103 | 96.724 × 103 |
| w | kN/m/m | 0.633 | 6.9436 |
| ν | - | 0.2 | 0.2 |